Chapter 1: Getting Started
Contents
1. main paste Tukey Mean Difference Q Q Plot for 1 11 A Tutorial 17 nReference Area TcCB Fitted to Lognormal Distribution sep Normal Q Q Plot for Log Transformed Reference Area TcCB Data Quantiles of log TcCB ppb 0 5 0 0 I i 1 0 1 5 T T T T T 2 1 0 1 2 Quantiles of Normal mean 0 sd 1 Figure 1 6 Normal Q Q plot for the log transformed Reference area TcCB data Tukey Mean Difference Q Q Plot for Reference Area TcCB Fitted to Lognormal Distribution oT Or o Oo 2 E g gt ie o o 3 o g o o o o 2000 ir 05 ooo b Seo ayoa 220o A i oo o o o Z o no 2 O w S4 2 j T T T T 1 5 1 0 0 5 0 0 Mean of Observed and Fitted Quantiles Figure 1 7 Tukey mean difference Q Q plot for the Reference area TcCB data fitted to a lognormal distribution 18 1 Getting Started 1 11 6 Estimating Distribution Parameters In ENVIRONMENTALSTATS for S PLUS you can estimate parameters for several parametric distributions For example for the lognormal distribution you can estimate the mean and standard deviation based on the log transformed data or you can estimate the mean and coefficient of variation based on the original data For either parameterization you can compute a confidence interval for the mean Here are the results for the log transformed Reference area TcCB data Results of Distribution Parameter Assumed Distribution Estimat2. 0 9789915 Test Statistic Parameter n 47 P value 0 5512532 Alternative Hypothesis True cdf does not equal Lognormal Distribution ENVIRONMENTALSTATS for S PLUS also contains a plotting method for the results of goodness of fit tests as well as a function or menu choice to produce four summary plots on one page as shown in Figure 1 8 Menu To perform the Shapiro Wilk goodness of fit test for lognormality on the Refer ence area TcCB data and produce a summary plot of the results follow these steps 1 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt Hypothesis Tests gt GOF Tests gt One Sam ple gt Shapiro Wilk This will bring up the Shapiro Wilk GOF Test dialog box 2 For Data to Use select Pre Defined Data For Data Set make sure epa 94b tccb df is selected for Variable select TeCB and in the Sub set Rows with box type Area Reference In the Distribution box select Lognormal 3 Click on the Plotting tab Under Plotting Information in the Signifi cant Digits box select 3 then click OK or Apply Command To perform the Shapiro Wilk goodness of fit test for lognormality on the Refer ence area TcCB data type these commands 1 11 A Tutorial 21 gt TcCB ref lt TcCB Area Reference gt sw list lt sw gof TcCB ref dist lnorm gt sw list To produce a summary plot of the results type this command gt plot gof summary sw list digits 3 Results of Shapir
3. This User s Manual concentrates on statistical methods to analyze chemical concentrations and physical parameters usually in the context of mandated environmental monitoring Environmental statistics is a special field of statistics Probability and statis tics deal with situations in which the outcome is not certain They are built upon the concepts of a population and a sample from the population Probability deals with predicting the characteristics of the sample given that you know the characteristics of the population e g the probability of picking an ace out of a deck of 52 well shuffled standard playing cards Statistics deals with inferring 2 1 Getting Started the characteristics of the population given information from one or more sam ples from the population e g after 100 times of randomly choosing a card from a deck of 20 unknown playing cards and then replacing the card in the deck no ace has appeared therefore the deck probably does not contain any aces The field of environmental statistics is relatively young and employs several statistical methods that have been developed in other fields of statistics such as sampling design exploratory data analysis basic estimation and hypothesis test ing quality control multiple comparisons survival analysis and Monte Carlo simulation Nonetheless special problems have motivated innovative research and both traditional and new journals now report on statistical methods t
