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1. 117 14 4 Creating Simple R Packages 2 20 117 14 4 1 The Bare Minimum to Create a Package 118 iii 15 Environment Customisation 16 ESS Using Emacs Speaks Statistics with R 16 1 Using ESS for Editing and Debugging R Source Files 16 2 Using ESS to Interact with a R Process 17 Using Sweave to Write Documents with R and ATEX 17 1 What s this Sweav so 0 i e es a 2 Usage oui ho nated oa Seah Red aa dae Be See eS 18 Sound Processing 18 1 Libraries for Sound Analysis and Signal Processing A Partial List of Packages by Category A 1 Graphics Packages ccccccccl 20000004 A 2 GUI Packages 2 2 d a e ee ee A Miscellaneous commands Other Manuals and Sources of Information on R Other Useful Statistics Resources Full Colours Table J a o a w GNU Free Documentation License APPLICABILITY AND DEFINITIONS VERBATIM COPYING 0 0 0 00 000548 COPYING IN QUANTITY LL MODIFICATIONS LL COMBINING DOCUMENTS 0 5 COLLECTIONS OF DOCUMENTS AGGREGATION WITH INDEPENDENT WORKS gt TRANSLATION taste soe eg ele weeds gale eee A TERMINATION LL 10 FUTURE REVISIONS OF THIS LICENSE ADDENDUM How to use this License for your documents 5 Dado uu NIH References Index 122 124 124 126 127 127 128 129 129 130 130 131 132 133 135 136 143 143 145 145 146 148 14
2. EN oO a a N wo a A q a D arg q par o N oO N N N N wo No PS 57 7 10 Adding Elements to a Plot 7 10 1 Adding a Legend Some graphics functions by default add a legend to the graph e g interaction plot or allow to add or discard a legend by setting an option inside the func tion e g barplot However the default settings for the legend such as positioning text or symbols might not be suitable to your graph in which case you need to turn off the default legend if there is one and add a customised legend with the legend function Below there is an example of an interaction plot with the legend added through the legend function the resulting graph is in Figure 7 13 gt interaction plot dats isi dats congr dats pcdirerr ylab Mean proportion of directional errors xlab SOA type b pch c 0 15 17 legend FALSE eliminate default legend gt legend topright legend c a congruent b inc goal directed c inc no goal directed lty c 3 2 1 pch c 0 15 17 bty n title Congruency here we first made the plot and afterwards we added the legend The first argument topright indicates the position where we want the legend to appear other possible values are bottomright bottomleft right bottom center and so on It is also possible to specify the position of the legend
3. gt d lt rnorm 15 4 2 gt e lt rnorm 15 9 3 gt plot d e type p pch 3 The following sections will give a more in depth explanation of some graphics parameters before that however we ll have a closer look at how to use par Saving and Restoring Graphics Parameters Often you ll want to change the graphics parameters only for a few plots and then reset them back to the defaults The function par when used to change the value of some graphics parameters returns a list with the old values of the graphics parameters that have changed gt par lwd col these are the default parameters 1wd 1 1 col 1 black gt oldpar lt par lwd 2 col red while changing the parameters gt we store the old values in a list gt oldpar 54 1wd 1 1 col 1 black gt s lt seq 0 10 1 gt plot s sin s we plot something gt par oldpar and then we restore gt the old parameters notice that calling par opens a graphics device if there is not one already open the changes you do using par apply only to this graphics device any other new graphic device that you open will have the default graphics parameters List of Graphics Parameters by Category Table 7 4 Parameters for Colours Parameter Function col plotting colour col axis colour for axis annotation col lab colour for x and y labels col main colour for main title col sub colour for sub titles bg background
4. gt rep 1 4 3 each 2 1 112233441122334411223344 There are other ways to achieve this same effect for example gt rep rep 1 4 c 2 2 2 2 3 1 112233441122334411223344 would yield the same effect Even if it can look pretty useless at first the rep function comes in very handy for example when you want to transform the data in a table from one row per subject to one row per observation which is necessary for example to run a repeated measures ANOVA with the aov function rep makes it all easier as you can create vectors in which the occurrence of the levels of a factor are repeated over and over 4 2 Matrix Facilities There are different ways for creating a matrix in R you often start from a vector and then transform it into a matrix with the matrix function 15 gt matr lt c 3 5 6 2 5 7 9 1 5 4 2 3 gt matr lt matrix matr ncol 3 byrow TRUE gt matr 1 2 3 1 3 5 6 2 2 5 7 3 9 1 5 4 4 2 3 you give to the matrix function either the ncol or the nrow parameters to specify the layout of the matrix The default method that R uses to fill in the matrix is by columns so if you want to fill it by rows you need to set true the option byrow as in the example above Matrix indexing is similar to vector indexing gt matr 2 1 1 2 the first index refers to the row number and the second index to the column number Omitting one of the two inde
5. col2 1 5 4 2 1 Matrix Operations The function t gives the transpose of a matrix The inverse of a matrix is obtained through the function solve Some other operators are listed in Table 4 3 Example gt beta lt solve t x hxhx Lh t x Z hy Table 4 3 Matrix Operations Operator Function h h Matrix Multiplication det Determinant solve Inverse 17 4 3 Lists Lists are objects that can contain elements of different modes e g numeric character logical as well as other objects vectors matrices and also other lists Let s build a small list to see how we can work on it gt veci lt 1 12 gt vec2 lt c w h m gt mylist lt list veci vec2 gt mylist 1 1 1 2 3 4 56 7 8 9101112 2 1 yg h m The syntax for subsetting a list is a bit awkward but as we ll see later naming the elements of a list makes things easier To access an element of a list you can use the double brackets notation for example gt mylist 1 1 1 2 3 4 5 6 7 8 9 10 11 12 returns the first element of the list mylist which is a vector of length 12 if you want to access say the third element of this vector the syntax is as follows gt mylist 1 3 1 3 Naming the elements of the list makes things easier gt mylist lt list a vec1 b vec2 gt mylist a 1 1 2 34 56 7 8 9101112 b 1 yg h m now the first element of the lis
6. m slategray DI mediumaquamarine 2 tani mediumorchid E mediumpurple E midnightblue mistyrose 70 thistlei m tomato2 w turquoise wheat ii black gray9 J gray25 E gray30 Table 7 8 Different shades of gray Ey gray40 E gray50 m gray60 gray65 71 gray75 gray85 gray94 white 7 15 Managing Graphic Devices 7 15 1 Opening Another Graphics Window When you issue the command for a graph R opens a window to show it if you afterwards issue another command for a graph if the previous window is still open R doesn t open another one but rather replaces the old graph with the new one If you wish to show the new graph in a separate window you have to open the graphic device yourself this is accomplished with the command X11 under Unix and with the command windows under the Windows OS The device window can also be closed from the command line with gt dev off if you have many device windows open and you want to close them all at once use gt graphics off For further functions to manage multiple device windows see dev set 7 15 2 Exporting Graphics With R it s also possible to export your graphics in different file formats such as JPEG or postscript files To do this you need to open first the graphics device you want to use then insert the command for the graphic and finally turn off the graphic device Here s an example of ho
7. ESS Using Emacs Speaks Statistics with R If you have the ESS package installed you can use Emacs for both editing R source files when working in batch mode and running a R process from within Emacs ESS provides an extended set of facilities for both these tasks among these are syntax highlighting indentation of code and the ability to work with multiple buffers To get syntax highlighting just use the R extension for naming your file To start an R session from within Emacs press M x type R in the minibuffer and press Enter Another nice way of running an R session from inside Emacs is to run first a shell in Emacs press M x and then type shell in the minibuffer and then calling R from that shell However this doesn t involve ESS so you won t have all the features that ESS adds to the Emacs editing facilities For sake of clarity the use of ESS for editing R source files and for running a R session will be addressed in two separate sections however this separation is quite artificial first because the most proficient use of ESS involves editing a R while running a R session and second because some of the tips given in one section apply also to the usage of ESS illustrated in the other section Therefore you re invited to at least skim through both sections even if you re interested on one usage of ESS only 16 1 Using ESS for Editing and Debugging R Source Files If you have a basic knowledge of Emacs you will
8. Shift AltGr for AltGr for if you still can t find them try pressing AltGr with some keys in the upper part of the keyboard and see if you can spot them In Microsoft Windows the braces can be accessed as above while to access the tilde in most applications including the R console you 125 have to write the ASCII code 126 with some modifier function key in my laptop that s Alt Fn 126 In Emacs however you can t write the tilde in this way a solution is to write the character in octal code by typing Ctrl q 176 RETURN 16 2 Using ESS to Interact with a R Process To start a R process type M x R C p and C n or C and C are for scrolling through the command history One thing you need to know is the ESS smart underscore behaviour that is if you press the underscore once you get the assignment operator lt if you press the underscore twice you get a literal underscore _ This shortcut for the assignment operator can be very annoying if you use the underscore often in variable names to turn off this smart behaviour you need to put the following line somewhere in your emacs file but before ESS is loaded ess toggle underscore nil When you are running R inside Emacs if the cursor is not positioned at the current command line and you try to retrieve some command from the command history with C p or C Emacs will complain saying that you are not at command line
9. To get at the command line without using the mouse press M Shift If you set the cursor at a previous command and then press Enter that command will be evaluated again There is a quick way to source a file C c C 1 filename will load and source your file C c C q is another way of quitting R in ESS mode but I guess C d remains the fastest one 126 Chapter 17 Using Sweave to Write Documents with R and lA TEX 17 1 What s this Sweave Sweave provides a great way of writing documents or reports that contain both text and R objects namely figures syntax and raw or nicely formatted output produced by R Sweave is also a way to automate the production of documents Usually when you write a document with some statistical content you first write the text and then add the graphics produced by some statistical software or spreadsheet application Of course this process is time consuming not to mention the fact that often you have to manually fill in tables with the statistics produced by the application you re using Even worse if you ve already prepared your report but then you have to change something in the statistical analyses for example you have to add or drop a subject the entire process must be repeated again from scratch Sweave is aimed at easing this process it works like this you write a single source file which contains your text written with the ATEX markup language and embed in it the R syntax needed
10. gt rm n_beers occupation sex we can t now access them directly by name gt mean n_beers Error in mean n beers Object n beers not found we have to retrieve them from the dataframe 20 gt mean dats n_beers 1 4 75 the example might seem artificial why did I remove them in the first place but very often you read in the data directly as a dataframe with the read table function see sec 5 1 1 so you ll have to access them from the dataframe Another option is to use the function attach which attaches the dataframe to the path that R searches when evaluating a variable in this way you don t have to refer to the dataframe to access the values of a variable gt attach dats gt mean n_beers 1 4 75 this is OK only if you re working with a single dataframe and you don t want to manipulate the variables in it In fact if you accidentally attach two dataframes that share some variable names or you try to change an object of a dataframe after it has been attached strange things may happen you ve been warned the details are in the R manual To function detach detaches the dataframe from the search path Change the Names of Variables in a Dataframe Sometimes you might want to change the names of the variables in a dataframe for example when you create new dataframes with the unstack function or just because you don t like the way you called it initially You can visualise the names for the variabl
11. lt lt gt gt after you ve finished with the R syntax chunk you need to add the following tag to start another piece of text written with ATEX in this way you can alternate chunks of R code with pieces of ATX syntax If you forget to add the O tag before a piece of TFX syntax Sweave will complain and abort the process if you instead make a mistake with ATX syntax Sweave won t complain and will normally produce the tex file however the compilation with ATEX won t work There are different options that determine which R objects will appear in the final document If you want both the R code and its output to appear in the document just use the lt lt gt gt empty tag They will both be inserted in the MT X file in a redefined verbatim environment Setting the option echo FALSE lines of R code are not included in the document while with the option results hide the output of the R code won t appear in the document Therefore if you want to run some R code but neither the code nor its output should appear in the document use lt lt echo FALSE results hide gt gt Another option will suppress all the output except the figures lt lt echo FALSE fig TRUE gt gt Sweave will automatically put a includegraphics command for a figure Finally if you want to use some utilities like xtable that automatically produce KTEX objects from R objects you will want to use the following options to tell Sweave not to put
12. 20 15 10 Figure 7 2 Values Connected by Lines 10 20 30 40 50 ti 41 7 3 Drawing Functions The plot function can be used for drawing mathematical functions for example gt vec lt seq from 0 to 4 pi length 120 gt plot vec sin vec type 1 in this case is necessary to use 1 as the type of plot otherwise the plot would resemble a messy scatterplot It is also possible to plot markers on the points in which the function is actually evaluated Using the option b for the plot type both a continuous line and markers are plotted There are lots of options to define the appearance of a plot next comes an overloaded example used just to introduce some of these options A more detailed description is given in Section 7 9 7 3 1 matplot Plotting the sine and cosine functions together with the matplot function the result is in Figure 7 3 gt a lt seq from 0 to 2 pi length 20 gt s lt sin a gt c lt cos a gt aa lt cbind a a matrix of hor coord gt cs lt cbind c s matrix of vert coord gt matplot x aa y cs type 1 lwd 1 8 ylab sine and cosine function 7 4 Barplots Barplots sometimes come in handy when you want to summarise your data Suppose we have administered a test to three different groups of people which we will designate as a b and c We want to summarise and compare the performance of each gro
13. n_beers lt c 6 8 4 8 9 4 5 3 4 2 3 1 occupation lt rep c s w 6 sex lt c rep m 6 rep f 6 occupation lt as factor occupation sex lt as factor sex VM MM MV 19 well now let s create the dataframe gt dats lt data frame n_beers occupation sex it s as simple as this you have just put the three vectors together let s have a look at it gt dats n_beers occupation sex 6 s OONDOFPFWN E HH H O sus ves ves nos aus Hh h heh hh BB 8 8B BB HH CON S WOOP 0 CO d 0 Es N as we said each row holds the data of a single observation in this case it corresponds to the data of a subject but as we ll see later this is not always necessarily true Each row gives a full specification for each observation we know that the first subject drunk 6 beers he s a student and he s male and we could tell the same data for the other subjects Since we have all this information we could now compare for example the number of beers drunk by male vs females or by male students vs female students There are special functions to compute these values quickly like tapply and by see sec 4 7 3 and other functions to get statistical tests they will be dealt with as we go along Accessing Parts of a Dataframe You can access or refer to a column of a dataframe with the operator in the example above suppose we removed all the original variables after creating the dataframe
14. 19 22 34 in this case the c concatenates a series of numerical data into a vector and the assignment operator lt assigns it to the variable temperature so that it can be retrieved later Once the variable is created you can apply functions to it for example gt mean temperature 1 30 81818 will compute the mean of the data vector If you want to save the result of this function you just have to assign it to another object gt mean_temp lt mean temperature notice that in this case the value is assigned to the object mean_temp but it is not printed you can display it with gt print mean_temp 1 30 81818 or for short just calling the object gt mean_temp 1 30 81818 12 You can also perform simple arithmetic operations on a vector for ex ample gt temperature 10 1 44 55 33 39 36 41 54 42 29 32 44 will add 10 to each element of the vector You can also build vectors of characters quoting each element of the vector gt colour lt c blue green red The length function is used to access the number of element present in a vector gt length colour 1 3 4 1 1 Indexing Vectors It is possible to access only subsets of data in a vector and also assign them to another vector The most basic form of indexing is based on the position of the data in the vector For example to access only the datum in the third position of a vector called temperature you would simply
15. 2001 Technische Universitat Wien Vienna Austria 2001 ISSN 1609 395X A J Rossini R M Heiberger K Hornik M Maechler R A Spara pani and S J Eglen ESS Emacs Speaks Statistics for version 5 2 11 The ESS Developers 2005 D Sarkar Lattice an implementation of trellis graphics in r R News 2 2 19 22 2002 D Sarkar Some notes on lattice In K Hornik and F Leisch editors Proceedings of the 3nd International Workshop on Distributed Statisti cal Computing March 20 22 2008 Technische Universitat Wien Vi enna Austria 2003 ISSN 1609 395X L Soliani Statistica univariata e bivariata parametrica e non parametrica per le discipline ambientali e biologiche 2005 R Stallman GNU Emacs Manual for version 21 3 Free Software Foundation 14 edition 2002 The R Development Core Team R Data Import Export Version 2 1 0 2005 04 18 The R Development Core Team R Documentation 2005 W N Venables and B D Ripley S Programming Springer 2000 W N Venables and B D Ripley Modern Applied Statistics with S Springer Fourth edition 2002 W N Venables D M Smith and the R Development Core Team An Introduction to R The R Development Core Team 2005 Version 2 1 0 J Verzani simpleR Using R for Introductory Statistics 2002 Version 0 4 Available http www math csi cuny edu Statistics R simpleR 153 Index ANOVA 97 one way 97 one way unequal sample sizes 99 repea
16. To perform the text we can use the following commands 95 gt levene test values groups The R output is given below as you can see we have an F value with its associated p value if the F value is significant then the variances in the groups are not equal In our case below the p value is far greater than 0 05 so we can safely accept the null hypothesis that the variances in the three groups are equal Levene s Test for Homogeneity of Variance Df F value Pr gt F group 2 0 3391 0 7154 27 96 Chapter 11 Correlation and Regression Let s imagine we want to see if there is a correlation between a manual and an oculomotor reaction time RT task The manual RT task requires to press one of two buttons depending on the colour assumed by the fixation point after a variable delay The oculomotor RT task requires to make a saccade towards the right or the left depending on the colour taken by the fixation point The mean RTs in milliseconds for 37 subjects are in the file m_o_rt txt We read in the data and then calculate the correlation for the sample gt dats lt read table m_o_rt txt header TRUE gt cor dats man dats ocul 1 0 5030888 gt cor dats man dats ocul 72 R squared 1 0 2530983 the correlation between the two measures in the sample is moderate and it would account for about 25 of the variance We need also to test if this correlation could be extended to the population gt cor test da
17. You can use the pnorm command to find out the probability value associated with a given z point in the normal distribution For example gt pnorm 1 96 will give the value of the area under the normal distribution curve from oo to 1 96 qnorm The qnorm command is the inverse of the pnorm command in that it gives the z point associated with a given probability area under the normal curve For example gt qnorm 0 975 dnorm The dnorm function provides the density function for the normal distribu tion Using the dnorm function we can for example make a nice plot of a normal distribution with mean equal to 0 and a standard deviation of 1 and colour its extreme right 0 05 tail with the following code The result is displayed in Figure 9 1 86 curve dnorm x 0 1 from 3 to 3 coord lt seq from 0 qnorm 95 1 to 3 length 30 dcoord lt dnorm coord 0 1 polygon x c 0 qnorm 95 1 coord 3 y c 0 dcoord 0 col blue V VV V Figure 9 1 The Normal Distribution dnorm x 0 1 0 2 0 3 0 4 0 1 0 0 3 2 1 0 1 2 3 We can use the pnorm function to test hypotheses with a z test Suppose we have a sample of 40 computer science students with a mean short term memory span of 7 4 digits that is they can repeat in sequence about 7 digits you read them without making a mistake and standard deviation of 2 3 The mean for the general population is 6 5 digits and the variance in the
18. dats lt stack dats this reshapes the dataframe into a one row per observation form Please note that R assigns names to the vectors in the new dataframe you can see them in the header of the dataframe you might need to know them for successive operations The unstack function simply does the opposite of the stack function and you can use it if you want to switch back to your original dataframe format gt dats lt unstack dats The unstack function can do more tricks if you have a dataframe with one observation per row a column with a response variable and two or more factor columns you can unstack the values of the response variable according to the levels of only one factors or according to the levels of two or more factors Suppose lat is your response variable and you have two factors congr with 3 levels and isi also with 3 levels The command gt dats lt unstack dats form lat congr unstack the values of the response variable according to the levels of the congr factor thus creating 3 columns one for each level The command gt dats lt unstack dats form lat congr isi unstacks the values of the response variable according to the levels of both factors thus creating 3x3 9 columns the first column contains the values at level 1 of congr and level 1 of isi the second one contains the val ues at level 1 of congr and level 2 of isi and so on for all the possible combinations 29 4 7 3 ta