4. adding the line module envstats to your First function If you do not have a First function you can create one by simply typing the following command gt First lt function module envstats If you want to automatically attach the ENVIRONMENTALSTATS for S PLUS module each time you start S PLUS and start the ENVIRONMENTALSTATS for S PLUS help system make sure your First function includes the following lines 1 10 Unloading Environmental Stats for S Plus 7 module envstats help module envstats If you are going to use ENVIRONMENTALSTATS for S PLUS for several differ ent projects it is a good idea to use separate directories for each project See the S PLUS documentation for how to create separate Chapters and have S PLUS ask you which directory you want to work in when you start S PLUS 1 10 Unloading ENVIRONMENTALSTATS for S PLUS To remove the ENVIRONMENTALSTATS for S PLUS module from your S PLUS session S PLUS Professional users can simply type the following command at the S PLUS prompt gt module envstats unload T This command removes the ENVIRONMENTALSTATS for S PLUS menu from the S PLUS menu bar and the library of ENVIRONMENTALSTATS for S PLUS func tions from your search list 1 11 A Tutorial This section is a brief tutorial that highlights some of the major features of ENVIRONMENTALSTATS for S PLUS There are several ways to use this section If you are fairly new to S PLUS you may want t
5. color green or blue or whatever color your help system uses for jumps are jumps to other help windows within the ENVIRONMENTALSTATS for S PLUS help system In each help file if a word appears under the paragraph heading SEE ALSO but is not underlined and highlighted you must use the S PLUS help system to look up this word For example in the help system for ENVIRONMENTALSTATS for S PLUS in the Table of Contents choose Functions gt Functions by Category This will bring up the help file EnvironmentalStats for S PLUS Functions By Category Click on Plotting Probability Distributions and then click on pdfplot Within that help file under the paragraph heading SEE ALSO you will see Distribution frame Probability Distributions and Random Numbers cdfplot ecdfplot gqqplot aqqplot gestalt plot plot default par title You can access the help files for Distribution frame Probability Distributions and Random Numbers cdfplot ecdfplot qqplot and qqplot gestalt directly by simply clicking on these words To look at the help file for the functions plot plot default par and title however you must use the S PLUS help system 1 9 Customizing ENVIRONMENTALSTATS for S PLUS If you plan to use ENVIRONMENTALSTATS for S PLUS extensively you may want to customize your S PLUS startup routine to automatically attach the ENVIRONMENTALSTATS for S PLUS module each time you start S PLUS S PLUS Professional users can do this by
6. for Reference Area TcCB Data To produce the quantile plot shown in Figure 1 4 comparing the Reference area TcCB data to a lognormal distribution type the following command gt cdf compare TcCB Area Reference dist l1norm xlab Order Statistics for Reference Area TcCB ppb main paste Empirical CDF for Reference Area TcCB solid line n with Fitted Lognormal CDF dashed line sep To produce the quantile plot shown in Figure 1 5 comparing the log transformed Reference area TcCB data to the log transformed Cleanup area TcCB data type the following command gt cdf compare log TcCB Area Reference log TcCB Area Cleanup xlab Order Statistics for log TcCB ppb main paste CDF for Reference Area solid line with CDF for Cleanup Area dashed line sep n 16 1 Getting Started 1 11 5 Assessing Goodness of Fit with Quantile Quantile Plots Figure 1 6 displays the normal Q Q plot for the log transformed Reference area TcCB data i e we are assuming these data come from a lognormal distribu tion along with a fitted least squares line Figure 1 7 displays the correspond ing Tukey mean difference Q Q plot As we saw with the quantile plot the log normal model appears to be a fairly good fit to these data Menu To create the normal Q Q plot for the log transformed Reference area data shown in Figure 1 6 follow these steps 1 In the Object Explorer h
7. m 77 n 47 quantile ub 0 928 P value 0 01136926 Note that the Wilcoxon rank sum test is not significant at the 0 10 level p 0 88 while the quantile test is significant at the 0 011 level The quantile test picked up the portion of large outlying values in the Cleanup area data Menu To perform the Wilcoxon rank sum test follow these steps 1 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt Hypothesis Tests gt Compare Samples gt Two Samples gt Linear Rank Test This will bring up the Two Sample Lin ear Rank Test dialog box For Data Set select epa 94b tecb df For Variable 1 select TcCB for Variable 2 select Area and check the box that says Variable 2 is a Grouping Variable For Test select Wilcoxon and for Shift Type select Location Under Alternative Hypothesis select greater then click OK or Apply To perform the quantile test follow these steps 1 2 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt Hypothesis Tests gt Compare Samples gt Two Samples gt Quantile Test This will bring up the Two Sample Quantile Test dialog box For Data Set select epa 94b tccb df For Variable select TeCB for Variable 2 select Area and check the box that says Variable 2 is a Grouping Variable Under Alternative Hypothesis select greater For Specify Target select Rank and for Target Rank type 9 then click OK or Apply Command To perform the Wilcoxo
8. numerous built in data sets from regulatory guidance documents and the en vironmental statistics literature ENVIRONMENTALSTATS for S PLUS combined with S SPATIALSTATS and S PLUS for ArcView GIS provide the environmental scientist statistician researcher and technician with all the tools needed to get the job done Because ENVIRONMENTALSTATS for S PLUS is an S PLUS module you automatically have access to all the features and functions of S PLUS including easy to use pull down menus powerful graphics standard hypothesis tests and the flexibility of a programming language In addition with ENVIRONMENTALSTATS for S PLUS you can 1 4 Intended Audience Users 3 e Compute quantities associated with probability distributions probabil ity density functions cumulative distribution functions and quantiles and generate random numbers from these distributions Several distributions have been added to the ones already available in S PLUS e Plot probability distributions so you can see how they change with the value of the distribution parameter s e Compute several different kinds of summary statistics e Estimate distribution parameters and quantiles and compute confidence intervals for commonly used probability distributions e Perform and plot the results of goodness of fit tests e Compute optimal Box Cox data transformations e Compute parametric and non parametric prediction and tolerance inter vals including simultane
9. the mean for the Cleanup area is much larger indicating a few or more outlying observations with large values This may be indicative of re sidual contamination that was missed during the cleanup process Menu To produce summary statistics for the original TcCB data using the ENVIRONMENTALSTATS pull down menu follow these steps 1 Open the Object Explorer If epa 94b tccb df is not visible in the Ob ject Column click on the Find S PLUS Objects button the binoculars icon and in the Pattern box type epa 94b tccb df then click OK 2 Highlight the shortcut epa 94b tccb df in the Object column of the Ob ject Explorer 3 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt EDA gt Summary Statistics This will bring up the Full Summary Statistics dialog box 4 In the Data Set box select or type epa 94b tccb df is selected In the Variable s box choose TeCB In the Grouping Variables box select Area 5 Click OK or Apply Command To produce summary statistics for the original TcCB data using the S PLUS Command or Script Window type this command gt full summary split TcCB Area 1 11 3 Looking at the TcCB Data with Histograms and Boxplots Figure 1 1 shows the histograms for the TcCB concentrations in the Reference and Cleanup areas Figure 1 2 shows side by side boxplots comparing the dis tribution of TcCB concentrations in the two areas Both graphs display concen trations on the l
10. 03307 qmle TcCB Area Reference 47 90 th Sile Exact two sided 95 LCL 0 8358791 UCL 1 215498 1 11 A Tutorial 23 1 11 9 Comparing Two Distributions Using Nonparametric Tests ENVIRONMENTALSTATS for S PLUS contains menu items and functions for per forming general two sample linear rank tests to test for a shift in location and a special quantile test that tests for a shift in the tail of one of the distributions In this example we will compare the Reference and Cleanup area TcCB data Here are the results for the Wilcoxon rank sum test Results of Hypothesis Test Null Hypothesis Fy t Fx t Alternative Hypothesis Fy t gt Fx t for at least one t Test Name Two Sample Linear Rank Test Wilcoxon Rank Sum Test Based on Normal Approximation Data x TcCB Area Cleanup y TcCB Area Reference Sample Sizes nx 77 ny 47 Test Statistic z 1 171872 P value 0 8793758 and here are the results for the quantile test Results of Hypothesis Test Null Hypothesis e 0 Alternative Hypothesis Tail of Fx Shifted to Right of Tail of Fy 0 lt e lt 1 where Fx t l e Fy t e Fz t Fz t lt Fy t for allt and Fy Fz Test Name Quantile Test Data x TcCB Area Cleanup y TcCB Area Reference Sample Sizes nx 77 ny 47 24 1 Getting Started Test Statistics k x obs of r largest 9 xr 9 Test Statistic Parameters