19. print troubles it s important that the else statement is on the same line where the previous command ends in the above example that s the closing brace on the fourth line otherwise the interpreter sees it as unrelated to the previous if and will give an error the if statement could also be used by itself so it would be seen as a complete statement if else does not appear on the same line It is also possible to execute more than one command upon the fulfilment of a given condition 113 money lt 900 expenses lt 1200 if money gt expenses print good shopping lt money expenses else print troubles shopping lt NA print Money available for shopping print shopping Finally it is possible to add branches to your control structure with the else if statement expenses lt 1000 laptop lt 1000 if money expenses gt 1000 print great buy new laptop shopping lt money expenses laptop else if money expenses gt 0 amp amp money expenses lt 1000 print no laptop just shopping and save some shopping lt money expenses 2 else print troubles shopping lt NA print Money available for shopping print shopping ifelse The ifelse function is handy for testing all the elements of a vector on a given condition the general form is ifelse condition value_if_cond_true value_if_cond_false for example let s say we want to
20. with the same format as that shown in the table but without any header and without the column specifying the subject s number We will first read in the data and apply Table 12 3 Example for repeated measures ANOVA with one within subjects factor Subj Blue Black Red 1 0 120 0 132 0 102 2 0 096 0 103 0 087 3 0 113 0 134 0 109 4 0 132 0 147 0 123 5 0 124 0 139 0 124 6 0 105 0 115 0 102 7 0 109 0 129 0 097 8 0 143 0 150 0 119 9 0 127 0 145 0 113 10 0 098 0 117 0 092 11 0 115 0 126 0 098 12 0 117 0 132 0 108 the usual transformations to get the one row per observation format data lt scan rts txt read in the data colour lt as factor rep c blue black red 12 create a factor for colours with 3 lev subj lt as factor rep 1 12 each 3 create factor for subjects VM MM MV 103 gt table lt data frame data colour subj gt put everything in a dataframe Now the data are ready for further analyses We can first have a look at variability for the three colours by drawing a boxplot gt boxplot table data table colour As you can see from fig 12 1 the variability for the three conditions is pretty much the same and the three distributions seems to be approximately normal The medians for the three distributions seems to differ our analysis will tell us if these differences are significant Figure 12 1 Boxplot showing the distribution of RTs for the three colours
21. yellow2 Ei yellow3 EE yellow4 yellowgreen Appendix F GNU Free Documentation License Version 1 2 November 2002 Copyright 2000 2001 2002 Free Software Foundation Inc 51 Franklin St Fifth Floor Boston MA 02110 1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The purpose of this License is to make a manual textbook or other func tional and useful document free in the sense of freedom to assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or noncommercially Secondarily this License pre serves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made by others This License is a kind of copyleft which means that derivative works of the document must themselves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License princi
22. 0 12 I 0 11 0 10 black blue red Below is shown the syntax for the analysis and with its output gt summary aov data colour Error subj colour data table Error subj Df Sum Sq Mean Sq F value Pr gt F Residuals 11 0 0053863 0 0004897 Error subj colour Df Sum Sq Mean Sq F value Pr gt F colour 2 0 0037722 0 0018861 95 365 1 447e 11 Residuals 22 0 0004351 0 0000198 Signif codes O 0 001 0 01 0 05 7 7 0 17 1 The statement 104 Error subj colour is a shorthand for Error subj subj colour It tells R to partition the residuals into two error terms one represents the effects of the differences between subjects subj and the other is the subjects by colour interaction subj colour which is the appropriate error term for testing the effects of colour on the RTs To understand this procedure we have to remember that while in a fully randomised design we use a common error term to test the effects of all the different factors and their interactions in a repeated measures design we have to split up this error term into different partitions some of which we will use to test the effects of our factors and their interactions In the case at hand the subjects error term will not be used to test any effects it will just be subtracted from the common residuals entry so that the variability due to differences between subjects doesn t inflate t
23. With an example this will be clearer Let s imagine that in a verbal memory task we have the measures number of words re called of three groups that have been given three different treatments three different rehearsal procedures We want to see if the variances of the three groups are equal The data are stored in a text file verbal txt as in the table 10 3 but with no headers whatsoever Table 10 3 Data for the Levene test example Procedure 1 Procedure 2 Procedure 3 12 13 15 9 12 17 9 11 15 8 7 13 7 14 16 12 10 17 8 10 12 7 10 16 10 12 14 7 9 15 First we will create the vector with the values of the dependent variables by reading in the file with the scan function gt values lt scan verbal txt Now we need to create the second vector defining the group to which a given observation on the data vector belongs to We will use the rep function to do this and for convenience will give the labels 1 2 and 3 to the three groups gt groups lt as factor rep 1 3 10 Notice that we have defined this vector as a factor this was necessary because we were using numerical labels it wouldn t have been if we had used a character or a string labels Now the data are in a proper format for using the levene test function This format can be called one row per observation and we will encounter it often later when we talk about ANOVA you can find more examples and clarifications on this format there
24. allows you to do most of the operations you can do using R from the command line through a point and click visual interface The R commander is just a R package so in order to use it you need to have R installed in the first place then you have to install the Remdr package and all the other packages it depends on After everything is installed correctly fire up R and call the R commander as you do with any other package gt library Remdr you will be greeted by a GUI with menus that allow you to type in data perform statistical analyses and create graphs The R commander works on both GNU Linux and Windows platforms For further information please refer to the R commander manual or look up the following web page http socserv socsci mcmaster ca jfox Misc Remdr Sciviews R Sciviews R is a project aimed at providing an user friendly GUI for R Cur rently it is only available for Windows It provides different functionality from the R commander but you can integrate the two together to get the best from each Please for further information refer to the Sciwies R web page http www sciviews org SciViews R index html JGR The JGR package provides a clean simple graphical user interface for R which is platform independent The package is written in JAVA and requires the JAVA SDK to run More info at the developer s web page http rosuda org JGR index shtml Chapter 3 Organising a Working Session 3 1 Setting
25. and Changing the Working Directory The command getwd displays the pathname of the current working direc tory that is where R will look for and store files if not otherwise instructed To change the current working directory use the command setwd dirname where dirname is the pathname of the working directory you re moving into Note that this has to be an existent working directory because R cannot create a new directory with this command Here s an example of how to specify the pathname gt setwd C mydata rats note that you have to use a slash and not backslash like you usually do in Windows to specify the pathname You can also specify a pathname relative to your current working directory without specifying the full path name It is indifferent using single or double quotes this holds true when you need to quote character strings If you want to see the files present in your current working directory use the command dir It is also possible to issue commands to the OS from within R with the system function for example gt system 1s under GNU Linux or Unix systems will list the files present in the current directory 3 2 Objects All the variables functions arrays etc you work with in R are stored and manipulated as objects To list all the objects currently active in your workspace you can use the command gt objects or alternatively gt 1s0 if you want to remove some o
26. colour fg foreground colour Table 7 5 Parameters for Fonts Parameter Function family font family font type of font plain bold italic etc 7 9 1 Line type lty There are six line types that you can call in R just with names or numbers These are listed in Table 7 6 and shown in Figure 7 11 There is a different more complicated way for setting many more line types please consult the manual for further information on that 1 Actually there are seven the first one is in fact blank or 0 which just draws nothing 55 Table 7 6 The Six Default Line Types in R Name solid dashed dotted dotdash longdash twodash DU CON HIZ Figure 7 11 The Six Default Line Types in R solid dashed 56 7 9 2 Symbols with pch pch is a graphical parameter for changing the way points are plotted in certain graphical functions This parameter can be set in two ways the first one is to give a symbol to be plotted as a character for example pch pch T pch pch 3 in this case you enclose the character you want to use between quotes you can t use more than a single character The other way to set the pch is to use a number between 0 and 25 which will select one of 26 special symbols available for plotting see Figure 7 12 like circles triangles and so on pch 1 pch 3 pch 5 Figure 7 12 Plotting Symbols in R O gt ae X gt lt og
27. dashed dotdash type b pch c 0 15 17 52 Figure 7 10 Interaction plot with different Line Types and Different Symbols oO A 4 n oO N N Congruency N N a a inc goal directed x 4 b inc no goal directed dA c congruent o 2 x o o N o N N fe x o tS N O N p 25 s N 2 x N o x N N x pes N O N N SJ a x o a x N A a Dita de a o 75 0 75 SOA 53 7 9 Setting Graphics Parameters Graphics parameters allow you to tweak many elements of a plot such as the font for the labels the symbols or line types to use and so on see par to get a full list and description of these parameters Graphics parameters can be set and accessed with the function par called without arguments as par it will give you a full list of the current defaults if you want to query only one or a few parameters use gt par lwd see current line width gt par c lwd pch see lwd and plotting symbols to change the value of a parameter you can use gt par lwd 1 4 change line width gt par pch change plotting symbol bg gray80 use a light gray background Moreover most plotting functions like plot barplot and so on allow you to set some of the parameters for the current plot as an argument to the function itself for example in plot you can choose the type of plot points vs lines and the plotting symbol as options with type and pch
28. function for reading in data is scan it can easily read in both tabular data in which all the columns are of the same type or they are of different type as long as they follow a regular pattern We ll read in the ratsData txt file as an example gt x lt scan file ratsData txt what list identifier character 34 height numeric weight numeric species character skip 1 Read 6 records gt str x List of 4 identifier chr 1 6 sa01 sa02 sa03 sb01 height num 1 6 3 2 2 6 2 9 2 4 2 5 2 4 weight num 1 6 300 246 317 229 230 245 species chr 1 6 A A A B the what argument tells the scan function the mode numeric character etc of the elements to be read in if what is a list of modes then each corresponds to a column in the data file So in the above example we have the first column the variable identifier which is of character mode the second column height is of numeric mode like the third column weight while the last column species is of character mode again Notice that we re telling scan to skip the first line of the file skip 1 because it contains the header The object returned by scan in this case is a list we can get the single elements of the list corresponding to each column of the data file with the usual methods for lists gt x 1 first item in list first column in file 1 sa01 sa02 sa03 sb01 sb02 sb03 gt x weight ite
29. have only two possible outcomes follows a Bernoulli distribution If the probability of one outcome is p the probability of the other outcome will be p 1 x p P X 0 p 1 The expected value of a Bernoulli random variable is p E X 1 p 0 p p the variance of a Bernoulli random variable is given by Var X E X E X 1 p 0 p p Var X p p p 1 p As far as I know there are no special functions in R for computations re lated to the Bernoulli distribution density distribution and quantile func tion However since the Bernoulli distribution is a special case of the binomial distribution with parameter size equal to 1 the R functions for the binomial distribution can be used for the Bernoulli distribution as well Most of the calculations involved are quite simple anyway The density function can be calculated as follows gt dbinom x 0 size 1 prob 0 7 1 0 3 gt dbinom x 1 size 1 prob 0 7 1 0 7 85 The cumulative distribution function can be computed as follows gt pbinom q 0 size 1 prob 0 7 1 0 3 gt pbinom q 1 size 1 prob 0 7 1 1 The quantile function can be computed as follows gt qbinom p 0 3 size 1 prob 0 7 1 0 gt qbinom p 1 size 1 prob 0 7 1 1 Finally one can generate a random sample from a Bernoulli distribution as follows gt rbinom n 10 size 1 prob 0 7 1 1010110101 9 2 The binomial distribution 9 3 The normal distribution pnorm
30. need to add another column that identifies the levels of the subjects factor as shown in Table 4 9 26 Table 4 7 Data Format Suitable for R with More than One Factor Value Group Condition 7 P 1 5 P 1 8 P 1 8 P 1 6 P 1 6 P 2 4 P 2 7 P 2 8 P 2 5 P 2 6 C 1 5 C 1 7 C 1 6 C 1 5 C 1 4 C 2 2 C 2 4 C 2 5 C 2 3 C 2 Table 4 8 Data Format Suitable for the Human Eye repeated measures design Drug No Drug Concrete Abstract Concrete Abstract T 6 6 4 5 4 5 2 8 T T 4 8 8 6 5 6 5 5 3 27 Table 4 9 Data Format Suitable for R repeated measures design Value Drug Exposure Word Type Subject q Ha 00 UH N amp di S x Ud S OFWON Sb gt Sa OW dI VAVANAVAVAVAVAVAWA WA O fool iolololeiefo rFrrrranadgaagnaorrrrePaanaa o 00 ND dI wa WNP OBR dI ND OFF B W N 28 4 7 2 The stack and unstack functions One of the utilities provided by R to manipulate the format of your data is the stack function If you have your data in a dataframe with a layout similar to that shown in Table 4 4 you can use the stack function to get a one row per observation format What the stack function does is to create a single long vector from the vectors you have in your dataframe and an additional factor vector which identifies the level for each observation Here s an example the data are in the file stack txt gt dats lt read table stack txt header TRUE this creates the dataframe gt
31. on the value of cex and pointsize e Normalised Device Coordinates NDC the device region is 1x1 NDC whatever the actual physical measure The lower left corner has co ordinates x 0 y 0 and the upper right corner x 1 y 1 Using NDC thus the size of regions inside the device can be specified in relative terms to the device size In the next paragraphs the graphics parameters for controlling the dif ferent regions inside the device will be explained Always keep in mind the layout of a graphics device in R see Fig 7 16 and Fig 7 17 Figure Region The figure region can be set either in inches or in normalised device coordi nates e fig NDC coordinates of the device in the form c x1 x2 y1 y2 where x1 yl are the coordinates of the lower left corner and x2 y2 are the coordinates of the upper right corner Example gt par fig c 0 1 0 5 0 1 0 6 gt plot 1 10 gt par fig c 0 5 1 0 1 0 6 the next call to plot will erase the gt current plot gt plot 1 10 gt par fig c 0 0 5 0 1 0 6 new TRUE the next call to plot will not gt erase the current plot gt plot 1 10 as shown in the example to change the figure region without start ing a new plot add new TRUE this may be used for creating complex arrangements for multiple plots within the same device 64 e fin the figure region dimension width height in inches Example gt par fin c 5 5 Plotting Region e pl
32. or data set present in the pack age The documentation files are written in a IXIEX like format called Rd package skeleton creates a skeleton of the documentation file which just needs to be edited the default fields are pretty much self explanatory For a more detailed explanation you can read the Writing R Extensions manual http cran r project org doc manuals R exts html Pll give you just a few tips It is possible to add additional sections beside the default ones for ex ample it may be useful to add a Warnings section if you have any warnings to give on the use of the function section Warning Calling this function with arguments foo foo2 can cause In the seealso section you can refer to other functions contained in your package for example code link functionFoo will automagically add a hyperlink to the documentation for the function functionFoo In the Examples section you write code as if you were writing it in a R script You can use datasets from your own package or from the standard R dataset Keep in mind that the examples should be directly executable by the user either through copy and paste or through the example function When the package is installed the examples will appear in a directory called R ex however you do not need to bother about this the R code for your examples needs to be written within the documentation Rd files 120 The documentation requires the presence of on
33. paleturquoise3 paleturquoise4 palevioletred J palevioletredi palevioletred2 m palevioletred3 C palevioletred4 papayawhip peachpuff peachpuff1 peachpuff2 a peachpuff3 peachpuff4 peru pink pinki pink2 E pink3 J pink4 oun plumi plum2 HEI prum E plum4 powderblue E purple 141 DI purplei purple2 purple3 E purple4 red redi red2 red3 red4 rosybrown rosybrowni rosybrown2 E rosybrown3 rosybrown4 royalblue J royalbluei royalblue2 E royalblue3 E royalblue4 saddlebrown salmon salmoni salmon2 salmon3 salmon4 sandybrown seagreen E seagreeni E seagreen2 seagreen3 E seagreen4 seashell seashelli seashell2 seashell3 J seashell4 sienna siennai sienna2 sienna3 sienna4 skyblue DI skybluel J skyblue2 E skyblue3 E skyblue4 LJ slateblue slatebluei slateblue2 slateblue3 slateblue4 slategray slategrayl slategray2 DD siategray slategray4 slategrey snow snowi snow2 snow3 snow4 springgreen springgreeni springgreen2 springgreen3 springgreen4 steelblue steelbluei steelblue2 steelblue3 steelblue4 tan tani tan2 tan3 tan4 thistle thistlel thistle2 thistle3 thistle4 tomato tomatol tomato2 tomato3 142 E tomato4 turquoise a turquoisel E turquoise2 turquoise3 E turquoise4 Ei violet violetred violetredi violetred2 violetred3 violetred4 wheat wheat 1 wheat2 wheat3 wheat4 whitesmoke yellow i yellowi
34. population is unknown We re interested in seeing if the memory span for computer science students is higher than that of the general population We ll run a z test as where 7 is the mean short term memory span for our sample and s is its standard deviation gt z lt 7 4 6 5 2 3 sqrt 40 1 gt z 87 1 2 443695 gt pnorm z 1 0 9927311 gt 1 pnorm z 1 0 007268858 this would do for a one tailed test gt 1 pnorm z 2 1 0 01453772 so the z value for our sample is 2 443695 we then get the area under the curve from oo to our z value which gives us the probability of a score lower than 7 4 To get the p value we subtract that probability value from 1 this would give us the probability of getting a score equal to or higher than 7 4 for a one tailed test Since we want a two tailed test instead we multiply that value by two to get our p value which is nonetheless significant The qnorm command on the other hand can be used to set confidence limits on the mean for the example above we would use the following for mula s vn l to set a 95 confidence interval on the mean short term memory span for the computer science students CI T Za 2 alpha lt 0 05 s lt 2 3 sgrt 40 1 zp lt 1 alpha 2 ciup lt 7 4 zp s cilow lt 7 4 zp s gt cat The 95 CI is n cilow lt mu lt ciup n The 95 CI is 7 040913 lt mu lt 7 759087 VM MM Mv The fol
35. the R output in a verbatim environment lt lt echo FALSE results tex gt gt 128 Chapter 18 Sound Processing 18 1 Libraries for Sound Analysis and Signal Pro cessing seewave seewave provides functions for analysing manipulating displaying editing and synthesising time waves particularly sound This package processes time analysis oscillograms and envelopes spectral content resonance qual ity factor cross correlation and autocorrelation zero crossing dominant fre quency 2D and 3D spectrograms http cran r project org src contrib Descriptions seewave html sound Basic functions for dealing with wav files and sound samples http cran r project org src contrib Descriptions sound html tuneR Collection of tools to analyse music handling wave files transcription http cran r project org src contrib Descriptions tuneR html signal A set of generally Matlab Octave compatible signal processing functions Includes filter generation utilities filtering functions re sampling routines and visualisation of filter models It also includes interpolation functions and some Matlab compatibility functions http cran r project org src contrib Descriptions signal html 129 Appendix A Partial List of Packages by Category A 1 Graphics Packages lattice http cran r project org src contrib Descriptions lattice html rgl http cran r project org src contrib Descriptions rgl html tkrplot
36. this is writing a panel function that combines two standard panel functions There is a number of prede fined panel functions see panel functions that can be used to add lines grids etc to a scatterplot barchart or other higher level plotting lattice function We will start with a very simple example adding a horizontal line at a fixed height in a dotplot The line_matching dataset described in the barchart example can be very well visualised also through a dotplot Fig ure 8 8 gt oldpar lt trellis par get superpose symbol gt trellis par set superpose symbol list col c darkslateblue indianred pch 19 dotplot error length group groups color data dats origin 0 ylab Error cm xlab Segment Length auto key TRUE aspect 1 as table TRUE V however since the data represent positive or negative displacements from zero it would be nice to add a horizontal line passing from zero In order to 81 have this we will write a panel function that combines the panel dotplot function with the panel abline function that we ll use to add the horizontal line gt panel hRefDotplot lt function x y ref NULL panel dotplot x y panel abline h ref our new panel hRefDotplot panel function accepts three arguments x and y which are the standard arguments given by the higher level plotting functions like dotplot to panel functions to specify the da
37. with error bars showing the standard deviation for each group We could achieve this result adding lines to the current graph but there is a better option we can use the barplot2 command which comes with the gplots library and provides an easy way of adding error bars to a barplot So once we have the gplots package installed we first load it gt library gplots and then we can draw our barplot with error bars To get them we need to set the option plot ci TRUE and then specify the upper and lower bounds of the error bars with the ci u and ci 1 commands So we first create the values for ci u and ci 1 so that the error bars represent one standard deviation around the mean We ll use the values from the two tables we had created before with means and standard deviations for the three groups gt upper lt test_means test_sd gt lower lt test_means test_sd Now we can draw our barplot you can see the result in figure 7 5 45 gt barplot2 test_means col c darkred salmon2 plum4 plot ci TRUE ci u upper ci l lower Figure 7 5 Barplot with Error Bars 46 7 5 Boxplots Boxplots provide a powerful way to visualise the central tendency and the dispersion of the data for a given sample and to directly compare these same characteristics for different samples Let s look at one of them the data are organised in a dataframe in the file boxplot1 txt They are the scores for two different groups grou
38. 0 1 in R you can use the chisq test Table 10 1 Handedness Frequencies for an Experimental Sample Right Left Both Tot 93 18 2 113 function to see if the distribution of your sample differs from that of the general population gt chisq test x c 93 18 2 p c 0 8 0 15 0 05 Chi squared test for given probabilities data c 93 18 2 X squared 2 4978 df 2 p value 0 2868 you give the function a vector x with the frequencies for each category in your sample and a vector p of the theoretical probability for each category R returns the value of the x statistics and its associated p value In our case the p value indicates that the x statistics is not significant assuming IFake data 90 a 0 05 so we can say that the distribution for the handedness variable in our sample does not differ from that of the general population Testing Hypotheses about the Association between Two Categor ical Variables The x test can also be used to verify a possible association between two categorical variables for example sex and cosmetic products usage classified as high medium or low In this case the data are best summarised by a contingency table as Table 10 2 which presents the data on cosmetic usage for a sample of 44 males and 67 females The formula for the x Table 10 2 Cosmetic Usage by Sex High Medium Low Tot Males 6 11 27 44 Females 25 30 12 67 Tot 31
39. 41 39 111 statistics is 5 x gt fe 3 fo 10 1 e where fe are the expected frequencies and f are the observed frequencies to get the statistics and perform a test of significance on it with R you can first arrange the data in a matrix gt cosm lt c 6 11 27 25 30 12 gt cosm lt matrix cosm nrow 2 byrow TRUE then you can directly give the matrix to the chisq test function to test the null hypothesis that there is no association between sex and cosmetic usage gt chisq test cosm Pearson s Chi squared test data cosm X squared 22 4159 df 2 p value 1 357e 05 the p value tells us that the null hypothesis does not hold there is indeed an association between sex and degree of cosmetic usage If you store the results of the test in a variable you ll be able to get the matrices of the expected frequencies and residuals gt cosmtest lt chisq test cosm 91 gt cosmtest expect expected frequencies gt under a true null hypothesis 1 2 3 1 12 28829 16 25225 15 45946 2 18 71171 24 74775 23 54054 gt cosmtest resid 2 1 2 3 1 3 217907 1 697374 8 615054 2 2 113252 1 114694 5 657647 gt sum cosmtest resid 2 1 22 41593 If you have only a few observations and want to use the Yate s correction for continuity you have to set the optional argument correct to true gt chisq test x mydata correct TRUE Very often you don t already have your dat
40. 7 11 1 mfrow and mfcol The parameters mfrow and mfcol allow you to divide the graphics device you re using e g X11 or pdf into multiple boxes each box will contain a new figure These parameters are set giving a vector of the form gt par mfrow c n_rows n_columns where n_rows is the number of rows and n_columns is the number of columns you want for your layout For example the following will create a layout with 2 rows and 3 columns as you can see in Figure 7 14 gt par mfrow c 2 3 gt symb lt as character 1 6 gt for i in 1 6 plot 1 1 pch symbli 60 Figure 7 14 A 2x3 Layout with mfrow Tell Td TT 06 08 10 1 2 14 06 08 10 1 2 1 4 0 6 08 1 0 1 2 1 4 TT T T_T_T T_T_T 0 6 08 1 0 1 2 14 0 6 08 1 0 1 2 1 4 0 6 08 1 0 1 2 1 4 mfcol is exactly the same as mfrow but the figures are drawn in sequence by column rather than by row for example the following code yields the Figure 7 15 gt par mfcol c 2 3 gt symb lt as character 1 6 gt for i in 1 6 plot 1 1 pch symbli of course you can get other layouts try gt par mfrow c 2 2 4 nice boxes gt par mfrow c 1 3 one row 3 cols Rather than having the figures drawn sequentially following the order determined by mfrow or mfcol it is possible to specify directly the position for the next figure using the mfg parameter The next example will draw the plo
41. 9 149 149 150 150 150 152 154 Chapter 1 Installing R The information provided in this section is quite generic and limited for de tailed information please refer to the R Installation and Administra tion Manual available at the CRAN website http cran r project org CRAN stands for Comprehensive R Archive Network and is the main point of reference for the R software where you can find R sources binaries documentation and add on packages 1 1 Installing the Base Program First of all you need to install the base R program This already implements most of the statistical functions you will ever need There are two ways of getting it you can either compile the source code yourself or you can fetch the precompiled binaries for your specific operative system The second way is the easiest one and usually you will want to go with it GNU Linux and Other Unices Precompiled binaries are available for some GNU Linux distributions there is a list of these on the R FAQ For other distributions you can build R from source There are precompiled binaries for Debian GNU Linux so you can install the R base system and a number of add on packages with the usual methods under Debian that is apt get Synaptic or whatever else you use Windows There are precompiled binaries for Windows you just have to download them then double click on the installer s icon to start the installation Most Windows versions a
42. A R GUIDE Version 0 07 12 30 Samuele Carcagno sam carcagno gmail com Copyright 2006 08 Samuele Carcagno Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 2 or any later version published by the Free Software Foundation with no Invariant Sec tions no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License Disclaimer This document comes with NO WARRANTY whatsoever of being correct in any of its parts This document is work in progress check out http samcarcagno altervista org soft carcagno R_ guide pdf to download the latest version This document will reach version number 1 when I think it s decent and complete enough For the moment version number is 0 followed by year month day of last modification Contents 1 Installing R 1 1 1 Installing the Base Program 0 1 1 2 Installing Add On Packages 2 008 2 2 A Simple Introduction to R 3 2 1 Firing up and Quitting Ro 3 2 2 Starting to Work with Ro 4 29 Gettine Helpi og siasi Se E SO BA Goma a ke Foe 5 2 4 Working with a Graphical User Interface 7 3 Organising a Working Session 9 3 1 Setting and Changing the Working Directory 9 32 Objects oe ara aS A a ee Ee EO A eS 9 3 3 Saving and Using the Workspace Image 10 3 4 Working i
43. Not all the possible procedures are avail able and some of them might not be applicable to the object resulting from the specific analysis you re doing Additional packages might cover your specific needs The p adjust function The function p adjust comes with the base R program in the package package stats so you don t need to install anything else on your machine apart from R to get it This function takes a vector of p values as an argument and returns a vector of adjusted p values according to one of the following methods e holm e BH e hochberg o BY e hommel e fdr e bonferroni e none So if for example you ve run 3 t test after a one way ANOVA with 3 groups to compare each mean group s mean with the others and you want to correct the resulting p values with the Bonferroni procedure you can use p adjust as follows gt ps lt c 0 001 0 0092 0 037 p values from the t tests gt p adjust ps method bonferroni 1 0 0030 0 0276 0 1110 111 the last line of the example gives the p values corrected for the number of comparisons made 3 in our case using the Bonferroni method As you can see from the output the first 2 values would still be significant after the correction while the last one would not You can use any of the procedures listed above instead of the Bonferroni procedure by setting it in the method option If you don t set this option at all you get the Holm procedure by de
44. a tabulated in a contingency table however if you have a series of observations classified according to two categorical variables you can easily get a contingency table with the table function The next example uses the data in the file hair_eyes txt that lists the hair and eyes colours for 118 people We will first build our contin gency table from that gt dats lt read table hair_eyes txt header TRUE gt tabdats lt table dats hair dats eyes gt tabdats eyes hair blue brown green blonde 16 9 6 brown 14 32 9 red 9 7 16 now we can perform the y test directly on the table to see if there is an association between hair and eyes colour gt chisq test tabdats Pearson s Chi squared test data tabdats X squared 21 8622 df 4 p value 0 0002135 the x statistics is highly significant so there clearly is an association be tween hair and eyes colour 92 10 2 Student s t test 10 2 1 One sample t test To test if a group s mean is different from a given population s mean u you can run a simple t test in R The syntax is as follows gt t test gri mu 17 where gr1 is the vector containing the data of the group and mu is an optional argument 2 specifying the population s mean e mu 0 Default or another value mu is the value specifying the population s mean e alternative two sided default or less or greater this option allows choosing whether the test sh
45. amp and lazy evaluation lt Minor than or equal to Union or gt Greater than or lazy evaluation gt Greater than or equal to Negation Equal to xor exclusive or l Not equal to isTRUE x It is also possible to apply labels to the positions of a vector and then access the datum in a given position through its label gt temperature lt c 34 45 23 29 26 gt names temperature lt c Johnny Jack Tony Pippo Linda gt temperature Tony Tony 23 4 1 2 The seq Function The seq function can be used to create evenly spaced sequences of num bers gt seq 1 10 1 12 3 4 5 6 7 8 9 10 the default increment is 1 but you can change it with the option by 14 gt seq 1 1 9 by 0 1 1 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 There s a shortcut for sequences with an increment of 1 gt a lt 1 10 gt a 1 1 2 3 4 5 6 7 8 9 10 4 1 3 The rep function You can use the rep function to create vectors which contain repetitions of the same elements Let s start from the most simple use gt vector lt rep 3 13 simply creates a vector of 13 elements all having the value 3 More inter estingly you can repeat sequences of numbers gt rep 1 4 3 111 123412341234 as you see the above command repeats the sequence 1 2 3 4 three times Furthermore you can also specify the number of times a given element of the sequence should be repeated
46. by giving the coordinates of its top left corner for the above example we might have written gt legend x 2 3 y 0 2 legend c a congruent b inc goal directed example not continued The text of the legend is given as a character vector each element of the vector represents one item of the legend Since we re using both different line types and different symbols to dif ferentiate the lines in the interaction plot for the legend we need to specify both in the legend with the 1ty and pch arguments the line types and symbols of course should be the same as those used for the plot In the above example we suppressed the drawing of a box around the legend setting the bty argument to n if you want a box set it to o this is the default anyway so you don t really need to specify it if you want the box If you choose to enclose the legend into a box you can set its background colour through the bg argument There are of course many other options to get a full listing please look up the manual 58 Figure 7 13 Plot with manually added legend a Congruency 2 lt 0 a congruent m b inc goal directed 4 c inc no goal directed 19 2 mA 2 fo o o 2 O D 5 o n 5 sS E Q x o O x 2 a Cc q ib X 4 A SOA 7 10 2 Adding Text You can insert text in a graph with the text function you have just to specify t
47. c Drug No Drug 16 each 2 gt drug lt as factor drug gt group lt rep c Yuppy Kalamani each 32 gt group lt as factor group gt dats lt data frame subj socialint alcohol drug group now the ANOVA gt summary aov socialint alcohol drug group Error subj alcohol drug data dats Error subj Df Sum Sq Mean Sq F value Pr gt F group 1 2 250 2 250 0 4615 0 508 Residuals 14 68 250 4 875 Error subj alcohol Df Sum Sq Mean Sq F value Pr gt F 109 alcohol 1 22 5625 22 5625 22 7658 0 0002982 xxx alcohol group 1 0 0625 0 0625 0 0631 0 8053669 Residuals 14 13 8750 0 9911 Signif codes O 0 001 0 01 0 05 7 7 0 17 1 Error subj drug Df Sum Sq Mean Sq F value Pr gt F drug 1 60 062 60 062 81 0482 3 376e 07 drug group 1 5 063 5 063 6 8313 0 02043 Residuals 14 10 375 0 741 Signif codes O 0 001 0 01 0 05 2 7 0 1 1 Error subj alcohol drug Df Sum Sq Mean Sq F value Pr gt F alcohol drug 1 4 00 4 00 16 0 001316 alcohol drug group 1 5 610e 32 5 610e 32 2 244e 31 1 000000 Residuals 14 3 50 0 25 Signif codes O 0 001 0 01 0 05 0 17 1 110 Chapter 13 How to Adjust the p values for Multiple Comparisons The base R program comes with a number of functions to perform multiple comparisons Here by multiple comparisons I mean both post hoc and planned comparisons procedures
48. categorise the results of a classroom test scored from 1 to 10 as pass if the score was equal to or greater than 6 and fail if the score was less than 6 gt score lt c 4 7 6 5 8 6 7 gt admission lt ifelse score gt 6 pass fail gt admission 1 fail pass pass fail pass pass pass 114 so the first argument of the ifelse function is the condition that we want to test the second argument is the value that should be returned if the condition is met and the third argument is the value that should be returned if it is not xor The function xor implements the exclusive logical or operator that is it evaluates to true if exclusively one of two alternative conditions is met otherwise it evaluates to false The latter occurs both when none of the conditions is met and when both are met simultaneously gt a lt 6 gt xor a gt 5 a gt 7 1 TRUE gt xor a gt 5 a gt 3 1 FALSE in the first example only the first condition a gt 5 is met so the function evaluates to true In the second example both conditions are satisfied but since we re using xor and you can have one thing or the other but not both together the function evaluates to false gt a 1 4573675936483519 gt a lt a which a gt 5 14 2 String Processing One of the strengths of R in my opinion lies in the way it deals with character strings Certain objects for example dataframes allow to mix s
49. command foo as if it were from the shell R administration library list all installed pack ages R version info on R version and the platform it is running on Syntax starts a comment mydata foo refer to the variable foo in the dataframe mydata interaction operator for model formulae a b is the interaction between a and b crossing operator for model for mulae axb atbta b 132 Appendix C Other Manuals and Sources of Information on R e R Project Homepage http www r project org e CRAN http cran r project org e R mailing lists http www r project org mail html e Notes on the use of R for psychology experiments and ques tionnaires by J Baron and Y Li http www psych upenn edu baron rpsych pdf e R manual for biometry by K J Hoff http www bioinf uni hannover de teaching Hoff RMANUAL_ENGLISH PDF e Introductory R course at the University of Lancaster http www cas lancs ac uk short courses intro r html e Generalised linear models course with R at the University of Lancaster http www cas lancs ac uk short courses gen models html e Simple R by J Verzani http www math csi cuny edu Statistics R simpleR e Simplified manual of some R functions for the Stem and Ten dril project http wiener math csi cuny edu st stRmanual e AR wiki http www sciviews org _ rgui wiki 133 e Using R for psychological research A very simple guide to a very elegant package by William R
50. cratch however is a very good way to learn how graphics parameters work which is often necessary to customise plots created with the high level plotting functions We ll start with a very simple example of a scatterplot gt plot new gt plot window xlim c 0 10 ylim c 0 10 the plot new command creates a frame for plotting and opens a graphics device if there is not one already opened plot window defines the limits for the x and y axes points outside these limits will not appear in the plot After these two commands we re ready to do the actual drawing gt points x c 1 2 3 4 5 9 y c 2 5 3 4 5 3 gt axis side 1 gt axis side 2 points will draw points at the coordinates given in the x an y arguments To complete this very minimal plot you need at least some axes The axis function adds the axis the side argument specifies where the axis should be drawn 1 means at the bottom 2 at the left side and so on in a clockwise fashion 68 7 14 Colours for Graphics The command colours gives a list of built in colours available for graphics in R You can see some of these colours in Table 7 7 There are 101 built in shades of gray from gray0 that is almost black to gray100 that is almost white you can see some of them in Table 7 8 A complete table of built in R colours is given in Appendix E You can also specify colours in rgb values By default R accepts values in the range 0 1 but you can cha
51. ction plot O barplot boxplot histogram matplot stripchart interaction plot 7 2 The plot Function The plot O function is most commonly used to draw a scatterplot of two variables however if given an R object with a plot method as an argument it will produce different types of graphics depending on the object it is plotting Let s see an example of a scatterplot with some fake data a lt rnorm 5 1 6 n 50 b lt rnorm 15 4 3 n 50 this creates two vectors of length 50 with values normally distributed now we can plot the values of vector b against the values of vector b with gt plot x a y b gt or for short gt plot a b 39 Figure 7 1 A Scatterplot o o o o 4 o N 9 o o o o 9 gS o o o o O o 2 o 0 19 o O o o o o O o o E o o o o o o o Q onig o o Q a Onc o T T T T 4 6 8 10 a the resulting scatterplot appears in Figure 7 1 If we were to plot the change of a variable over time it could be a good idea to connect the values at different time points in the plot with lines this is easily achieved setting the option type Below is an example the result is shown in Figure 7 2 gt ti lt 1 50 gt b lt rnorm 15 4 3 n 50 gt plot ti b type 1 Some other possible values for the option type are p for points the default b for both points and lines and o for overplotted points and lines very similar to b 40 25
52. e gt print another_foo 1 25 or for short just type its name and press Enter gt another_foo 1 25 2You can also use the symbol as an assignment operator however the use of the arrow symbol is more straightforward in that it clearly shows the direction of the assignment and doesn t create confusion with the equal to logical operator since the two objects we have created are both numeric we can also do gt foo another_foo 1 30 Let s look at something more interesting we can create an object that stores a series of numbers for example the money we have spent each day of a week in Euros we can do this using the c function which concatenates a series of values in a vector gt expenses lt c 7 8 15 20 9 45 3 you might want to find out how much you ve spent in average during the week this is easily accomplished with the function mean gt mean expenses 1 15 28571 the function sd O gives you the standard deviation gt sd expenses 1 14 24446 Surely you ve wondered what the hell is that 1 that appears every time R gives you a result now that we ve introduced the vector we can get to it Try to create a long vector you can easily do this by creating a sequence of numbers for example gt long vec lt c 1 100 will create a vector containing the sequence of numbers from 1 to 100 now try to display it and see what happens All the elements of the vector won t fit
53. e as in the case the samples have the same size If the data are not in the one row per observation format however the details of the procedures to use to format them properly are slightly different Let s see an example We want to see if rats run faster in galleries painted in red rather than galleries painted in green or blue We wanted to run 20 subjects for each condition in this experiment however for various reasons 8 out of the total number of rats 3 from the red group 4 from the green group and 1 from the blue group had to be dropped from further analyses The data are shown in table 12 2 the time taken to run all over the gallery for each subject is shown in seconds The data are store in a file called ratsrun txt Table 12 2 Data for the one way ANOVA example with unequal sample sizes Red Green Blue 120 133 115 90 127 163 130 113 121 103 126 104 145 97 132 127 105 144 138 107 121 165 102 104 104 126 142 123 143 123 120 135 124 142 126 143 130 111 122 103 132 134 115 141 96 122 107 105 128 126 139 112 We read in the data as usual gt runtimes lt scan ratsrun txt Now we need to create a vector with the levels of the colour factor for each observation We will call the three levels r g and b 101 gt colour lt as factor c rep c r E g p 2 16 5 y i h i Up p Now we can put all together in a data frame gt data lt data f
54. e number of levels and the second argument the number of consecutive repetitions of each level the pattern is repeated up to the number of elements specified by the length argument Notice the different pattern created when the number of consec utive repetitions is set to 1 and the total length is left unchanged gt sex lt gl 2 1 label c male female length 6 gt sex 1 male female male female male female Levels male female 4 6 Getting Info on R Objects The most useful function to summarise information about many R object is str gt a lt seq 0 10 1 gt str a num 1 101 0 0 0 1 0 2 0 3 0 4 gt b lt c a Db c gt str b chr 1 3 a b c 23 in the example shown str gives information on the storage mode of the two vectors numeric for a and character for b it also gives information on the number of elements present and on the shape of the array compare the output of str for a vector and a matrix str gives also useful compact summaries of the contents of lists including nested lists Another useful function is mode which gives the storage mode of an R object gt mode a 1 numeric gt mode b 1 character 4 7 Changing the Format of Your Data In general statistical software require your data to be entered in a specific format in order to perform statistical analyses on them and R is no excep tion R provides many powerful functions to change the fo
55. e or more standard key words One way to get a list of these keywords is to download the tarball with the R sources after unpacking it you can find the keywords in a file within the doc directory called KEYWORDS db Converting Rd files to Other Formats HTML and BTFX versions of the documentation files are automatically pro duced in the package installation process you can find them in the html and latex directories of your package installation directory respectively You can also produce a single pdf or dvi file containing all the documentation using the following command from a shell produce dvi R CMD Rd2dvi path to your package sources produce pdf R CMD Rd2dvi pdf path to your package sources Adding additional Function or Data Files to the Package Adding additional function files is quite straightforward the files contained in the R sub directory of your package directory are plain R files so you can just write your functions drop the files with your functions there and next time you build the package the new functions will be included The function prompt can be used to build the documentation templates for new functions gt myfun lt function arg val lt arg 3 gt prompt myfun this will create a Rd file which you can edit and drop in the man directory Datasets can be saved using the save function gt mydata lt seq 1 10 1 gt save mydata file mydata rda documenta