11. 1 Getting Started 1 1 Introduction Welcome to ENVIRONMENTALSTATS for S PLUS This User s Manual provides step by step guidance to using this software ENVIRONMENTALSTATS for S PLUS is an S PLUS module for environmental statistics This chapter is an in troduction to environmental statistics in general and ENVIRONMENTALSTATS for S PLUS in particular and includes information on system and user requirements installing the software loading and using the module and getting technical sup port The last section of the chapter is a tutorial 1 2 What is Environmental Statistics Environmental statistics is simply the application of statistical methods to prob lems concerning the environment Examples of activities that require the use of environmental statistics include e Monitoring air or water quality e Monitoring groundwater quality near a hazardous or solid waste site e Using risk assessment to determine whether a potentially contaminated area needs to be cleaned up and if so how much e Assessing whether a previously contaminated area has been cleaned up according to some specified criterion e Using hydrological data to predict the occurrences of floods The term environmental statistics must also include work done in various branches of ecology such as animal population dynamics and general ecological modeling as well as other fields such as geology chemistry epidemiology oceanography and atmospheric modeling
12. B ppb ylab Number of Observations main Histogram for Cleanup Area To produce the boxplots shown in Figure 1 2 using the S PLUS Command or Script Window type these commands gt boxplot split log TcCB Area xlab Area ylab log TcCB ppb main Boxplots for Log Transformed TcCB Data 1 11 4 Quantile Empirical CDF Plots Figure 1 3 shows the quantile plot also called the empirical cumulative distribu tion function cdf plot for the Reference area TcCB data You can easily pick out the median as about 0 55 ppb and the quartiles as about 0 4 ppb and 0 75 ppb compare these numbers to the ones listed on page 8 You can also see that the quantile plot quickly rises then pretty much levels off after about 0 8 ppb which indicates that the data are skewed to the right see the histogram for the Refer ence area data in Figure 1 1 Figure 1 4 shows the quantile plot with a fitted lognormal distribution We see that the lognormal distribution appears to fit these data quite well Figure 1 5 compares the empirical cdf for the Reference area with the empirical cdf for the Cleanup area for the log transformed TcCB data As we saw with the histo grams and boxplots the Cleanup area has quite a few extreme values compared to the Reference area Cumulative Probability Cumulative Probability 1 0 0 8 0 6 il 0 4 0 2 0 0 1 0 0 8 0 6 0 4 0 2 0 0 1 11 A Tutorial Quantile Plot for
13. K To produce the quantile plot shown in Figure 1 4 comparing the Reference area TcCB data to a lognormal distribution follow these steps 1 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt EDA gt CDF Plot gt Compare Two CDFs This will bring up the Compare Two CDFs dialog box 1 11 A Tutorial 15 2 The Data Set box should display new epa 94b tccb df In the x Vari able box choose TcCB In the Subset Rows with box type Area Reference Under the Distribution Information Group make sure that the Estimate Parameters box is checked In the Distri bution box select Lognormal 3 Click OK or Apply To produce the quantile plot shown in Figure 1 5 comparing the log transformed Reference area TcCB data to the log transformed Cleanup area TcCB data follow these steps 1 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt EDA gt CDF Plot gt Compare Two CDFs This will bring up the Compare Two CDFs dialog box 2 For the Compare Data to choice select Other Data The Data Set box should display new epa 94b tccb df In the Variable 1 box choose log TcCB In the Variable 2 box choose Area Click on the Variable 2 is a Grouping Variable box to check it 3 Click OK or Apply Command To produce the quantile plot of the Reference area TcCB data shown in Figure 1 3 type the following command gt ecdfplot TcCB Area Reference xlab TcCB ppb main Quantile Plot