56. e the Title of the section and preserve in the section all the sub stance and tone of each of the contributor acknowledgements and or dedications given therein Preserve all the Invariant Sections of the Document unaltered in their text and in their titles Section numbers or the equivalent are not considered part of the section titles Delete any section Entitled Endorsements Such a section may not be included in the Modified Version 147 N Do not retitle any existing section to be Entitled Endorsements or to conflict in title with any Invariant Section O Preserve any Warranty Disclaimers If the Modified Version includes new front matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document you may at your option designate some or all of these sections as invariant To do this add their titles to the list of Invariant Sections in the Modified Version s license notice These titles must be distinct from any other section titles You may add a section Entitled Endorsements provided it contains nothing but endorsements of your Modified Version by various parties for example statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard You may add a passage of up to five words as a Front Cover Text and a passage of up to 25 words as a Back Cover Text to the end of the list of Cover Texts in the Mod
57. ed t test is performed note that in this case the number of observations has to be equal in the two groups Missing values are removed if paired is TRUE A shortcut to choose a paired t test is gt t test gr1 gr2 e var equal FALSE Default or TRUE Tells whether the variances of the two groups should be treated as equal If TRUE is selected then the pooled variance is used to calcu late the variance If the option is left to default or FALSE is selected then the Welch or Satterthwaite approximation to the degrees of freedom is used e conf level 0 95 Default or another value this option sets the confidence level for the estimation of the confidence interval 10 3 The Levene Test for Homogeneity of Vari ances The Levene test can be used to test if the variances of two samples are equal or not This procedure is important because some statistical tests such as the two independent sample t test are based on the assumption that the variances of the samples being tested are equal In R the function to perform the Levene test is contained in the car package so in order to call it the package must be installed and the car library has to be loaded with the command gt library car The syntax to run a Levene test is 94 gt levene test y group where y is a vector with the values of the dependent variable we are measuring and group is another vector defining the group to which a given observation belongs to
58. ed to know these names to use the tapply function Now we ll create the two summary tables using the tapply function one with the means and one with the standard deviations for the three groups gt test_means lt tapply X test2 values IND test2 ind FUN mean gt test sd lt tapply X test2 values IND test2 ind FUN sd Now we can draw a simple barplot displaying the means for each group gt barplot test_means col c darkred salmon2 plum4 we ve added colours to the graph using the col option You can look at the resulting graph in figure 7 4 You can control the width of the bars specifying the width option and setting the range for the x axis with the xlim option specifying only the width does nothing you must also set the xlim You set xlim with a vector of the form xlim c from to in which from is the origin and to is the end of the axis In the example below we will set xlim to go from 0 to 3 and the bars to have a width of 0 5 gt barplot test_means col c darkred salmon2 plum4 xlim C 0 3 width 0 5 this sets the width of all bars at 0 5 we could specify the width for each single bar instead by giving to width a vector with the width values for each bar You can also control the spacing between the bars with the space option The default is set to 0 2 44 Figure 7 4 Simple Barplot Barplots with Error Bars Now let s say we want to get the same barplot but
59. ent is included in an aggregate this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document If the Cover Text requirement of section 3 is applicable to these copies of the Document then if the Document is less than one half of the entire aggregate the Document s Cover Texts may be placed on covers that bracket the Document within the aggregate or the electronic equivalent of covers if the Document is in electronic form Otherwise they must appear on printed covers that bracket the whole aggregate 8 TRANSLATION Translation is considered a kind of modification so you may distribute translations of the Document under the terms of section 4 Replacing Invari ant Sections with translations requires special permission from their copy right holders but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections You may include a translation of this License and all the license notices in the Document and any Warranty Disclaimers provided that you also include the original English version of this License and the original versions of those 149 notices and disclaimers In case of a disagreement between the translation and the original version of this License or a notice or disclaimer the original version will prevail If a section in the Document is Entitled Acknowledgements Dedica tions or History
60. er also in this case it is possible to simply read in each column of the file as the element of a list gt x lt scan rts txt what list vi numeric v2 numeric v3 numeric Read 12 records gt str x List of 3 vi num 1 12 0 12 0 096 0 113 0 132 0 124 0 105 0 109 v2 num 1 12 0 132 0 103 0 134 0 147 0 139 0 115 0 129 v3 num 1 12 0 102 0 087 0 109 0 123 0 124 0 102 0 097 5 1 3 Low Level File Input Sometimes the file to be read is not nicely organised into separate columns each representing a variable in this case the function readLines can either read the file one line at the time or all the lines at once to be then further processed to extract the data 5 2 Writing Data to a file 5 2 1 The write table function The function write table provides a simple interface for writing data to a file It can be used to write a dataframe or a matrix to a file For example if mydats is a dataframe the command gt write table mydats file my_data txt col names TRUE row names FALSE 36 will store it in the text file my_data txt with the labels for the variables or factors it contains in the first row col names T but without the numbers associated with each row row names F The sep option is used to choose the separator for the data the default is a blank space sep but you can choose a comma sep a semicolon sep or other meaningful separators 5 2 2 Low Level File O
61. es with the function names gt names dats 1 n_beers occupation sex P or if you want to see just the first one gt names dats 1 1 n_beers you can change it with a simple assignment gt names dats 1 lt beers or if you want to change more than one gt names dats lt c brs occ sx 21 Other Ways to Subset a Dataframe A dataframe actually is just a special kind of list a list of class dataframe so we can use the normal list notation to subset dataframes gt dats 1 11 684894534231 Sometimes it s useful to think of a dataframe as a matrix and use matrix notation for subsetting gt dats 1 extract first row all columns n_beers occupation sex 1 6 s m dats which dats n beers gt 4 records for subjs who drink gt 4 beers n_beers occupation sex v 1 6 s m 2 8 W m 4 8 W m 5 9 s m 7 5 s f 4 5 Factors Data Vectors can be made not only of numerical values or of strings but also factors Factor vectors are very similar to character vectors and could be seen as character vectors with some special properties A factor vector usually consists of two or more levels and can be created with the factor command For example suppose we are studying the drinking habits of 6 individuals if one of the factors we are interested in is their sex we can create a factor vector to encode it if the first 3 are males and the other 3 females gt sex lt factor c m
62. evelle http personality project org r e Practical Regression and Anova Using R by Julian J Faraway http www stat lsa umich edu faraway book pra pdf e Jonathan Baron s R page http finzi psych upenn edu e Yuelin Li s R page http idecide mskcc org stats e Deepayan Sarkar Page http www stat wisc edu deepayan e Vincent Zoonekynd s R page http zoonek2 free fr UNIX 48_R all html e Christian Hoffman s R Howto http www wsl ch staff christian hoffmann R Howto ehtml e P M E Altham s page on multivariate analysis with R notes http www statslab cam ac uk pat e Ecological models and data in R by Ben Bolker http www zoo ufl edu bolker emd book e Patrick Burns R page http www burns stat com In Italian e Laboratorio di statistica con R Universita Ca Foscari di Venezia Dipartimento di Statistica http www dst unive it laboratorior download materiale html e Luca Scrucca R s page http www stat unipg it luca e Roberto Boggiani R s page http digilander libero it robicox e Tecniche multivariate di Corrado Caudek Universita di Trieste Dipartimento di Psicologia http www psico univ trieste it caudek multivariata 134 Appendix D Other Useful Statistics Resources e Statistics short courses at the University of Lancaster http www cas lancs ac uk short_ courses outline_methodology html mfs e David Howell s statistics page http www uvm edu dhowell S
63. example 4 hours 6 hours 8 hours 12 13 15 9 12 17 9 11 15 8 7 13 7 14 16 12 10 17 8 10 12 7 10 16 10 12 14 7 9 15 The data are stored in a text file sleepdep txt in the above format but without any header First we read in the data with the scan function and assign them to a vector that we ll call recalled 99 recalled lt scan sleepdep txt then we need to create another vector which holds the level of the factor hours of sleep for each observation this vector can contain either numbers to be assigned as factors or single characters such as c or d but not strings such as cod1 cod2 and so on Since our data stored in the vector recalled are organised in an ordered sequence with observations belonging to treatment 4 h 6 h 8 h repeated 10 times we need to mimic this structure to create our new vector We ll use the rep function to do this we ll call our levels 1 2 and 3 for sake of simplicity gt treatment lt as factor rep 1 3 10 now we ll put the two vectors together into a data frame gt sleepdata lt data frame recalled treatment well the data are now in a proper format to perform our analysis of variance we can call this format one row per observation since in each row of our data frame we hold the value of the dependent variable in one column and the level of the factor that we are manipulating in the other column for a single
64. f these objects from memory you can use the command gt rm X Y W foo rats you can also give the variables to be removed as a character vector rm list c X uy y foo 3 rats if you want to remove all the objects in your workspace you can combine the 1s and rm commands as follows gt rm list 1s this however doesn t remove objects whose name starts with a dot to remove also those you can use gt rm list 1s all TRUE 3 3 Saving and Using the Workspace Image You can use a workspace image that you have previously saved by starting R from the directory in which it was saved In this way you can use the objects created in a previous session and the up arrow as well to retrieve commands from that session To take full advantage from workspace images you d better use different working directories for different analyses studies experiments and so on in this way you can restore the workspace image of a specific analysis you were running and above all you avoid accidentally overwriting objects from different analyses by creating another object with the same name during your current analysis When saving the workspace image R stores two files in the current work ing directory one with the objects and one with the command history This files begin with a dot under GNU Linux and so are hidden You can save the workspace image either on exit answering yes to the prompt you re given or during a sess
65. fault Look up the Reference Manual for further information on these methods The method none returns the p values without any adjustment The mt rawp2adjp function The package multtest contains a function very similar to p adjust and offers some other correction methods gt library multtest gt ps lt c 0 001 0 0092 0 037 p values from the t tests gt mt rawp2adjp ps proc Bonferroni adjp rawp Bonferroni 1 0 0010 0 0030 2 0 0092 0 0276 3 0 0370 0 1110 index 1 123 or if you want to see the adjusted p values with more than one method at once gt library multtest gt ps lt c 0 001 0 0092 0 037 p values from the t tests gt mt rawp2adjp ps proc Bonferroni adjp rawp Bonferroni SidakSS Holm SidakSD 1 0 0010 0 0030 0 002997001 0 0030 0 002997001 2 0 0092 0 0276 0 027346859 0 0184 0 018315360 3 0 0370 0 1110 0 106943653 0 0370 0 037000000 index 1 12 3 112 Chapter 14 R Programming 14 1 Control Structures If Else Conditional Execution It is possible to insert and execute control structures directly from the R interpreter but for the following examples I ll assume you re writing the commands to a batch file and then executing them through the source command The general form of conditional execution in R is if cond do_this else do_this_other here s a silly example money lt 1300 if money gt 1200 print good else
66. feel at home A good way to use ESS is to split the Emacs window horizontally C x 2 and have a R source file in one buffer and a R process running in the other buffer You 124 basically write the R code in the first buffer and then send it to the R pro cess for evaluation Here are the shortcuts for sending input to the R process C c C b Evaluate buffer This means that all the commands present in the source file will be executed C c C j Evaluate only the current line C c C r Evaluate selected region There is a set of commands that is equivalent to the above but moves the cursor to the R process window after the evaluation that is they Eval uate and go to the other window C c M b Evaluate buffer and go C c M j Evaluate line and go C c M r Evaluate region and go To comment uncomment a region you can use M x comment region Comment region M x uncomment region Uncomment region M Comment Uncomment region If you want to switch from a buffer to the other one you can use C x o Moreover when you are in a buffer you can make the other window scroll without moving the cursor with C M v Italian Keyboard Mapping Issues Many Italian keyboards don t have the braces gt and some other sym bols like the tilde however in Linux if you ve chosen an Italian keyboard layout they re mapped somewhere and you can access them through a com bination of keys likely combinations are Shift AltGr for
67. for producing the figures and tables to appear in your document You process this file with Sweave through R and you get a plain ISTFX source file which you can run with well IXTEX of course to get your nicely formatted output If your data happen to change for any reasons you don t have to start again from scratch you can just run your old Sweave source file on your new dataset and everything will be updated automatically If you already know MTFX and R learning to use Sweave will be easy the additional syntax required by Sweave to integrate R and MTFX source code is minimal As a caveat I have to say that Sweave is still in its infancy so for the moment probably you won t automatically get all the tables with 127 complicated layouts that you d like to add to your document In my opinion however Sweave already does a great job and it s well worth using 17 2 Usage Recent versions of R come with Sweave already in the base system in the package utils so you don t need to install it separately Of course you need TFX installed to produce the document later Sweave only outputs a TFX source file and all the graphics needed for your document You start the Sweave source file as a normal ETEX document with the usual preamble if you name the file with the Rnw extension Emacs should recognise it and highlight the syntax for you Then at the point where you want to embed a chunk of R syntax you add the following tag
68. h the name you want to give to your package as the argument for example mypkg gt package skeleton mypkg this will create a directory called mypkg with two sub directories R con taining your code and man containing the documentation files Further more a file called DESCRIPTION will be created If the objects you are packaging include datasets a data directory will also be created These are the essential elements needed to build a package The exact content of these files and directories and how to edit them will be explained later for the moment Ill give an overview of the steps required to start using your package The next step consists of building the package Start a shell not a R session move one directory above the mypkg directory we ve just created and give the command R CMD build mypkg to build the package this will create a tar gzipped file with everything necessary to install the package the next step to do is indeed the installation I would recommend installing your own packages in a separate directory from the default package installation directory let s say personalRLibrary to install the package in this directory still from the shell call R CMD INSTALL 1 personalRLibrary name0fTarFile tar gz now from a R session you can call your package with gt library mypkg lib personalRLibrary if you want to add permanently your personal R library to the library search path y
69. hart function is shown below and the resulting graph can be seen in Figure 8 7 gt myGraph lt barchart error length group session groups color data dats origin 0 ylab Error cm xlab Segment Length auto key TRUE as table TRUE gt print myGraph 8 4 dotplot 8 5 histogram gt histogram dats adj gt histogram dats adj dats congr 8 6 Interaction Plots Example of interaction plot with 3 factors gt print bwplot dats lat dats congr dats acc groups dats isi panel panel superpose panel groups panel linejoin auto key list points FALSE lines TRUE space top scales list cex 8 ylim c 280 400 ylab Medie delle latenze in ms xlab S0A 80 8 7 Customising Lattice Graphics 8 7 1 Textual Elements Strip Labels The labels of the panels strips are the names of the levels of the conditioning factor variable To change the labels just change the names for the factor levels gt levels dats acc 1 e h gt levels dats acc 1 1 e gt levels dats acc 1 lt imprecise gt levels dats acc 2 lt corrette gt levels dats acc 1 imprecise corrette 8 8 Writing Panel Functions 8 8 1 Combining Panel Functions Rather than writing a new panel function from scratch often you just want to add some elements to a plot for example a regression line or error bars The easiest and probably best way to do
70. harti txt 49 and they are arranged in the same way as the data in boxplot1 txt just the sample sizes are smaller with 6 observations per group gt stripchart dats score dats group method jitter jitter 0 1 pch 1 vertical TRUE The resulting graph is shown in figure 7 8 Figure 7 8 Stripchart 1 10 50 7 8 Interaction Plots Interaction plots can be used to visualise the means for the levels of a factor at the levels of another factor for example in a two way ANOVA design and in this way they allow to spot possible interactions between the two factors involved The following graph comes from a two way ANOVA design in which the variable of interest was the proportion of errors in a task as a function of the spatial congruency and SOA stimulus onset asincrony of a distracting stimulus presented during the execution of the task gt interaction plot dats soa dats congr dats errors ylab Proportion of errors xlab SOA trace label Congruency lty c solid dashed dotdash Figure 7 9 Interaction Plot with Different Line Types N 7 N o x N Congruency N N a inc goal directed aR b inc no goal directed x lt c congruent LO N Do SIA x o o x o N N T x e x O x 8 x N 2 3s e S o 2 E le N 5 5 o Be o x o N LO o 4 SOA well the essential ingredients to get the plot are just the first three arg
71. he error term we will use to test for the effects of colours The subjects error terms is in this case just the Sum of Squares Between The second error term the subject by colour interaction is the one we want to use to test for the effects of colour This term is what s left from the Sum of Squares Total once you have subtracted the effects do to the subjects and the effects due to the colour so in the specific design of this experiment it represents just random variability errors All this is quite tricky at first Don t worry remember as a rule of thumb that in a repeated measures design with R you have to add the Error term to the formula and this error term is defined as subjects your within subj factors More examples with Between and Within Subjects factors will be presented in the next sections As for the results of this analysis the F statistics for the colour effect is significant The RTs for detecting stimuli of these three different colours are different 12 2 2 Two Within Subjects Factors The basic principles for running a repeated measures ANOVA with more than one within subject factors are the same as in the case of a within subjects factor only with just some further complications due to the fact that now we also want to test for interactions between our factors We ll start straight with an example Let s say your data look something like the ones in table 12 4 imagining that you have 15 rats exposed to tw
72. he variances for the two groups are likely not to be equal 47 Figure 7 6 Boxplots comparing the distribution for two groups o o i o 4 i 1 i 1 1 l i o 1 N 7 o TO Ts t i j wo 1 i n T T group a group b 48 7 6 Histograms Histograms are a good way to visualise the distribution of a sample the function hist can be used to plots a histogram of frequencies counts of the sample or of its density function setting the option freq F Let s first create a sample with a normal distribution and then plot its histogram the result is in Figure 7 7 gt my_distr lt rnorm 100 5 1 7 gt hist my_distr Figure 7 7 Frequency Distribution of a Random Sample Histogram of my_distr 20 15 Frequency 10 0 2 4 6 8 my_distr 7 7 Stripcharts If the groups contain a small number of observations it might be better to use a stripchart to visualise their distributions In a stripchart each point represents a single observation By default they are drawn on a line so if two observations have the same score they overlap To avoid this problem you can give a certain amount of jitter to the plot so that observations with the same score are scattered a little and can be easily distinguished Here s the code for producing a stripchart the data are in the file stripc
73. he x and y coordinates of the point on which to center the text gt plot x y gt text x 3 y 1 5 mean for control group if you want to use AITFX mathematical symbols you have to use the expression function gt text x 3 y 1 5 expression alpha 7 10 3 Adding a Grid A grid can be easily added to an existing plot with the function grid O 59 gt s lt seq from 0 to 2 pi length 100 gt plot s sin s gt plot s sin s type 1 gt grid add the grid The default colour for the grid is lightgray you can choose another colour setting the col option gt grid col red 7 10 4 Setting the Axes If you don t like the way the axes are set for a given plot you can draw the plot without them first and then add customised axes with the axis function There are several ways to get rid of the default axes on a plot gt plot 1 10 axes FALSE do not draw any axes or box around gt the plot gt plot 1 10 xaxt n don t draw the x axis alone gt plot 1 10 yaxt n don t draw the y axis alone Once you ve got rid of one or more axis you can draw them calling axis gt axis 1 at seq 1 10 3 labels as character seq 1 10 3 the first argument specifies the side on which the axis should be drawn 1 means the bottom axis 2 the left axis 3 the top axis and 4 the right axis See axis for other arguments to the function 7 11 Creating Layouts for Multiple Graphs
74. http cran r project org src contrib Descriptions tkrplot html iplots http cran r project org src contrib Descriptions iplots html rpanel rpanel provides a set of functions to build simple GUI controls for R func tions These are built on the tcltk package Uses could include changing a parameter on a graph by animating it with a slider or a doublebutton up to more sophisticated control panels http cran r project org src contrib Descriptions rpanel html 130 A 2 GUI Packages Remdr http cran r project org src contrib Descriptions Remdr html JGR http cran r project org src contrib Descriptions JGR html pmg Simple GUI for R using gWidgets http cran r project org src contrib Descriptions pmg html http www math csi cuny edu pmg 131 Appendix B Miscellaneous commands Data head dats print the first part of the object dats tail dats print the last part of the object dats Help foo find help on command foo Objects class foo get the class of object Foo 1ls orobjects list objects present in the workspace Organise a session dir or list files list the files in the current directory getwd get the current directory library foo load library foo library list all available pack ages q or quit O quit from current ses sion require foo require the library foo use in scripts setwd home foo set the work ing directory system foo execute the system
75. ified Version Only one passage of Front Cover Text and one of Back Cover Text may be added by or through arrangements made by any one entity If the Document already includes a cover text for the same cover previously added by you or by arrangement made by the same entity you are acting on behalf of you may not add another but you may replace the old one on explicit permission from the previous publisher that added the old one The author s and publisher s of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version 5 COMBINING DOCUMENTS You may combine the Document with other documents released under this License under the terms defined in section 4 above for modified versions provided that you include in the combination all of the Invariant Sections of all of the original documents unmodified and list them all as Invariant Sections of your combined work in its license notice and that you preserve all their Warranty Disclaimers The combined work need only contain one copy of this License and multiple identical Invariant Sections may be replaced with a single copy If there are multiple Invariant Sections with the same name but different contents make the title of each such section unique by adding at the end of it in parentheses the name of the original author or publisher of that section if known or else a unique number Make the same ad
76. igure region is composed of the plotting regions plus the margins where the plot can be annotated with labels for the axes a title etc e the outer margins surround the figure regions The outer margins are usually set to zero i e there are no outer margins they become useful however for annotating multiple plots that appear on the same page e g plots generated with mfrow When multiple plots are arranged on the same page or device each is assigned a figure region with its own margins so the outer margins can be used for annotating the overall page see Fig 7 17 The width and height of the device is usually specified when the device is opened for example gt X11 width 8 height 8 63 opens a X11 device measuring 8x8 inches The size of an open device can be queried with par din this is a read only graphics parameter which I guess means that once a certain device is opened its size cannot be changed an X11 window however can be re sized with the mouse and par din correctly reports the new size Different units of measure can be used to specify the size of the areas inside a device some of these units will be shortly introduced here others will be explained when they are first used e inches an inch is 2 54 centimetres notice that the actual physical measure of what you see on your monitor may depend on your moni tor s settings e g dpi screen resolution etc e lines of text this measure depends
77. in a single line of the screen and at the start of each line you ll get between the index that is the position of the first element on that line There s also a shorthand to create such a vector gt long vec lt 1 100 2 3 Getting Help R comes with an excellent online help facility which documents and gives examples for all available functions There is also a web interface for the help system which is easier to use you can start it with gt help start this fires up a web browser from which you can access a search engine for all the available documentation The documentation is also available as a pdf file the Full Reference Manual which documents the base system Printable pdf manuals are also available for all the other additional packages The Online Help System You can quickly look up the documentation for a function for example sd with gt sd or gt help sd it is often indifferent using quotes or not but sometimes they are required for example gt doesn t work gt Error syntax error gt 7 HH this works to quit the help screen press You can easily run the example code given in the help pages for a given function with gt example function_name it is better to set the graphics parameter ask as TRUE before running the examples gt par ask TRUE to pause between successive plots if there is more than one The online help system searches by default the available d
78. info e Some notes on lattice 17 http www ci tuwien ac at Conferences DSC 2003 Proceedings Sarkar pdf e R Lattice Graphics 14 http www ci tuwien ac at Conferences DSC 2001 Proceedings Murrell pdf e Lattice an implementation of Trellis graphics in R 16 http cran r project org doc Rnews Rnews 2002 2 pdf 73 e The Visual Design and Control of Trellis Display 3 http cm bell labs com stat doc trellis jcgs col ps e Trellis Display Modelling Data from Designed Experiments 5 http cm bell labs com stat doc doe trellis col ps 8 1 Overview of Lattice Graphics Table 8 1 Lattice Graphics Functions Function xyplot barchart dotplot stripplot bwplot 8 2 Introduction to model formulae and multi panel conditioning We will use the rats_trellis txt dataset to illustrate how conditioning based on one or more factors work in lattice The dataset contains data from a fictitious experiment in which a researcher is investigating the ef fects of alcohol and drug consumption on social interactions in rats The researcher has studies two species of rats Kalamani vs Yuppy each rat has been observed in four experimental conditions given by the combination of two factors administration of drug Drug vs No Drug and administration of alcohol Al vs No Al The dependent variable is the number of social interactions observed in each of the four conditions We ll read in the data first gt dats lt read table
79. ing to your First function This goes in Rprofile in First lt function source sourceDir R sourceDir myRfunctions Building a R package requires a bit more work The detailed docu mentation for doing this is provided in the Writing R Extensions manual available at the CRAN website http cran r project org That documentation looks at best daunting for a beginner indeed writing a R package is not trivial however if all you have is pure R code and you just want to build a simple package for your own use the task should not be too difficult to achieve A very useful document is An introduction to the R package mechanism it can be found at the following URL http biosunl harvard edu courses individual bio271 lectures L6 Rpkg pdf In the following sections I ll try to explain how to build a simple R package much of what I say is drawn from the above cited documents 14 4 1 The Bare Minimum to Create a Package The quickest way to get started is to use the function package skeleton to create the first draft of your package Start a R session make sure that there are not R objects in your session otherwise they will be bundled in your package gt rm list 1s all TRUE now source all the function files you want to include in your package for example gt source home sam myFunctions R gt source home sam soundFunctions R 118 and the call the package skeleton function wit
80. ion Entitled XYZ according to this definition The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document These Warranty Disclaimers are considered to be included by reference in this License but only as regards disclaiming warranties any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License 2 VERBATIM COPYING You may copy and distribute the Document in any medium either com mercially or noncommercially provided that this License the copyright no tices and the license notice saying this License applies to the Document are reproduced in all copies and that you add no other conditions whatsoever to those of this License You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute However you may accept compensation in exchange for copies If you dis tribute a large enough number of copies you must also follow the conditions in section 3 You may also lend copies under the same conditions stated above and you may publicly display copies 3 COPYING IN QUANTITY If you publish printed copies or copies in media that commonly have printed covers of the Document numbering more than 100 and the Doc ument s license notice requires Cover Texts you must enclose the copies in 145 covers that carry clearly and legibly all these Cover Text
81. ion with the command save image the latter is a good measure against accidental losses of objects due to a power failure 10 3 4 Working in Batch Mode Executing commands written in a file from an R session Instead of writing and executing commands line by line it is often convenient to write the commands in a text file and then run them all at once in batch mode You just write the commands with a text editor in a file as if it were on the R console save it in a directory and then from within an R session issue the command gt source C mydata myfile txt By default R displays only the results of the commands written in the source file you can change this using the option gt source C mydata myfile txt echo TRUE Executing commands written in a file from a shell It is also possible to execute R commands written in a file without starting an R session From within your system s shell for example bash on GNU Linux or dos on Windows issue the command R CMD BATCH myfile r where myfile r is the file you ve written the R commands in 11 Chapter 4 Data Types and Data Manipulation 4 1 Vectors One of the simplest and among the most important data types in R is the vector which can be numerical or containing strings of characters A simple way to build a vector is through the function c which concatenates a series of data for example gt temperature lt c 34 45 23 29 26 31 44 32
82. ions are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the notice that says that the Document is released under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are none The Cover Texts are certain short passages of text that are listed as Front Cover Texts or Back Cover Texts in the notice that says that the Document is released under this License A Front Cover Text may be at most 5 words and a Back Cover Text may be at most 25 words A Transparent copy of the Document means a machine readable copy represented in a format whose specification is available to the general public that is suitable for revising the document straightforwardly with generic text editors or for images composed of pixels generic paint pro grams or for drawings some widely available drawing editor and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters A copy made in an other wise Transparent file format whose markup or absence of markup has been arranged to thwart or discourage subsequent modification by readers is not Transparent An image format is not Transparent if used for any substantial amount of text A copy that is not Tra
83. irectory and write a function that systematically sources them all e build a R package The first solution is rather simple give the R extension to your R function files and put them in a directory Although there is not a built in function to source all the R files present in a directory the documentation for the source function gives an example on how to do it see source If you want to source a bunch of files something like the following may be useful sourceDir lt function path trace TRUE for nm in list files path pattern RrSsQq if trace cat nm source file path path nm if trace cat n the function sources all the files with the R extension found in the directory indicated by the path argument You can copy this function to a file let s say 117 sourceDir R put it in your HOME directory and source it in your First function in Rprofile see Chapter 15 for details the First function and the Rprofile file This goes in Rprofile in First lt function source sourceDir R F now each time you call sourceDir with a directory as an argument you will have all the functions defined there available If you want them available at the beginning of each session just add a call to sourceDir for the directories you want to add in your First function as well So for example if your R function files are in the directory myRfunctions add the follow
84. justment to the section titles in the list of Invariant Sections in the license notice of the combined work 148 In the combination you must combine any sections Entitled History in the various original documents forming one section Entitled History likewise combine any sections Entitled Acknowledgements and any sec tions Entitled Dedications You must delete all sections Entitled En dorsements 6 COLLECTIONS OF DOCUMENTS You may make a collection consisting of the Document and other docu ments released under this License and replace the individual copies of this License in the various documents with a single copy that is included in the collection provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects You may extract a single document from such a collection and distribute it individually under this License provided you insert a copy of this License into the extracted document and follow this License in all other respects regarding verbatim copying of that document 7 AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent documents or works in or on a volume of a storage or distribution medium is called an aggregate if the copyright resulting from the compilation is not used to limit the legal rights of the compilation s users beyond what the individual works permit When the Docum
85. ked up first by R is the one defined by the R_PROFILE environment variable if this variable is set To verify the value of this variable you can use gt Sys getenv R_PROFILE gt system echo R PROFILE if the variable is unset R looks for a file called Rprofile site that is in the etc sub directory of your R installation directory To find out your R installation directory on a Unix like system you can use 122 gt system echo R_HOME The Rprofile site or the file pointed to by the R PROFILE environment variable can be used for system wide configuration Note that if the R PROFILE environment variable is set the file pointed to by this variable is used and if this is not Rprofile site the latter is ignored The Rprofile file in the user s HOME can be used for user specific ini tialisation and the functions written in this file overwrite or better mask functions with the same name defined in either the file pointed to by the R_PROFILE variable or in Rprofile site Moreover a Rprofile file can be put in any directory then if R is started from that directory this file is sourced and it masks the definitions given in the user s HOME Rprofile file in this way it is possible to customise the initialisation for a particular data analysis Finally a directory specific initialisation can be given in a RData file the definitions given here mask also the definitions given in any Rprofile files 123 Chapter 16
86. le MathSoft Inc Murray Hill Bell Labs 2002 R A Becker W S Cleveland and M J Shyu The visual design and control of Trellis display Journal of Computational and Graphical Statistics 5 123 155 1996 R A Becker W S Cleveland M J Shyu and S P Kaluzny A Tour of Trellis Graphics 1996 Available http cm bell labs com stat doc trellis tour col ps W S Cleveland and M Fuentes Trellis display Modeling data from designed experiments Technical report Bell Labs 1997 P Dalgaard Introductory Statistics with R Springer 2002 J J Faraway Practical Regression and Anova using R 2002 R M Heiberger and B Holland Statistical Analysis and Data Dis play An Intermediate Course with Examples in S Plus R and SAS Springer 2004 K J Hoff R Manual for Biometry 2005 Unpublished Bachelor Thesis at the Teaching Unit Bioinformatics University of Hannover D C Howell Statistical Methods for Psychology Duxbury Pacific Grove CA USA fifth edition 2002 A Krause and M Olson The Basics of S Plus Springer third edition 2002 F Leisch Sweave User Manual 2005 A M Mineo Una Guida all utilizzo dell Ambiente Statistico R 2003 152 14 15 16 17 18 19 20 21 22 23 24 25 P Murrell R Lattice graphics In K Hornik and F Leisch editors Pro ceedings of the 2nd International Workshop on Distributed Statistical Computing March 15 17
87. lightgoldenrodi E lightgoldenrod2 lightyellow2 lightgoldenrod3 lightyellow3 lightgoldenrod4 lightyellow4 bienteoidenzodyein MA limegreen lightgray linen lightgreen magenta lightgrey E magental lightpink magenta2 lightpink1 E magenta3 lightpinko magenta4 lightpink3 maroon lightpink4 maroon lightsalmon o E lightsalmon1 SAN lightsalmon2 mediumaquamarine E lightsalmon3 E mediumblue E lightsalmon4 mediumorchid lightseagreen mediumorchidi lightskyblue mediumorchid2 lightskybluet DD 1 ghtskyblue2 mc Tgr gl PLUS DI mediumpurplei lightskyblue4 mediumpurple2 lightslateblue E isdiuntivieples J lightslategray E lightslategrey lightsteelblue lightsteelbluei lightsteelblue2 lightsteelblue3 lightsteelblue4 lightyellow lightyellowi 140 LJ mediumpurple4 mediumseagreen E mediumslateblue mediumspringgreen DI mediumturquoise DI mediumvioletred midnightblue mintcream mistyrose mistyrosel mistyrose2 mistyrose3 E mistyrose4 moccasin navajowhite navajowhitel navy E navyblue oldlace olivedrab olivedrabi olivedrab2 olivedrab3 olivedrab4 orange orangel E orange2 E orange3 orange4 I orangered J orangeredi orangered2 J orangered3 E orangered4 E orchid orchidi orchid2 orchid3 orchid4 palegoldenrod palegreen BM navajowhite2 navajowhite3 ii navajowhite4 Ea palegreeni palegreen2 palegreen3 palegreen4 paleturquoise paleturquoisel paleturquoise2
88. lowing code summarises the situation graphically as shown in Fig ure 9 2 gt s lt 2 3 sgrt 40 1 gt up lt seq from 6 5 qnorm 975 s to 9 5 length 30 gt low lt seq from 3 5 to 6 5 qnorm 975 s length 30 gt dup lt dnorm up 6 5 s gt dlow lt dnorm low 6 5 s gt curve dnorm x 6 5 s from 3 5 to 9 5 gt polygon x c 6 5 qnorm 975 s up 9 5 y c 0 dup 0 col orange gt polygon x c 3 5 low 6 5 qnorm 975 s y c 0 dlow 0 col orange gt text x c 7 38 5 62 y c 0 02 0 02 expression alpha 2 88 VM VV text x c 6 5 y c 0 3 expression 1 alpha lines x c 8 7 4 y c 0 28 0 text x c 7 4 y c 0 025 expression 7 4 text x c 8 4 y c 0 3 comp science group score Figure 9 2 Short Term Memory Span Experiment z test 1 0 0 8 dnorm x 6 5 s 1 a amp omp science group score 89 Chapter 10 Hypothesis Testing 10 1 x test Testing Hypotheses about the Distribution of a Categorical Vari able You can use the x test to verify hypotheses about the distribution of a categorical variable for example you might want to know whether as far as handedness is concerned your experimental sample is representative of the general population and follows a distribution of 80 right handed 15 left handed and 5 using both hands indifferently The frequencies for your sample are given in Table 1
89. m m f gt sex 1 mmmf ff Levels f m as you can see a factor has a levels attribute that specifies the possible values the factor can assume and by default it is given by the unique values the factor vector can assume sorted in alphabetical order In some cases you might want to assign a label to each factor level This is useful when you want to keep the level name short and simple for ease of manipulation but at the same time you would like to have it print nice labels in plots When assigning a label it is best to also explicitly assign the factor levels in the same order otherwise you might accidentally assign the wrong label to a given level 22 gt Sex lt factor e m m Um pi pe MEMO levels c m f labels c male female gt sex 1 male male male female female female Levels male female In some cases it is also useful to set the factor as ordered this might allow for example to have the levels of a factor plotted in a given order different from the alphabetical order gt sex lt factor c m mM m gni MEM MEMO levels c m f labels c male female ordered TRUE Creating Factors with gl A handy function for creating factors for data with a regular pattern of factor levels is gl gt sex lt gl 2 3 label c male female length 6 gt sex 1 male male male female female female the first argument to the function specifies th
90. m a local repository this is necessary for example if you don t have an internet connection from the computer you want to install the package on In this case you can download the package you want from another computer as a zip file and then transfer it to your computer At this point to install the package don t unzip it just start the R GUI and click on etc Chapter 2 A Simple Introduction to R This chapter will give a simple introduction to R just to get familiar with it and get a general idea of how it works This chapter assumes no previous knowledge of programming or anything similar If you know other computer languages or have even a basic knowledge of programming getting started will be easy If you don t don t worry R syntax is very elegant and simple it might take a little while but after looking at some examples and impor tantly trying them out yourself you ll be up and running without problems This tutorial deals only with learning to use R from the command line if you d rather use R with a GUI that is with a point and click interface please have a look at section 2 4 for some information on how to get started 2 1 Firing up and Quitting R Under GNU Linux systems you can start R from a shell just type R and press Under Windows you can click on the R icon to start the R GUL You can save yourself a lot of typing by using the up arrow key to retrieve past commands Commands can be terminated ei
91. m grey6 gray49 gray82 E grey7 gray50 gray83 ii greys gray51 gray84 w grey9 gray52 gray85 w grey10 gray53 gray86 S grey11 gray54 gray87 O grey12 gray55 gray88 H grey13 gray56 gray89 mi grey14 138 C grey15 m grey48 grey81 grey16 grey49 grey82 grey17 E grey50 grey83 grey18 E grey51 grey84 grey19 J grey52 grey85 grey20 E grey53 grey86 grey21 T grey54 grey87 grey22 J grey55 grey88 grey23 E grey56 grey89 grey24 E grey57 grey90 grey25 E grey58 grey91 grey26 E grey59 grey92 grey27 grey60 grey93 grey28 J grey61 grey94 grey29 m grey62 grey95 grey30 E grey63 grey96 grey31 grey64 grey97 grey32 grey65 grey98 grey33 grey66 grey99 grey34 grey67 grey100 grey35 grey68 honeydew grey36 grey69 honeydewi grey37 grey70 honeydew2 grey38 grey71 honeydew3 grey39 grey72 m honeydew4 grey40 grey73 E hotpink grey41 grey74 E hotpink1 grey42 grey75 J hotpink2 grey43 grey76 E hotpink3 grey44 grey77 E hotpink4 grey45 grey78 E indianred grey46 grey79 indianredi grey47 grey80 indianred2 indianred3 139 E indianred4 ivory ivory1 ivory2 ivory3 E ivory4 E khaki khaki1 khaki2 khaki3 khaki4 lavender lavenderblush lavenderblushi lavenderblush2 lavenderblush3 lavenderblush4 lawngreen lemonchiffon lemonchiffoni lemonchiffon2 lemonchiffon3 lemonchiffon4 lightblue lightbluel lightblue2 lightblue3 E lightblue4 lightcoral lightcyan lightcyani lightcyan2 lightcyan3 lightcyan4 lightgoldenrod
92. m named weight in list third column in file 1 300 246 317 229 230 245 scan can do much more than what was shown in this example like specifying the separator between the fields of the data file comma tabs or whatever else defaults to blank space or specifying the maximum number of lines to be read see scan for more details I ll present just another simple example in which we ll read in a file whose data are all numeric The file is rts txt gt x lt scan rts txt what numeric Read 36 items gt str x num 1 36 0 12 0 132 0 102 0 096 0 103 0 087 0 113 in this case the object returned is a long vector of the same mode as the what argument a numeric vector The file is however organised into three columns which represent three different numeric variables It is easy to reorganise our vector to reflect the structure of our data gt nRows lt length x 3 gt xm lt matrix x nrow nRows byrow TRUE gt xm 1 2 3 35 1 0 120 0 132 0 102 2 0 096 0 103 0 087 3 0 113 0 134 0 109 4 0 132 0 147 0 123 5 0 124 0 139 0 124 6 0 105 0 115 0 102 7 0 109 0 129 0 097 8 0 143 0 150 0 119 9 0 127 0 145 0 113 10 0 098 0 117 0 092 11 0 115 0 126 0 098 12 0 117 0 132 0 103 so we ve got a matrix with the 3 columns of data originally found in the file turning it into a dataframe would be equally easy at this point xd lt as data frame xm Howev