14. Reference Area TcCB Data 1 0 2 T T T T T 0 4 0 6 0 8 TcCB ppb Figure 1 3 Quantile plot of Reference area TcCB data Empirical CDF for Reference Area TcCB solid line with Fitted Lognormal CDF dashed line T T T T T 0 6 0 8 1 0 Order Statistics for Reference Area TcCB ppb 13 Figure 1 4 Empirical cdf of Reference area TcCB data compared to a lognormal cdf 14 1 Getting Started CDF for Reference Area solid line with CDF for Cleanup Area dashed line Pe a 0 6 1 1 s Cumulative Probability 0 4 T T T T 2 0 2 4 Order Statistics for log TcCB ppb Figure 1 5 Quantile plots comparing log transformed TcCB data at the Reference and Cleanup areas Menu To produce the quantile plot of the Reference area TcCB data shown in Figure 1 3 using the ENVIRONMENTALSTATS for S PLUS pull down menu follow these steps 1 In the Object Explorer highlight the Data folder in the left hand col umn In the right hand Object column highlight the shortcut new epa 94b tccb df for the version of this data frame that you created earlier 2 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt EDA gt CDF Plot gt Empirical CDF This will bring up the Plot Empirical CDF dialog box 3 The Data Set box should display new epa 94b tccb df In the Vari able s box choose TeCB In the Subset Rows with box type Area Reference 4 Click O
15. S PLUS To start ENVIRONMENTALSTATS for S PLUS you must have already started S PLUs You can load the module either from the menu or from the Command Window e To load the module from the menu on the S PLUS menu bar make the following selections File gt Load Module This brings up the Load Module dialog box In the Module box select envstats For the Ac tion buttons select Load Module Make sure the Attach at top of search list box is checked Click OK e To load the module from the Command Window type module envstats at the S PLUS prompt Loading the module adds the EnvironmentalStats menu to the S PLUS menu bar and also attaches the library of ENVIRONMENTALSTATS for S PLUS functions to the second position in your search list S PLUS Professional users can type search at the S PLUS prompt to see the listing of directories on the search list S PLUS Standard and S PLUS Professional users can access functions via the ENVIRONMENTALSTATS for S PLUS pull down menu S PLUS Professional users can access any of the functions in the ENVIRONMENTALSTATS for S PLUS module via the command line as well Note Some of the functions in ENVIRONMENTALSTATS for S PLUS mask built in S PLUs functions The masked functions are modified versions of the built in functions and have been created to support the other functions in ENVIRONMENTALSTATS for S PLUS but the modifications should not affect normal use of S PLUS If you experience unexpected behavior
16. e Function box choose log Click on the Add button then click OK At this point you will get a warning message telling you that you have created a new copy of the data frame epa 94b tccb df that masks the original copy Close the message window Also the modified data frame pops up in a data window Close the data window In the left hand column of the Object Explorer click on the Data folder In the right hand column of the Object Explorer right click on epa 94b tccb df and choose Properties In the Name box rename this data frame to new epa 94b tccb df and click OK To produce the histograms shown in Figure 1 1 using the S PLUS pull down menus or toolbars follow these steps 1 In the Object Explorer highlight the Data folder in the left hand col umn In the right hand Object column left double click the shortcut new epa 94b tccb df This will bring up a data window On the S PLUS menu bar make the following menu choices Graph gt 2D Plot This will bring up the Insert Graph dialog box Un der the Axes Type column Linear should be highlighted Under the Plot Type column select Histogram and click OK Alternatively left click on the 2D Plots button then left click on the Histogram but ton The Histogram Density dialog box should appear Under the Data Col umns group in the Data Set box select new epa 94b tccb df Under the Data Columns group in the x Columns box choose log TcCB Click on the Options tab Under Histo