93. ments To use this License in a document you have written include a copy of the License in the document and put the following copyright and license notices just after the title page Copyright Q YEAR YOUR NAME Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 2 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License 150 If you have Invariant Sections Front Cover Texts and Back Cover Texts replace the with Texts line with this with the Invariant Sections being LIST THEIR TITLES with the Front Cover Texts being LIST and with the Back Cover Texts being LIST If you have Invariant Sections without Cover Texts or some other com bination of the three merge those two alternatives to suit the situation If your document contains nontrivial examples of program code we rec ommend releasing these examples in parallel under your choice of free soft ware license such as the GNU General Public License to permit their use in free software 151 References 10 11 12 13 J Baron and Y Li Notes on the use of R for psychology experiments and questionnaires 2003 R A Becker and W S Cleveland S PLUS Trellis Graphics User s Manual Seatt
94. n Batch Mode 11 4 Data Types and Data Manipulation 12 Ail Vectors rastrear Boece Bol ane eR ee ee Seas 12 4 1 1 Indexing Vectors 00 4 13 4 1 2 The segO Function LL 14 4 1 3 TherepQ function LL 15 A D Matrix Facilities ego go aden eae Ge Se e pe ea 15 4 2 1 Matrix Operations 17 DS LIS ag ee Kos teias ari hd on Lhe TAS DEAR Gy ts pet id a PO Sa 18 dA Datalrames se sim cu dose Sadi o Bee ee whee Gene Ae ed 19 AiBn Factis spia ee BAe pe Bee Se E oe 22 4 6 Getting Info on R Objects 2 23 4 7 Changing the Format of Your Data 24 4 7 1 The One Row per Observation Format 25 4 7 2 The stack and unstack functions 29 4 7 3 tapply and aggregate 30 4 8 Creating and Editing Data Objects through a Visual Interface 31 4 9 Visualising Your Data 0 32 4 10 Reading Numbers in Exponential Notation File Input Output 5 1 Reading In Data from a File Bl sead table ssa po paella e Gaels Biles scan pps ar sl nie de AA a 5 1 3 Low Level File Input 2 22 5 2 Writing Data to a file 0 5 2 1 The write table function 5 2 2 Low Level File Output 2 20 Descriptive 6 Tables coloni he e a a 6 2 The scale Function 200 4 Graphics 7 1 Overview of R Graphics 2 2204 7 2 The plot Function ig dii 7 3 Drawing Fu
95. n a single sub region to a figure for example gt m lt matrix c 1 1 2 3 nrow 2 byrow TRUE gt m 1 2 1 1 1 2 2 3 gt layout m 62 divides the graphics window into 4 sub regions as above but the first figure is assigned the two sub regions on top while the bottom left sub region is assigned to the second figure and the bottom right to the third The second key difference with mfrow is that with layout it is possible to define the width of the columns and the height of the rows composing the array of sub regions in the graphics window Width and height are given as vectors of relative widths and heights For example gt m lt matrix c 1 1 2 3 nrow 2 byrow TRUE gt m 1 2 1 1 1 2 2 3 gt layout m width c 1 4 3 4 height c 2 3 1 3 will make the first column 1 4 of the total width and the second column the other 3 4 the same reasoning applies to the row heights The command layout show n where n is the number of n figure that is going to be plotted will show the outline of its layout in the graphics window 7 12 Graphics Device Regions and Coordinates In traditional R graphics the graphics device e g the X11 window where your plot and annotations appear is divided into different regions see Fig 7 16 e the plotting region is the area in which the drawing of points or lines representing your data occur The plotting region is contained into the figure region e the f
96. nctions LL TSL m tplot 24 eek aasar da a aa ADE ee a a TA Barplotess ate od ga DE Lai i Do ie a ale de E Tio BoxplotS a rage det LEIA SRS a Gy oe eh ie Ge ee Li T 0 s HISLOBLAMS sayeye rio poison Pe EAS Ske Se TT DLTIPCNALES e ae mod wk Belew aide Lele ke aon hw aes 1 8 Interaction Plots e iL ida po eee ed bal e PA dae 7 9 Setting Graphics Parameters 00004 TIL Line type ty sais ebr PALA Be RR ER ca 7 9 2 Symbols with pch LL 7 10 Adding Elements to a Plot 7 10 1 Adding a Legend LL T 10 2 Adding Text msgs fee pn the E t 10 3 Adding a Grid iii pa ale a RO eS E 7 10 4 Setting the Axes 2 2 ee eee 7 11 Creating Layouts for Multiple Graphs 7 11 1 mfrow and mfcol 2 TD layout salone i tant elia dee de ga a 7 12 Graphics Device Regions and Coordinates 7 13 Plotting from Scratch 2 0 0 0 020000004 7 14 Colours for Graphics 2 0 0 0 02 22 2008 7 15 Managing Graphic Devices 004 7 15 1 Opening Another Graphics Window 7 15 2 Exporting Graphics ii 34 34 34 34 36 36 36 37 38 38 38 8 Lattice or Trellis Graphics 73 8 1 Overview of Lattice Graphics 74 8 2 Introduction to model formulae and multi panel conditioning 74 8 3 Darchart d sco yea wife e fae ee Bde wey odin eS 78 8 4 dotplots wisi te ay aoe hw Gel ot Bele ole Gee A ae ed 80 8 52 histopram i gt Ac
97. ne at Bese a ood he Be aes 80 8 6 Interaction Plots 02 0002000008 80 8 7 Customising Lattice Graphics 81 8 7 1 Textual Elements L2L0 81 8 8 Writing Panel Functions 81 8 8 1 Combining Panel Functions 81 9 Probability Distribution Functions 85 9 1 The Bernoulli distribution 85 9 2 The binomial distribution 2 86 9 3 The normal distribution 86 10 Hypothesis Testing 90 TO NO Esta as pod tie E a DN dp RD DE Do ae AG a ahs 90 10 2 Student st test 93 10 2 1 One sample t test 2 0 20 2 0 000000 8 93 10 2 2 Two samples t test LL 93 10 3 The Levene Test for Homogeneity of Variances 94 11 Correlation and Regression 97 11 1 Linear Regression LL 98 12 ANOVA 99 12 1 One Way ANOVA LL 99 12 1 1 One Way ANOVA with Unequal Sample Sizes 101 12 2 Repeated Measures ANOVA 2 02 0004 102 12 2 1 One Within Subjects Factor 102 12 2 2 Two Within Subjects Factors 105 12 2 3 Two Within Subjects Factors and One Between 108 13 How to Adjust the p values for Multiple Comparisons 111 14 R Programming 113 14 1 Control Structures 0200 02000002 2 eee 113 14 2 String Processing 000002 ee eee 115 14 2 1 Using Regular Expressions 116 143 Tipssand Tricks sila elia ia 117 14 3 1 Convert a String into a Command
98. nge the range with the max option to set the range as 0 255 Please note that changing the range doesn t change the colours you can use it just changes the values you use to specify them so for example the following graphs will have the same colours vec lt c 3 6 barplot vec col c rgb 0 176 0 262 0 49 rgb 0 568 0 254 0 654 barplot vec col c rgb 45 67 125 max 255 rgb 145 65 167 max 255 V V V the first uses the default range and the second uses the range 0 255 but I simply derived the values for the first graph dividing those for the second by 255 The function col2rgb can be used to get the rgb values of a built in colour from its name The rgb values are given in this case in the range 0 255 Here s an example gt col2rgb lightslateblue 1 red 132 green 112 blue 255 69 Table 7 7 Some built in colours in R aliceblue antiquewhite2 E aquamarine beige bisque LJ brown3 m burlywood2 chocolate4 cornflowerblue cornsilk coral2 E darkkhaki E darkolivegreen E darkred E dodgerblue E firebrick2 forestgreen E gold honeydew2 indianred ivory E khaki2 lightgreen E lightgoldenrod lavender lemonchiffon lightblue lightcyan linen DI lightslateblue i magenta olivedrab orange papayawhip peachpuff peru ESEN powderblue J rosybrown salmon2 E sandybrown seashell sienna
99. ning variable gt barchart error length group color data dats origin 0 ylab Error cm xlab Segment Length auto key TRUE as table TRUE 78 Figure 8 4 Social Interactions by Species Alcohol Administration and Drug with Multi panel Conditioning No Drug No Drug AI No Al 4 7 4 6 4 5 l a o I E E T Drug Drug 9 AI No Al D 74 6 4 5 L 4 Kalamani Yuppy Kalamani Yuppy Figure 8 5 Social Interactions by Species Alcohol Administration and Drug with Grouping Factor Robrug E AI No Al socialint Kalamani Yuppy Kalamani Yuppy 79 in this case the bars for each level of the factor would have been drawn in different panels the number of panels would have doubled The fill colour for the bars can be modified changing the colour option for superpose polygon The great thing about trellis graphics is that they allow you to display the relationship between a dependent variable and multiple factors seamlessly Suppose that continuing the above example the psychophysician has tested the line matching accuracy on the three groups both before and after a period of visuo motor training The dataset containing the data with this new factor is in the file line matching training txt We just need to add the new factor session pre training vs post training to the conditioning variables to obtain the new plot The modified call to the barc
100. nsparent is called Opaque Examples of suitable formats for Transparent copies include plain ASCII without markup Texinfo input format LaTeX input format SGML or XML using a publicly available DTD and standard conforming simple HTML 144 PostScript or PDF designed for human modification Examples of trans parent image formats include PNG XCF and JPG Opaque formats include proprietary formats that can be read and edited only by proprietary word processors SGML or XML for which the DTD and or processing tools are not generally available and the machine generated HTML PostScript or PDF produced by some word processors for output purposes only The Title Page means for a printed book the title page itself plus such following pages as are needed to hold legibly the material this License requires to appear in the title page For works in formats which do not have any title page as such Title Page means the text near the most prominent appearance of the work s title preceding the beginning of the body of the text A section Entitled XYZ means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language Here XYZ stands for a specific section name mentioned below such as Acknowledgements Dedications Endorsements or History To Preserve the Title of such a section when you modify the Document means that it remains a sect
101. o decide at which height to draw the horizontal line The resulting plot can be visualised in Figure 8 9 82 Error cm 0 6 0 4 0 2 0 0 Error cm Figure 8 7 Line Matching Training Barchart 0 6 7 0 4 4 0 2 4 0 0 0 2 4 Figure 8 6 Line Matching Barchart blue red GRI na na m 0 6 F 0 4 M 0 2 m 0 0 M 0 2 L1 L2 L3 L4 Segment Length blue red post training post training post training Segment Length 83 G1 G2 G3 Bu Em _ mnp a pre training pre training pre training G2 m 0 6 m 0 4 IL 0 2 E E mam 00 n ne Li L2 L3 14 Li L2 L3 14 Li L2 L3 L4 Error cm Figure 8 9 Dotplot of the Line Matching Dataset with Horizontal Reference Error cm Figure 8 8 Dotplot of the Line Matching Dataset 0 6 5 0 4 7 0 2 4 0 0 4 blue e red o GRI GR2 e e e e e e e e e e GR3 0 6 e H 0 4 e H 0 2 H 0 0 e Pi L 0 2 e Li L2 L3 L4 Segment Length Line blue e red o GRI GR2 0 6 4 0 44 0 24 e 0 0 4 e e e e 0 2 4 e e e GR3 0 6 e H 0 4 e H 0 2 o 0 0 e 4 si L 0 2 e Li L2 L3 L4 Segment Length 84 Chapter 9 Probability Distribution Functions 9 1 The Bernoulli distribution A random variable X that takes a value of 0 or 1 depending on the result of an experiment that can
102. o describe the second column is to say that in the above case Group is a factor and A B and C define the levels of this factor for each group You could also be running an experiment in which you manipulate more than one factor For example you might have two groups Patients and Controls which are tested under two conditions 1 and condition 2 In this case you might display your data as shown in Table 4 6 to make them easily readable to humans However for analysing your data with R in this case you would need to add another column specifying the levels of the other factor for each observation as shown in Table 4 7 Table 4 6 Data Format Suitable for the Human Eye with More than One Factor Patients Controls Condition 1 Condition 2 Condition 1 Condition 2 7 6 6 4 5 4 5 2 8 7 7 4 8 8 6 5 6 5 5 3 Finally you might be running an experiment with a repeated measures design in which all subjects are exposed to all the levels of all the within subjects factors For example you might have your subjects recall word lists either under the effects of a drug or not factor 1 and with words concrete or abstract words factor 2 In this case the data for presentation might look like the ones in Table 4 8 in which each row represents a single subject Again for R you need to rearrange the data so that each row represents a single observation and in the case of a repeated measures design you
103. o factors Alcohol 1A subject is faster with blue stimuli and gets depressed with black ones while another subject does just the opposite We re not interested in these differences in this exper iment though we might want to test similar effects in other case So for this time this interaction is just errors 105 Table 12 4 Data for the repeated measures ANOVA example Drug No Drug Alcohol No Alcohol Alcohol No Alcohol 7 6 6 4 5 4 5 2 8 7 7 4 8 8 6 5 6 5 5 3 8 7 7 6 5 5 5 4 7 6 6 5 8 7 6 5 7 6 5 4 9 8 5 4 4 4 3 2 7 7 5 3 7 5 5 0 8 T 6 3 and Drug with two levels each administered and not administered and the dependent variable is the number of social interaction in a cage with other rats Here each row represents a subject you need to reorganise the data so that each row contains a single observation and the different columns represent 1 an identifier for the subject 2 the values of the dependent variable the data that you see in the table 3 the level of the first factor for each observation 4 the level of the second factor for each observation The measures you have collected are stored in a text file rats txt in the format of the table above but with no header whatsoever and no number indicating each subject The first thing we can do is to read in these data in R as a number vector gt socialint lt scan rats txt then we need a column specifying to which subject each
104. observation As for the analysis we go like this gt oneway test sleep treat data data var equal TRUE the summary command tells R to print out a nicely formatted summary with the results of our analysis The actual command that performs the analysis is aov and what follows this command is the specification of our model for the analysis In this case we want to see if the number of words recalled depends on the treatment the recalled treatment statement does just this because the tilde means explain recalled on the basis of treatment Finally the data statement specifies the object in which are stored the data for this analysis Below there is the summary produced by R for this analysis Df Sum Sq Mean Sq F value Pr gt F treatment 2 194 867 97 433 27 838 2 746e 07 xxx Residuals 27 94 500 3 500 Signif codes O 0 001 0 01 0 05 2 7 0 17 1 We have the sums of squares for the treatment effect and for the error term and the F value for the treatment effect with its significance value Since the p value in this case is very very small it is written in scientific notation However we can use the significance codes given at the bottom of the print out to interpret the p value as very close to zero at least smaller than 0 001 so it is highly significant 100 12 1 1 One Way ANOVA with Unequal Sample Sizes The commands to perform an univariate ANOVA with unequal sample sizes in R are the sam
105. observation of the socialint vector belongs to In addition we want this new vector to be considered as a factor vector rather than as numerical vector We can use the rep function to do this 106 gt subj lt as factor rep 1 15 each 4 next we need to specify in a new vector the levels of the first factor for each observation If we use a character vector to store the levels of the factor it is not necessary to use the as factor command as later when we will put the all the vectors in a data frame R will automatically interpret character vectors as factors gt alcohol lt rep c Al No Al 30 we do basically the same for the second factor gt drug lt rep c Drug No Drug 15 each 2 It s almost done we need now to put all this vectors in a data frame gt rats lt data frame subj socialint alcohol drug Done Now the analysis gt summary aov socialint alcohol drug Error subj alcohol drug data rats the above formula specifies our model for the analysis we are telling R we want to explain the variable socialint by the effects of the factors alcohol drug and their interaction in the case of a repeated measures ANOVA however we also have to specify the error terms that R will use to calculate the F statistics The statement Error subj alcohol drug is a shorthand for Error subj subj alcohol subj drug subj alcohol drug Again as in the example with only one
106. ocumentation for the base system and all the packages that are currently loaded If you want to look the documentation for a function present in a package that is not loaded you need to specify the package in question gt help levene test package car if you know the function exists but don t know the package it is in try gt help levene test try all packages TRUE Help for topic levene test is not in any loaded package but can be found in the following packages Package Library car usr lib R site library The function help search can be used when you don t exactly know the name of the function you re looking for gt help search levene Help files with alias or concept or title matching levene using fuzzy matching levene test car Levene s Test 2 4 Working with a Graphical User Interface The version of R for Windows comes with a very limited graphical user interface GUI while the GNU Linux version comes with no GUI at all There are however several independent projects aimed at developing a GUI for R The following sections give some information on them An extensive GUI for R might be useful for beginners however Td recommend learning to use R from the command line because it is a very elegant language and its syntax is pretty much easy to learn Besides working from the command line is faster The R Commander An extensive GUI for R is provided by the Remdr package R commander This GUI
107. of the data for example to do some checking or because the data object is too big and it s not printed nicely on the console The functions head and tail let you look only at the first or the last part of your data respectively For example suppose dats is a dataframe the command gt head dats will print only the first 6 observations You can visualise more or less than 6 observations by setting the n option gt head dats n 10 32 4 10 Reading Numbers in Exponential Notation Often R prints out numbers in exponential notation this may lead to con fusion In order to understand the exponential notation is first necessary to introduce the scientific notation A number in scientific notation is in the form a 10 for example 300 could be written in scientific notation as 3 102 The components of a number in scientific notation are also named as mantissa 10 lt haracteristic Remember that a number with a negative exponent for example 107 can be rewritten as ie go ao 7 so for example 0 003 can be rewritten in scientific notation as 3 1073 because 1 3 107 3 777 0 003 R as most calculators doesn t actually use the scientific notation it uses instead the exponential notation The exponential notation is a shorthand version of the scientific notation in which for example 103 is replaced by e3 where e stands for exponent So in our previous examples 300 would be written as 3e2 and 0 003 would be w
108. ors The dataset line_matching txt contains data on an imaginary experiment in which a psychophysician wants to mea sure the accuracy of matching the length of a segment for three groups of people Gr 1 Gr 2 Gr 3 for segments of four different lengths L1 L2 L3 L4 The third factor the psychophysician is interested in is whether matching accuracy changes depending on the colour blue vs red of the segment to be matched he measures this as a within subjects factor The matching accuracy is measured as the error or displacement positive or negative from the actual segment length The dataset contains the mean values for the three groups Below is the code for producing the barchart the resulting plot can be seen in Figure 8 6 dats lt read table line_matching txt header TRUE trellis device oldpar lt trellis par get superpose polygon trellis par set superpose polygon list col c darkslateblue indianred myGraph lt barchart error length group groups color data dats origin 0 ylab Error cm xlab Segment Length auto key TRUE as table TRUE print myGraph trellis par set superpose polygon oldpar VV Vt V V VV We re showing the bars for the two levels of the colour factor side by side in the same panel this is done by using the factor in the groups argument A different display could have been achieved by putting the colour factor as an additional conditio
109. ou can add the following line to the First function in your Rprofile This goes in Rprofile in First lt function libPaths c libPaths personalRLibrary in this way after starting a new session you ll be able to load your package without having to specify in which library it is located gt library mypkg The one described above is a very quick but rough way of creating a package in order to properly create a R package a number of additional steps like writing the documentation and adding examples need to be followed Some of these steps will be described in the following sections Always remember that a very useful thing to do when learning how to build a package is to download some source packages and explore their contents 119 Editing the DESCRIPTION file The DESCRIPTION file follows the Debian control format and has a key value pair syntax The default fields created by package skeleton are pretty much self explanatory Other fields that can be added are e Depends If your package depends on a particular version of R or on other packages these should be listed here For example Depends R gt 1 9 0 gtools gdata stats e URL The URL of a website where you can find out mode about the package For example URL http www example com Editing the Documentation The documentation files reside in the man directory of your package There is one documentation file for each function
110. ould be two tailed or one tailed In particular the alternative hypothesis H becomes two sided true mean of the group is not equal to mu less true mean of the group is lesser than mu greater true mean of the group is greater than mu e conf level 0 95 Default or another value this option sets the confidence level for the estimation of the confidence interval 10 2 2 Two samples t test With R you can easily run a t test to find out whether the difference between the means of two groups is significant The syntax is as follows gt t test gri gr2 where gr1 is the data vector of the first group and gr2 is the data vector of the second group The following options can also be selected The following options can also be selected e mu 0 Default or another value mu is the value given by the difference between the means under Ho in other words it is the value against which you test the alternative hypothesis 2If you leave it out it defaults to 0 93 e alternative two sided default or less or greater this option allows choosing whether the test should be two tailed or one tailed In particular the alternative hypothesis H becomes two sided true mean of the group is not equal to mu less true mean of the group is lesser than mu greater true mean of the group is greater than mu e paired FALSE Default or TRUE If the TRUE option is selected then a pair
111. p the b value TRUE 1 the theme therion gt match only when pattern appears at the end gt grep the b value TRUE 1 the jjthe gt match exactly the not followed or preceded by anything gt grep the b value T 1 the gt match the followed by i or m gt grep thel i m b value TRUE 1 atheist theme gt match the followed by anything except i gt grep the 7i b value TRUE 1 theme therion gt match the followed by anything gt grep the b value TRUE 1 atheist theme therion gt match the preceded by anything gt grep the b value TRUE 1 atheist jjthe 116 glob2rx translates a wildcard pattern as used in most shells for exam ple for listing files with the Unix 1s in a regular expression so if you re used to wildcards this comes is handy gt glob2rx the 1 the gt glob2rx the 1 the 14 3 Tips and Tricks 14 3 1 Convert a String into a Command gt cmd lt vec lt c 1 2 3 gt eval parse text cmd 14 4 Creating Simple R Packages If you start writing your own functions and you use them often probably you will soon get tired of sourcing the files containing each function to make them available at each session There are at least two ways around this problem e put all your function files in a d