17. ed Parameter s Estimation Method Data Sample Size Confidence Interval for Confidence Interval Method Confidence Interval Type Confidence Level Confidence Interval Estimation Lognormal meanlog 0 6195712 sdlog 0 467953 mvue TcCB Area Reference 47 meanlog Exact two sided 95 LCL 0 7569673 UCL 0 4821751 and here are the results for the original Reference area TcCB data Results of Distribution Parameter Estimation Assumed Distribution Estimated Parameter s Estimation Method Data Sample Size Confidence Interval for Lognormal mean 0 5989072 cv 0 4899539 mvue TcCB Area Reference 47 mean 1 11 A Tutorial 19 Confidence Interval Method Land Confidence Interval Type two sided Confidence Level 95 Confidence Interval LCL 0 5243786 UCL 0 7016992 Menu To compute the estimated mean and standard deviation for the log transformed Reference area TcCB data follow these steps 1 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt Estimation gt Parameters This will bring up the Estimate Distribution Parameters dialog box 2 For Data to Use make sure the Pre Defined Data button is selected In the Data Set box select or type epa 94b tccb df In the Variable box select TcCB In the Subset Rows with box type Area Reference 3 In the Distribution Estimation
18. gram Specs in the Output Type box select Density For Lower Bound type 2 5 For Interval Width type 0 5 Click OK A histogram of the data for both areas is displayed in a graphsheet Click on the data window to bring it forward Left click on the top of the Area column to highlight that column then left click in a cell of the column then drag the column to the top of the graphsheet and drop it To produce the boxplots shown in Figure 1 2 using the S PLUS pull down menus or toolbars follow these steps 1 On the S PLUS menu bar make the following menu choices Graph gt 2D Plot This will bring up the Insert Graph dialog box Un der the Axes Type column Linear should be highlighted Under the Plot Type column select Boxplot and click OK Alternatively left click on the 2D Plots button then left click on the Box button 12 1 Getting Started 2 The Boxplot dialog box should appear The Data Set box should dis play new epa 94b tccb df In the x Columns box choose Area In the y Columns box choose log TcCB 3 Click OK Command To produce the histograms shown in Figure 1 1 using the S PLUS Command or Script Window type these commands gt par mfrow c 2 1 gt hist log TcCB Area Reference xlim range log TcCB xlab log TcCB ppb ylab Number of Observations main Histogram for Reference Area gt hist log TcCB Area Cleanup xlim range log TcCB nclass 25 xlab log TcC
19. has to make sense of environmental data including statisticians environmental scientists hydrologists soil scientists atmospheric scientists geochemists environmental engineers and consultants hazardous and solid waste site managers and regulatory agency analysts and enforcement officers Some parts of ENVIRONMENTALSTATS for S PLUS incorporate statistical meth 4 1 Getting Started ods that have appeared in the environmental literature but are not commonly found in any statistical software package Some parts are specifically aimed at users who are required to collect and analyze environmental monitoring data in order to comply with federal and state Superfund RCRA CERCLA and Subti tle D regulations for environmental monitoring at hazardous and solid waste sites All of the functions in ENVIRONMENTALSTATS for S PLUS however are useful to anyone who needs to analyze environmental data ENVIRONMENTALSTATS for S PLUS is an S PLUS module In order to use it you need to know how to perform basic operations in S PLUS such as using the pull down menu or Command and Script Windows reading data into S PLUS and creating basic data objects e g data frames See the S PLUS documenta tion for more information on S PLUS In addition you need to have a basic knowledge of probability and statistics The User s Manual and the help system are not meant to be a text book in environmental statistics See the references listed in References Envi
20. hat have been developed in the context of environmental monitoring See the help topic References Environmental Statistics General References for a list of general text books on environmental statistics In addition environmental legislation such as the Clean Water Act the Clean Air Act the Comprehensive Emergency Response Compensation and Liability Act CERCLA and the Resource and Recovery Act RCRA have spawned environmental regulations and agency guidance documents that man date or suggest various statistical methods for environmental monitoring see the help topic References Guidance Documents and Regulations 1 3 What is ENVIRONMENTALSTATS for S PLUS ENVIRONMENTALSTATS for S PLUS created by Dr Steven P Millard of Prob ability Statistics amp Information PSD is a new comprehensive software package for environmental statistics An add on module to the statistical software pack age S PLUS from Insightful Corporation it provides a set of powerful yet sim ple to use menu items and functions for performing graphical and statistical analyses of environmental data ENVIRONMENTALSTATS for S PLUS brings the major environmental statistical methods found in the literature and regulatory guidance documents into one statistical package along with an extensive hyper text help system that explains what these methods do how to use these methods and where to find them in the environmental statistics literature Also included are
21. ighlight the Data folder in the left hand col umn In the right hand Object column highlight the shortcut epa 94b tccb df 2 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt EDA gt Q Q Plot gt Q Q Plot This will bring up the Q Q Plot dialog box 3 The Data Set box should display epa 94b tccb df In the x Variable box choose TcCB In the Subset Rows with box type Area Reference In the Distribution box make sure Lognormal is selected 4 Click on the Plotting tab Click on the Add a Line box to select this option 5 Click OK or Apply To create the Tukey mean difference Q Q plot for the Reference area TcCB data fitted to a normal distribution shown in Figure 1 7 follow the same steps as above but in Step 3 also check the Estimate Parameters box and in Step 4 un der Plot Type select Tukey M D Command To produce the Q Q plot of the Reference area TcCB data fitted to a lognormal distribution shown in Figure 1 6 type the following command gt qqplot TcCB Area Reference dist l1norm add line T ylab Quantiles of log TcCB ppb main paste Normal Q Q Plot for Log Transformed Reference Area TcCB Data To create the Tukey mean difference Q Q plot for the Reference area data fitted to a lognormal distribution shown in Figure 1 7 type the following command gt qqplot TcCB Area Reference dist l1norm plot type Tukey estimate params T add line T
22. lars icon type epa 94b tccb df and click OK In the Object Explorer Window under the Object column double click on epa 94b tccb df This will bring up a data sheet Alternatively in the Com mand Window type epa 94b tccb df gt epa 94b tccbh df TcCB orig TcCB Censored Area 1 0 22 0 22 F Reference 2 0 23 0 23 F Reference 124 168 64 168 64 F Cleanup For the remainder of this tutorial we will assume that you have attached the data frame epa 94b tccb df to your search list with the following com mand gt attach epa 94b tcch df Note that if you are only going to follow the instructions for using the Menu you do not have to execute the above command 1 11 2 Computing Summary Statistics The summary statistics for the TcCB data are shown below Cleanup Referenc Sample Size 77 47 Missing 0 0 Mean 3 925 0 5985 Median 0 43 0 54 10 Trimmed Mean 0 6846 0 5728 Geometric Mean 0 5784 0 5382 Skew 7 717 0 9019 Kurtosis 62 67 0 132 Min 0 09 0 22 Max 168 6 133 Range 168 6 dell lst Quartile 0 23 0 39 3rd Quartile 1 1 0 75 Standard Deviation 20 02 0 2836 Geometric Standard Deviation 3 898 1 597 Interquartile Range 0 87 0 36 Median Absolute Deviation 023558 0 2669 Coefficient of Variation 5411 2 0 4739 1 11 A Tutorial 9 These summary statistics indicate that the observations for the Cleanup area are extremely skewed to the right The medians for the two areas are about the same but