112. p a and group b in a test With the boxplot we want to see how the scores are distributed in the two groups The dataframe contains a column score with the score for each subject and another column group that defines the group a given observation comes from So we first read in the dataframe and then ask for the boxplots with the distribution of scores as a function of the group they belong to gt dats lt read table boxplot1 txt header TRUE gt boxplot dats score dats group names c group a group b The results are in figure 7 6 the thick black lines in the middle of the boxes represent the median if this is about the middle of the box the distribution of the data should be normal The two lines that delimit the box are called hinges and they are approximately the first and the third quartiles The horizontal lines that form the Ts above and below the box are called whiskers and inside them are contained all the observations that fall within a distance of 1 5 times the size of the box upwards or downwards Points that fall outside this distance are outliers and they are represented as a circle In our case there are two outliers in group a Apart from checking if the distribution is normal you can also check if the variances are approximately equal by comparing the size of the boxes the distance between the hinges If one boxplot is clearly bigger than the other one for example two times bigger then t
113. pally for works whose purpose is instruction or reference 1 APPLICABILITY AND DEFINITIONS 143 This License applies to any manual or other work in any medium that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated herein The Document below refers to any such manual or work Any member of the public is a licensee and is addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and or translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document s overall subject or to related matters and contains nothing that could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary Section may not explain any mathematics The relationship could be a matter of historical connection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them The Invariant Sect
114. pply and aggregate The tapply function allows you to extract information from a dataframe for example the mean or standard deviation of a given variable on the bases of one or more factor The function name is related to the fact that it is used to apply a function e g the mean to a subsets of the dataframe chosen on the basis of one or more factors We ll use the InsectSprays dataset to illustrate the use of tapply The dataset contains the number of insects still alive in agricultural experimental units treated with six different types of pesticide gt data InsectSprays gt head InsectSprays count spray 10 A 7 20 14 14 12 meanSpray lt tapply X InsectSprays count INDEX InsectSprays spray FUN mean VtItVWDOUIO0SWINE rrr Po eS meanSpray A B C D E F 14 500000 15 333333 2 083333 4 916667 3 500000 16 666667 the arguments to tapply are X the column of the dataframe to which the function should be applied INDEX the factor used for subsetting the dataframe and FUN the function to be applied The function returns an array in this case a vector but can be a matrix or multi dimensional array The INDEX argument indeed can be a list of factors in this case the function chosen is applied to group of values given by a unique combination of the levels of these factors We ll see an example by modifying the InsectSprays dataset including another fictitious factor The new factor will be the season in which the fields were
115. rame runtimes colour Now the data are in a proper format to perform the analysis Well this was a bit an extreme example of course it would have been easier if the data in the text file would have been in another format It was just to show you that once you master some basic functions like rep and c concatenate in R you can laid out your data or vectors you need pretty much as you like and you can adapt even to the most adverse situations Since we have unequal sample sizes we should pay particular attention that the variances of the three groups are homogeneous To check for this we can use the Levene test for homogeneity of variances gt library car gt levene test runtimes colour Levene s Test for Homogeneity of Variance Df F value Pr gt F group 2 0 0562 0 9454 49 as you can see from the print out the resulting F value is far from being significant so we can safely accept the null hypothesis that the variances in the three groups are homogeneous Now we can run the test gt oneway test runtimes colour data data var equal TRUE One way analysis of means data runtimes and colour F 0 2731 num df 2 denom df 49 p value 0 7622 The F statistics is not significant so there is no difference in running times for rats with the three different colours 12 2 Repeated Measures ANOVA 12 2 1 One Within Subjects Factor The syntax for performing a repeated measures ANOVA is a little more complex than
116. rats_trellis txt header TRUE gt dats subj lt as factor dats subj gt head dats subj socialint alcohol drug species 1 7 Al Drug Yuppy No Al Drug Yuppy Al No Drug Yuppy No Al No Drug Yuppy Al Drug Yuppy No Al Drug Yuppy SO ME WN EF NV HR PoP OO 74 we ll start visualising the data along one dimension the species This is a single dimension that can be easily handled by the base graphics system but can be equally well displayed with lattice Since the high level lattice plotting functions require the data to be entered as a dataframe we ll use the aggregate function to get a dataframe with the mean values of socialint the dependent variable on the bases of the species bySpec lt aggregate dats socialint by list species dats species FUN mean names bySpec which names bySpec x lt socialint bySpec species socialint Kalamani 5 3125 Yuppy 5 6875 VV Mv N e lattice uses a model formula syntax you give it a dataframe and specify how you want a variable to be displayed along the dimensions of one or more factors In our case we want socialint species you could read the as explained by species the barchart can be produced with the code below and is displayed in Figure 8 1 gt trellis device gt pli lt barchart socialint species data bySpec gt print p11 Now suppose we want to visualise the relationship between socialint and species on the bases of alcohol admini
117. rchid4 darkred darksalmon darkseagreen darkseagreeni _ darkseagreen2 darkseagreen3 E darkseagreen4 m darkslateblue darkslategray O ERR E darkslategray2 E darkslategray3 E darkslategray4 LJ darkslategrey E darkturquoise darkviolet deeppink deeppinki deeppink2 deeppink3 deeppink4 deepskyblue deepskybluei deepskyblue2 deepskyblue3 J deepskyblue4 dimgray dimgrey dodgerblue dodgerbluei J dodgerblue2 il dodgerblue3 dodgerblue4 E firebrick firebrick1 firebrick2 firebrick3 firebrick4 floralwhite forestgreen gainsboro ghostwhite gold E goldi 137 E gold2 E gold3 E gold4 E goldenrod E goldenrodi goldenrod2 E goldenrod3 E goldenrod4 sray gray0 grayl gray2 EH gray3 gray4 gray5 gray6 gray7 grays gray9 gray10 gray11 gray12 gray13 gray14 gray15 gray16 gray17 gray18 gray19 gray20 E gray21 gray22 gray23 E gray24 LJ gray57 gray90 gray25 E gray58 gray91 gray26 DI gray59 gray92 gray27 m gray60 gray93 gray28 gray61 gray94 gray29 E gray62 gray95 gray30 E gray63 gray96 gray31 gray64 gray97 gray32 gray65 gray98 gray33 gray66 gray99 gray34 gray67 gray100 gray35 gray68 iz green gray36 gray69 E green1 gray37 gray70 E green2 gray38 gray71 E green3 gray39 gray72 E green4 gray40 gray73 E greenyellow gray41 gray74 grey gray42 gray75 EE grey0 gray43 gray76 E greyl gray44 grayTT E grey2 gray45 gray78 w grey3 gray46 gray79 E grey4 gray47 gray80 E grey5 gray48 gray81
118. re supported Mac Os X Precompiled binaries are also available for Mac Os X you can download them and then double click on the installer s icon to start the installation 1 2 Installing Add On Packages There is a growing number of packages that implement statistical functions that are not available with the base program though you can pretty easily write your own functions with R or provide other utilities They re not strictly necessary but if you keep using R sooner or later you will end up wanting to install some of these packages GNU Linux and Other Unices There are different ways to get packages installed For Debian there are precompiled versions of some packages so you can get them with apt get or whatever else you usually use to install Debian packages this will also take care of possible dependencies some packages need other packages to be installed in order to work For other packages a way to install them is to download the related tarball and then from a root console issue the command R CMD INSTALL packagename where packagename is the full path to the tarball you have downloaded There are other ways and other specific options to install add on packages Again refer to the R Installation and Administration Manual for further information Windows The R s GUI on Windows provides an interface to download and install the packages directly from the internet You can also install packages fro
119. riable it will just be named x However it can be changed afterwards here s a solution that should work whatever the number of factors in the dataframe gt names InsDf 1 sprayType season Nag gt names InsDf which names InsDf x lt count gt names InsDf 1 sprayType season count 4 8 Creating and Editing Data Objects through a Visual Interface If you want to use a visual interface for creating a dataframe first create an empty dataframe with 31 gt mydataframe lt data frame then you can call a spreadsheet like editor to fill in the dataframe with gt data entry mydataframe or gt fix mydataframe If the data object is a vector fix will call a text editor to edit the object instead of the spreadsheet like interface so if you want the latter use the function data entry instead However using a simple text editor for fixing a vector might be more practical if you want to use a different text editor from the one that fix calls by default you can change the editor option gt fix myvector editor emacs or just call the editor on the object gt emacs myvector On Windows you could try gt fix myvector editor notepad 4 9 Visualising Your Data As you probably have already noticed after you ve created a data object just typing its name on the console and pressing Enter will display the values it contains Sometimes however you might want to see only part
120. ritten as 3e3 Below are a few conver sion examples Number Scientific Notation Exponential Notation 10 1 10 lel 20 2 10 2el 200 2 10 2e2 350 3 5 102 3 5e2 0 00353 3 53 1073 3 53e 3 As a quick and dirty rule remember that when you re multiplying a number by 10 lt zpoment as you add to the exponent you re adding a 0 to the number or shifting the point by one position towards the right if it s a decimal number As you subtract to the exponent you re deleting a 0 to the number or shifting the point by one position towards the left 33 Chapter 5 File Input Output 5 1 Reading In Data from a File 5 1 1 read table If the data are in a table like format with each row corresponding to an ob servation or a single case and each column to a variable the most convenient function to load them in R is read table This function reads in the data file as a dataframe For example the data in the data file ratsData txt that contain information height weight and species of 6 rats can be easily read in with the following command gt ratsData lt read table file ratsData txt header TRUE gt ratsData identifier height weight species 1 sa01 3 2 300 A 2 sa02 2 6 246 A 3 sa03 2 9 317 A 4 sb01 2 4 229 B 5 sb02 2 5 230 B 6 sb03 2 4 245 B in this case we ve set the option header TRUE because the file contains a header on the first line with the variable names 5 1 2 scan Another very handy
121. rmat of your data if they happen to be in a format that is not proper for applying a given statistical function on them The process of changing the format of your data with these functions might seem very complicated at first however you should keep in mind the following things e You don t really need to learn all of the functions that R provides to manipulate your data and change their format Once you learn a procedure that does the job you can stick on it and you ll be fine most of the times e Once you understand the logic and the structure of the data format that R expects to apply some statistical functions changing the layout of your data to match this structure will be easy Moreover the data format R wants is most of the times one and only one The one row per observation format which will be explained below e In this tutorial you will see different examples in which the format of the data stored in a given file don t match the format R wants This is just for illustrative purposes In real life if you re doing a research or an experiment you can often gather your data in a format that is already suitable for performing statistical analyses e You don t really have to use R to change the layout of your data if you don t like the functions it provides to do this job You can always use some external programs to achieve the same results for example spreadsheets programs such as gnumeric or the one provided wi
122. s Front Cover Texts on the front cover and Back Cover Texts on the back cover Both covers must also clearly and legibly identify you as the publisher of these copies The front cover must present the full title with all words of the title equally prominent and visible You may add other material on the covers in addition Copying with changes limited to the covers as long as they pre serve the title of the Document and satisfy these conditions can be treated as verbatim copying in other respects If the required texts for either cover are too voluminous to fit legibly you should put the first ones listed as many as fit reasonably on the actual cover and continue the rest onto adjacent pages If you publish or distribute Opaque copies of the Document numbering more than 100 you must either include a machine readable Transparent copy along with each Opaque copy or state in or with each Opaque copy a computer network location from which the general network using public has access to download using public standard network protocols a complete Transparent copy of the Document free of added material If you use the latter option you must take reasonably prudent steps when you begin dis tribution of Opaque copies in quantity to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year af ter the last time you distribute an Opaque copy directly or through your agents or retailers of that edi
123. socialint species alcohol data bySpecAl gt print p13 the resulting graph is displayed in Figure 8 3 we could have swapped species Figure 8 3 Social Interactions by Species and Alcohol Administration with Multi panel Conditioning Al No Al socialint Kalamani Yuppy Kalamani Yuppy for alcohol as the conditioning factor which way gives the more effective display depends from case to case and it s up to the user to decide Finally we ll consider the case in which all factors are included in the display this cannot be easily achieved with traditional graphics but it is easily done in lattice we just add drug to the conditioning factors Figure 8 4 gt bySpecAlDrug lt aggregate dats socialint by list species dats species alcohol dats alcohol drug dats drug FUN mean gt names bySpecAlDrug which names bySpecAlDrug x lt socialint gt pl4 lt barchart socialint species alcohol drug data bySpecAlDrug gt print p14 TT we could have used a grouping variable also in this case rather than using two conditioning factors Figure 8 5 gt pl5 lt barchart socialint species alcohol groups drug data bySpecAlDrug auto key TRUE gt print p15 again what is the best display is up to the user to decide and depends from case to case 8 3 barchart We will look at an example of a barchart display of a dependent measure conditional on three fact
124. sprayed The values will be returned in a matrix gt season lt gl 4 3 72 labels c winter spring summer autumn gt Ins lt data frame InsectSprays season gt meanSpray lt tapply X Ins count INDEX list Ins spray Ins season FUN mean gt meanSpray winter spring summer autumn 30 ee N 333333 13 333333 16 666667 15 666667 333333 13 666667 17 666667 13 666667 666667 2 000000 2 000000 1 666667 666667 4 333333 5 000000 3 666667 666667 4 666667 1 666667 4 000000 666667 17 666667 16 333333 21 000000 Mm Dot HW HH O ONO 1 The tapply is often very useful for example after having calculated the means in this way it is very easy to visualise the data with a barplot gt barplot meanSpray beside TRUE legend T The aggregate function is very similar to tapply but rather than return ing an array it returns a dataframe which can be useful in some situations InsDf lt aggregate x Ins count by list sprayType Ins spray season Ins season FUN mean InsDf sprayType season x A winter 12 333333 winter 16 333333 winter 2 666667 winter 6 666667 winter 3 666667 winter 11 666667 spring 13 333333 spring 13 666667 0 NOD IHS WINE V V YU Pon iva if you don t give a name to the grouping factors as we did with SprayType Ins spray a default name will be given One slightly annoying thing is that as far as I know it is not possible to assign a name to the resulting va
125. stration We could achieve also this with the barplot in the base graphics system In lattice there are two ways of doing it one is by the use of a grouping factor this yields a display similar to the barplot function The second way is by multi panel factor conditioning The advantage of multi panel conditioning as we will see soon is that it can be extended to an unlimited number of factors Let s start with the first solution in which we use a grouping factor First we create a suitable dataframe gt bySpecAl lt aggregate dats socialint by list species dats species alcohol dats alcohol FUN mean gt names bySpecAl which names bySpecAl x lt socialint then we produce the barchart Figure 8 2 gt pl2 lt barchart socialint species groups alcohol data bySpecAl auto key TRUE gt print p12 79 socialint Figure 8 1 Social Interactions by Species 5 7 7 E 5 6 5 5 7 5 4 4 5 3 7 Kalamani Yuppy Figure 8 2 Social Interactions by Species and Alcohol Administration with socialint Grouping Factor ton E No Al 6 0 4 fe Kalamani Yuppy the grouping factor is given by the groups argument notice also that we have set auto key to TRUE in order to add an automatic legend the second way of doing the graph is by multi panel conditioning we achieve this by putting alcohol as a conditioning factor with the syntax gt pl3 lt barchart
126. t a vector of the form c x1 x2 y1 y2 giving the coordinates of the plot region as fractions of the current figure region e pin the current plot dimensions width height in inches Margins e mar the width of the margins for the four sides of the plot speci fied in terms of lines of text The margins are specified in the form c bottom left top right The default is c 5 4 4 2 0 1 Example gt par mar get current margins size 1 5 1 4 1 4 1 2 1 gt par mar c 6 2 3 0 0 1 set new margins size e mai the same as mar but the unit of measure is inches rather than lines of text Outer Margins e oma a vector of the form c bottom left top right giving the size of the outer margins in lines of text e A vector of the form c bottom left top right giving the size of the outer margins in inches e A vector of the form c x1 x2 y1 y2 giving the outer margin region in normalised device coordinates NDC 65 Figure 7 16 The Figure Region Includes the Plotting Region and the Mar gins 66 Figure 7 17 Device with Outer Margins and Multiple Figure Regions 67 7 13 Plotting from Scratch The high level plotting functions such as plot histogram barplot and so on provide a good and quick way to produce graphs Plotting from scratch using the low level plotting commands is generally not necessary unless you want to create some new customised plotting functions Learning to plot from s
127. t in the slot defined by the crossing between the second row and the first column of a 2 x 2 layout gt par mfrow c 2 2 create 2x2 layout gt par mfg c 2 1 set next fig at 2dn row Ist col gt plot 1 100 sin 1 100 7 11 2 layout A more flexible way to divide a graphics device into multiple plotting regions is given by the layout function With the layout function the graphics 61 Figure 7 15 A 2x3 Layout with mfcol RR T ER ea T Tara T 0 6 08 1 0 1 2 14 0 6 08 1 0 1 2 14 0 6 08 1 0 1 2 14 T_T T TT T T da T 0 6 08 1 0 1 2 14 0 6 0 8 1 0 12 14 0 6 0 8 1 0 12 14 device is divided into a matrix of n_rows x n_cols sub regions and each figure is assigned to one or more of these sub regions Let s look at an example gt m lt matrix c 1 2 3 4 nrow 2 byrow TRUE gt m 1 42 1 1 2 2 3 4 gt layout m the matrix m we ve created completely defines our layout for the graphics window The window is divided into 2 x 2 4 sub regions Moreover the first figure is assigned the sub region on the top left of the window the second figure the sub region at the top right the third the region at the bottom left and the fourth the region at the bottom right This example is in itself not very different from what we would get with mfrow however two key differences make layout more powerful than mfrow First it is possible to assign more tha
128. t is named a and the second b and we can access them with a special dollar sign notation gt mylist a return element of the list named a 1 1 2 3 4 5 6 7 8 9101112 gt mylist a 1 3 1 123 18 It is also possible to use the double brackets notation with names gt mylist a 3 1 3 To eliminate an element of a list set it to NULL gt veci lt c i 2 3 gt vec2 lt c a b c gt myList lt list veci vec1 vec2 vec2 gt myList veci 1 123 vec2 1 a h c gt myList vec1 lt NULL gt myList vec2 1 a b c notice that this is different from eliminating an element of the vectors con tained in the list you can do the latter with gt myList vec2 lt myList vec2 1 gt myList vec2 1 h o 4 4 Dataframes Dataframes are one of the most important objects in R You can think of it as a rectangular data structure in which each column stores either the values of a numeric variable or the levels of a factor and each row represents an observation Let s look at an example we ll build a dataframe from 3 vectors the first vector stores a variable number of beers drunk during a week for twelve young people the second is a factor vector that specifies for each person whether he she is a university student or not so it has two levels the third is also a factor vector which tells the sex of each person so it has two levels as well
129. ta to draw The third argument represents the position at which to draw the horizontal line of reference for the data we want it to be zero in this case but passing the argument as a variable rather than hard coding the value into the panel function will allow us to recycle this panel function in case we want the horizontal reference line drawn at some other points in the future Besides these arguments our panel function accepts also an undefined number of other arguments which are designated by the notation These are usually graphics parameters that can be specified in the high level plotting function The contents of our panel hRefDotplot function are very simple we call first panel dotplot to draw the standard dotplot and then we call panel abline giving it the value of ref to draw the horizontal line in each panel The actual plot is done by calling the high level dotplot function specifying panel hRefDotplot as the panel function to use gt dotplot error length group groups color data dats origin 0 ylab Error cm xlab Segment Length auto key TRUE aspect 1 as table TRUE ref 0 panel panel hRefDotplot notice the last line of the call first we re telling dotplot to use our hRefDotplot function to do the plotting by specifying the panel argument second we re specifying another argument ref in the call this is not a standard argu ment but it will be automatically passed to our panel function t
130. tatPages StatHomePage html e Weaver s stats page http www angelfire com wv bwhomedir stats html In Italian e Statistica univariata e bivariata parametrica e non parametrica per le discipline ambientali e biologiche di Lamberto Soliani http www dsa unipr it soliani soliani html 135 Appendix E Full Colours Table white blanchedalmond E chartreuse3 aliceblue blue chartreuse4 antiquewhite bluei chocolate antiquewhitel blue2 chocolatel ant iquewhite2 blue3 chocolate2 ti hite3 blue4 D chocolate3 antiquewhite DI q blueviolet chocolate4 antiquewhite4 brown coral E aquamarine brown1 corall E aquamarinei brown2 coral2 aquamarine2 brown3 coral3 E aquamarine3 brown4 coral4 E f burlywood cornflowerblue aquamarine4 E aaa burlywood1 cornsilk anne E burlywood2 ces cornsilk2 azure2 burlywood3 DI cornsilk3 azure3 burlywood4 EH cornsilk4 azure4 mi cadetblue H cyan beige cadetbluel cyani bisque cadetblue2 Di cyan2 bisquel cadetblue3 E r cyan bisque2 cadetblue4 ES hisques chartreuse cyan4 E chartreusel E darkblue Diepe chartreuse2 darkcyan m black 136 darkgoldenrod DI darkgoldenrodi darkgoldenrod2 a darkgoldenrod3 al darkgoldenrod4 darkgray darkgreen darkgrey darkkhaki darkmagenta darkolivegreen E darkolivegreeni E darkolivegreen2 darkolivegreen3 c darkolivegreen4 J darkorange darkorangel J darkorange2 E darkorange3 darkorange4 E darkorchid darkorchidi darkorchid2 darkorchid3 darko
131. ted measures 100 assignment 12 attach 21 barplot 42 barplot2 45 with error bars 45 bitmap 72 boxplot 47 102 cat 37 colour 69 list 70 control structures 111 dataframes 19 create 20 naming elements of 21 subsetting 20 22 detach 21 Emacs Speaks Statistics 122 graphics devices 72 export 72 with INDEX symbols 59 head 32 histogram 49 if else 111 ifelse 112 interaction plot 51 JPEG 72 latex in graphics 59 Sweave 125 legend 58 Levene test 92 lists 18 naming elements of 18 subsetting 18 logical operators 14 lty 55 matplot 42 matrix 15 operations 17 subsetting 16 transpose 17 normal distribution 88 oneway test 98 par 54 mfcol 60 mfg 61 mfrow 60 pch 57 pdf 72 plot add text 59 png 72 postscript 72 read table 34 relational operators 14 rep 15 98 154 scale 38 scan 34 scan 97 seq 14 sequences 14 stack 29 stripchart 49 Sweave 125 symbols 57 t test 90 one sample 90 two samples 91 tail 32 unstack 29 vectors 12 indexing 13 naming elements of 14 of characters 13 write table 36 xor 113 155
132. th the open office suite What s really important is that you understand the structure of the format the R expects 24 This said I would advice you to learn some of the functions that R provides to rearrange your data for at least two reasons 1 They re very powerful and can actually save you time once you learn them and 2 many examples in this tutorial and in other books use them so you ll often need to know them to understand what s going on 4 7 1 The One Row per Observation Format While statistic textbooks and scientific articles often show data in a format that is suitable and immediate for the human eye like the one shown in table 4 4 statistical software often don t quite like it and would rather have the same data rearranged as shown in Table 4 5 Table 4 4 Data Format Suitable for the Human Eye Group A Group B Group C 5 4 7 2 4 5 3 5 7 4 5 8 6 4 7 Table 4 5 Data Format Suitable for R Value Group Or NonNraonhaoaakh Db 19 N So090000tWWWWOPPrrp The main difference is that while in the first format you have more than one observation in the same row and you can identify the group to 25 which each observation belongs to through the column headers Group A Group B and Group C in the second format you have only one observation for each row This observation is then fully identified with a label that appears in the second column A better way t
133. the requirement section 4 to Preserve its Title section 1 will typically require changing the actual title 9 TERMINATION You may not copy modify sublicense or distribute the Document except as expressly provided for under this License Any other attempt to copy modify sublicense or distribute the Document is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such parties remain in full compliance 10 FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new revised versions of the GNU Free Documentation License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns See http www gnu org copyleft Each version of the License is given a distinguishing version number If the Document specifies that a particular numbered version of this License or any later version applies to it you have the option of following the terms and conditions either of that specified version or of any later version that has been published not as a draft by the Free Software Foundation If the Document does not specify a version number of this License you may choose any version ever published not as a draft by the Free Software Foundation ADDENDUM How to use this License for your docu
134. the syntax for fully randomised designs In a repeated mea sures design we take into account the effects of the subjects on our measures that is the fact that different subjects will have different different baseline 102 means on a given measure e g on a reaction time test In this way we are able to tell apart the variability given by inter individual differences between our subjects from the variability due to the manipulation of one or more independent variables with a view to identify the latter with more precision A consequence of this procedure is that while with other designs we used a common error term in a repeated measures design we have to use different error terms to test the effects we are interested in and we have to specify this in the formula we use with R for aov A good explanation of repeated measures designs in R is given by Baron and Li 2003 1 and what follows in this discussion is mainly inspired by their work We will start with a simple example of a repeated measures design with one within subject factor at three levels Let s imagine we want to test the effects of three different colours on a simple detection task The data are presented in table 12 3 and represent subjects reaction times measured with a button press for the detection of squares of three different colours blue black and red Each subject was tested under all the three conditions The data are store in the file rts txt
135. ther by a semi colon or by pressing and starting a newline If you start a newline before a command is complete R will prompt you to complete the command with a sign you can then complete the command If you don t know how to complete the command and get stuck you can stop R prompting you with the plus sign by pressing the and keys simultaneously To quit R type quit or q R will ask you if you want to save the current session if you answer y R will save all the objects active in the current session and the command history On a Unix terminal you can also press Ctrl d to exit 2 2 Starting to Work with R The first thing you can try is doing some math at the command prompt type 5 4 and press the result will be gt 5 4 1 9 well obviously 9 Other arithmetic operators are listed in Table 2 1 Table 2 1 Arithmetic Operators Symbol Function Addition Subtraction Multiplication Division E Exponentiation Now let s create a variable we ll call it foo and assign to it a number gt foo lt 5 the arrow lt is the assignment operator in R2 in the above case it means the value of foo is 5 foo is an object since it is of a numeric type we can perform arithmetic operations on it gt foo 2 1 10 we can also store the results of an arithmetic operation in an object gt another_foo lt 5 2 if you want to display the value of this new object you can us
136. tion again can be produced using the prompt function gt prompt mydata Checking the Package The sanity check for the package can be done by issuing the following com mand from a shell R CMD check path to your package sources 121 Chapter 15 Environment Customisation Perhaps the best way to customise your R environment is through the use of a Rprofile file that you put in your HOME directory This is a simple text file that is sourced every time R is started so you can put in it your own functions and any operations that you would like R to perform at start up Also in this file you can write two special functions the First is executed first at the beginning of a session and the Last is executed at the end of a session The First function is normally used to initialise the environment setting the desired options Here s an example of a Rprofile file This is my Rprofile in First lt function options prompt gt gt gt continue t change the prompt options digits 5 length 999 display max 5 digits setwd rwork Start R in this directory for a full listing of the options that can be set see options You can change temporarily the options only for the running session directly from R for example gt options digits 9 The Rprofile file in the user s HOME is only one of the files that can be used to initialise the environment and set the options The file that is loo
137. tion to the public It is requested but not required that you contact the authors of the Document well before redistributing any large number of copies to give them a chance to provide you with an updated version of the Document 4 MODIFICATIONS You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above provided that you release the Modified Version under precisely this License with the Modified Version filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version A Use in the Title Page and on the covers if any a title distinct from that of the Document and from those of previous versions which should if there were any be listed in the History section of the Docu ment You may use the same title as a previous version if the original publisher of that version gives permission B List on the Title Page as authors one or more persons or entities responsible for authorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all 146 of its principal authors if it has fewer than five unless they release you from this requirement State on the Title page the name of the publisher of the Modified Version as the publisher Preserve all the copyright notices of the Doc
138. trings with other data types subsets of certain objects again dataframes are an example but also lists can be easily given meaningful names and retrieved This adds much flexibility and ease of use of R compared to other languages e g MATLAB One aspect that is perhaps less known however are the powerful string processing functions that R gives you Once you get to know them you ll realise you can do all your data analysis in R without the need to use other languages like python or perl for pre processing The simplest thing you can do with a string is counting its characters which you can do with the nchar function gt mystr lt I love R gt nchar my string 1 8 115 The second thing you can do with strings is extracting parts of them There are various way to achieve this Two of the most useful functions are substr and strsplit substring as the name suggests returns part of a string gt substr my_string start 1 stop 4 1 I lo if you want to get a portion of a string from some point in the middle to the end gt substr my_string start 5 stop nchar my_string 1 ye R substr can be also used to replace parts of a string gt substr my_string start 1 stop 3 lt qqq gt my_string 1 aggove R 14 2 1 Using Regular Expressions gt b lt c the atheist theme therion thin jjthe gt match only when pattern appears at the beginning gt gre
139. ts man dats ocul Pearson s product moment correlation data dats man and dats ocul t 3 4439 df 35 p value 0 001505 alternative hypothesis true correlation is not equal to 0 95 percent confidence interval 0 2139450 0 7111784 sample estimates cor 0 5030888 97 the p value tells us that we can extend our finding in the population so people with a quick hand would also have a quick eye 11 1 Linear Regression Regression models are expressed in R with a symbolic syntax that is clean and convenient If you have a dependent variable rts and you want to check the influence of an independent variable age on it this would be expressed as gt rtfit lt lm rts age gt plot rts age gt abline rtfit if you want to add another predictor score gt rtfit2 lt Im rts age score 98 Chapter 12 ANOVA 12 1 One Way ANOVA We ll start directly with an example to show how to perform a one way ANOVA Let s imagine an experimenter is studying the effects of sleep de privation on verbal memory He selects a random sample of healthy subjects and assigns them to three treatments 4 hours 6 hours and 8 hours of total sleep The subjects are then given a memory test consisting of a long list of words to remember after a minute of delay from their presentation The dependent variable is the number of words correctly recalled in a minute time The data are shown in table 12 1 Table 12 1 Data for the one way ANOVA
140. type gt temperature 3 if you would like to access the data in more than one position of the vector let s say the first the third and the sixth you can again use the function concatenate inside the indexing command gt temperature c 1 3 6 to access the data from say the third position to the tenth position you can use gt temperature 3 10 and if you want to assign this subset to another vector called white you can just type gt white lt temperature 3 10 if you want to access all the vector but the first five positions gt temperature 1 5 since in R there is not a delete command you can use this form of subset ting to remove elements of a vector for example if you would like to cancel the fourth element of the temperature vector you would write 13 gt temperature lt temperature 4 Furthermore to access subsets of data you can do much more magic using logical operators and other tricks for example if you want to access in a vector only the data greater than a certain value you can use the gt greater than logical operator gt temperature temperature gt 30 In order to concatenate logical commands you can use the amp and logical operator gt temperature temperature gt 30 amp temperature lt 35 Table 4 1 Logical Operators Table 4 2 Relational Operators Operator Description Operator Description amp Intersection and lt Minor than amp
141. ument E Add an appropriate copyright notice for your modifications adjacent to the other copyright notices Include immediately after the copyright notices a license notice giving the public permission to use the Modified Version under the terms of this License in the form shown in the Addendum below Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice Include an unaltered copy of this License Preserve the section Entitled History Preserve its Title and add to it an item stating at least the title year new authors and publisher of the Modified Version as given on the Title Page If there is no section Entitled History in the Document create one stating the title year authors and publisher of the Document as given on its Title Page then add an item describing the Modified Version as stated in the previous sentence Preserve the network location if any given in the Document for pub lic access to a Transparent copy of the Document and likewise the network locations given in the Document for previous versions it was based on These may be placed in the History section You may omit a network location for a work that was published at least four years before the Document itself or if the original publisher of the version it refers to gives permission For any section Entitled Acknowledgements or Dedications Pre serv
142. uments the others are optional the default order in which you have to give them 51 is a bit awkward because the variable of interest in our case dats errors is the third argument the first one is the factor that goes on the x axis and the second one is the trace factor whose levels will be represented as lines of a different type or of different colours The y axis yields the measure for our variable of interest You can see the plot in Figure 7 9 Another good way to represent the levels for the trace factor is through the use of symbols in the following graph see the result in Figure 7 10 both line type lty and symbols pch are used to differentiate between the levels of the trace factor in order to get this you need to set the option type to b that means use both line type and points symbols setting this option to 1 will give just different line types while setting it to p will give just different symbols In these examples I specified the line types and the symbols to use but this is not necessary if you don t R will cycle through its different line types and or symbols as necessary to represent all the levels of the trace factor See Section 7 9 1 for a description of the different line types and Section 7 9 2 for a description of the different symbols available in R gt interaction plot dats soa dats congr dats errors ylab Proportion of errors xlab SOA trace label Congruency lty c solid
143. up with a nice graph a barplot will make it The data are stored in the file test txt in the format shown in table 7 2 We can read in the file directly as a dataframe gt test lt read table test txt header TRUE We want to use the tapply function to get quickly summary tables with the means and standard deviations for the three groups However the format of the data frame at this point is not suitable for the tapply function because it has 3 observations for each row and the tapply function can be used only 42 sine and cosine function 1 0 0 5 0 0 0 5 1 0 Figure 7 3 sine and cosine functions with matplot Table 7 2 Data for the test example a b c 4 6 5 5 8 3 3 7 8 6 5 4 5 9 9 7 7 8 5 6 5 8 5 7 5 8 6 4 10 4 43 with the format one row per observation in which we have the values of the observations in one column and a set of labels identifying the group to which a given observation belongs to in another column Fortunately we can easily change the format of our dataframe with the stack command What it does is just to create a single values vector from the three columns we had previously and to add automatically another index vector with the labels we need gt test2 lt stack test we can have a look at the new dataframe simply typing gt test2 please notice that the stack function has automatically named the two vectors values and ind we ne
144. us that there is a significant effect of both the alcohol and the drug factors as well as their interaction 12 2 3 Two Within Subjects Factors and One Between Now let s see the case in which we also have a between subjects factor Suppose we want to run again the experiment on the effects of alcohol and drug on the social interactions in rats but this time we want to use two different species of rats the yuppy rats and the kilamany rats as we have reasons to believe that the kilamany will have different reactions to alcohol and drugs from the yuppy that is the species that we had tested before So we manage to gather 8 rats from each species and run our experiment The results are shown in table 12 5 the data are in the file two_within_one_between txt in each row of this file are recorded the number of social interactions for a rat under the 4 experimental conditions it participated in We need to get the one row per observation format gt subj lt rep 1 16 each 4 read in the data gt subj lt as factor subj gt alcohol lt rep c Al No A1 32 108 1 1 1 Table 12 5 Data for the repeated measures ANOVA example Drug No Drug Alcohol No Alcohol Alcohol No Alcohol Yuppy 7 6 6 4 5 4 5 2 8 7 7 4 8 8 6 5 6 5 5 3 8 7 7 6 5 5 5 4 7 6 6 5 Kalamani 8 7 6 5 7 6 5 4 9 8 5 4 4 4 3 2 7 7 5 3 7 5 5 0 8 7 6 3 5 6 4 5 gt alcohol lt as factor alcohol gt drug lt rep
145. utput Perhaps the most user friendly low level function for writing to a file is cat Suppose you have two vectors one with the heights of 5 individuals and one with an identifier for each and you want to write these data to a file gt height lt c 176 180 159 156 183 gt id lt c s1 Medi USS s4 s5 you can use cat in a for loop to write the data to the file but let s first write an header gt cat id height n file foo txt sep append FALSE the first argument is the object to write in this case a character string with the names of our variables to make a header and a newline character to start a new line Now the for loop gt for i in 1 length id cat id i heightlil An file foo txt sep append TRUE notice that this time we ve set append TRUE to avoid overwriting both the header and any previous output from the preceding cycle in the for loop We ve been using a blank space as a separator but we could have used something else for example a comma sep 37 Chapter 6 Descriptive 6 1 Tables 6 2 The scale Function The scale function can be used to easily transform your data into z scores Here s a silly example gt a lt c 1 2 3 gt scale a 1 1 1 2 0 35 1 attr scaled center 1 2 attr scaled scale 1 1 38 Chapter 7 Graphics 7 1 Overview of R Graphics Table 7 1 R Graphics Functions Fun
146. w to produce a graphic in JPEG format gt jpeg file plot jpeg gt plot x y gt dev off Other devices you can use with their corresponding file format are pdf postscript png and bitmap 72 Chapter 8 Lattice or Trellis Graphics The lattice package in R provides an alternative to the base graphics system it is an implementation of the ideas developed and implemented by Rick Becker and Bill Cleveland in the Trellis graphics system for the S language Trellis displays were developed as a framework to make it easy the display of the relationship between a dependent variable and multiple factors The lattice package allows you to do some wonderful things however it s not always easy to use and its syntax differs from the R base graphics system Since lattice is mostly compatible with the Trellis graphics system in S Plus the following documents written for Trellis probably provide the best introduction to lattice and to the concept of trellis displays e S PLUS Trellis Graphics User s Manual 2 e A Tour of Trellis Graphics 4 they can both be downloaded at the following URL http cm bell labs com cm ms departments sia project trellis software writing html As usual the definitive reference is provided by the especially in this case not very beginner friendly package documentation e Lattice Reference Manual http cran r project org doc packages lattice pdf the following articles also contain useful
147. within subjects factor we are telling R to partition the residuals into different error terms The first is the ef fect due to differences between subjects It will not be used to test any effects it will just be subtracted from the residuals to compute the other error terms The subj alcohol and the subj drug interactions are the error terms to be used to test the effects of alcohol and drug respectively while the subj alcohol drug interaction will be used to test the interac tion between between alcohol and drug Below there is the output from the analysis Error subj Df Sum Sq Mean Sq F value Pr gt F Residuals 14 69 433 4 960 107 Error subj alcohol Df Sum Sq Mean Sq F value Pr gt F alcohol 1 26 6667 26 6667 42 264 1 399e 05 xxx Residuals 14 8 8333 0 6310 Signif codes O 0 001 0 01 0 05 2 0 1 Error subj drug Df Sum Sq Mean Sq F value PrF drug 1 60 000 60 000 57 931 2 434e 06 Residuals 14 14 500 1 036 Signif codes O 0 001 0 01 0 05 0 1 Error subj alcohol drug Df Sum Sq Mean Sq F value Pr gt F alcohol drug 1 4 2667 4 2667 18 474 0 0007362 xxx Residuals 14 3 2333 0 2310 Signif codes O 0 001 0 01 0 05 0 1 As you can see R splits the summary into different sections based on the partition of the error terms that we have specified Each effect is then tested against its appropriate error term The results tell
148. xes is useful for slicing for example gt matr 2 1 5512 gives all the rows in the second column This could alternatively been writ ten as gt matr 1 4 2 where the index is a range of rows This notation is useful when you want to extract only part of the rows or columns for example gt matr 2 4 2 1 512 When the rows or columns to be extracted are not consecutive you can use a vector of indexes for slicing gt matr c 2 4 2 1 52 To query the dimension of the matrix you can use the dim function in this case our matrix has 4 rows and 3 columns gt dim matr 1 43 The rows and columns of a matrix can also be assigned a name attribute through the dimnames function The dimnames have to be a list of character vectors the same length as the matrix dimensions they refer to 16 gt dimnames matr lt list c rowi row2 row3 row4 c coli col2 col3 gt dimnames matr dimnames is a list 1 1 rowt row2 row3 row4 2 1 coli col2 col3 gt matr now the matrix is printed with its dimnames col1 col2 col3 rowl 3 5 6 row2 2 5 7 row3 9 1 5 row4 4 2 3 the names of the rows can be retrieved with rownames and the names of the columns with colnames gt rownames matr 1 row1 row2 row3 row4 gt colnames matr 1 coli col2 col13 and these names can be indirectly used for sub setting gt matr 1 which colnames matr

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