23. n rank sum test type this command gt wilcox test TcCB Area Cleanup TcCB Area Reference alternative greater or this command gt two sample linear rank test TcCB Area Cleanup TcCB Area Reference alternative greater 1 12 Summary 25 Note that by default the S PLUS function wilcox test computes the cor rected z Statistic while the ENVIRONMENTALSTATS for S PLUS function two sample linear rank test computes the uncorrected z statistic To perform the quantile test type this command gt quantile test TcCB Area Cleanup TcCB Area Reference alternative greater target r 9 1 12 Summary Environmental statistics is the application of statistics to environmental problems ENVIRONMENTALSTATS for S PLUS is an S PLUS module for environ mental statistics It includes several menu items and functions for cre ating graphs and performing statistical analyses that are commonly used in environmental statistics To use ENVIRONMENTALSTATS for S PLUS you should be familiar with the basic operation of S PLUS and have an elementary knowledge of probability and statistics ENVIRONMENTALSTATS for S PLUS has an extensive help system that includes basic explanations in English as well as equations and refer ences
24. o Wilk GOF Test for TcCB ref Histogram of Observed Data Empirical CDF for TcCB ref solid line with Fitted Lognormal Distribution with Fitted Lognormal CDF dashed line 2J wo Bo roy Bo 5 Ep E S ii v D aE Z Bol So 5 ee Ea Ooo 2 2 o c T T T T T 1 oL T T T T T 0 2 0 4 0 6 0 8 1 0 1 2 1 4 0 2 0 4 0 6 0 8 1 0 1 2 TcCB ref Order Statistics for TcCB ref and Lognormal meanlog 0 62 sdlog 0 468 Distribution Quantile Quantile Plot Results of Shapiro Wilk GOF with 0 1 Line Hypothesized T o Distribution Lognormal a o 0020 Estimated Parameters meanlog 0 62 Qs sdlog 0 468 5 Data TcCB ref 2 Sample Size 47 3 Test Statistic W 0 979 2 Test Statistic Parmeter n 47 s 50 P value 0 551 ej wo 1 1 5 1 0 0 5 0 0 0 5 Quantiles of Normal mean 0 62 sd 0 468 Figure 1 8 Summary plots of Shapiro Wilk goodness of fit test for Reference area TcCB data 1 11 8 Estimating Quantiles and Computing Confidence Limits ENVIRONMENTALSTATS for S PLUS contains a menu item and functions for es timating quantiles and optionally constructing confidence limits for the quan tiles Here we will estimate the 90 percentile of the distribution of the Refer ence area TcCB assuming the true distribution is a lognormal distribution and compute a 95 confidence interval for this 90 percentile Menu To estimate the 90 percentile and compute a two sided 95 confidence inter val for this
25. o briefly skim this section to get an idea of what you can do in ENVIRONMENTALSTATS for S PLUS and then come back later after you have read the other chapters of this manual If you have used S PLUS for a long time and have just installed ENVIRONMENTALSTATS for S PLUS you may want to follow this tutorial in depth right now to get ac quainted with some of the features available in this S PLUS module Throughout this section we assume you have started S PLUS and also loaded ENVIRONMENTALSTATS for S PLUS 1 11 1 The TcCB Data The guidance document Statistical Methods for Evaluating the Attainment of Cleanup Standards Volume 3 Reference Based Standards for Soils and Solid Media USEPA 1994b pp 6 22 6 25 contains measures of 1 2 3 4 Tetrachlorobenzene TcCB concentrations ppb from soil samples at a Refer ence site and a Cleanup area There are 47 observations from the Reference site and 77 in the Cleanup area These data are stored in the data frame epa 94b tccb df see the help file Datasets USEPA 1994b There is one observation coded as ND in this data set as presented in the guidance document Here we ll assume this observation is less than the smallest ob 8 1 Getting Started served value which is 0 09 ppb For the purposes of this tutorial we ll set this one censored observation to the assumed detection limit of 0 09 To look at the raw data open the Object Explorer Window click on the Find Objects button binocu
26. of S PLUS after attaching ENVIRONMENTALSTATS for S PLUS try unloading the module see Unloading ENVIRONMENTALSTATS for S PLUS below All of the functions in ENVIRONMENTALSTATS for S PLUS whether they mask built in functions or not are described in the help system 1 8 Getting Help You may start the help system for ENVIRONMENTALSTATS for S PLUS in one of five ways 1 On the menu bar select Help gt Available Help gt EnvironmentalStats 2 On the menu bar go to the EnvironmentalStats menu and select an item A dialog box will be displayed In the lower right hand corner click on the Help button At the command line type he lp module envstats 4 At the command line use the operator and help function just as you do in S PLus For example type pdfplot to call up the help file for the pdfplot function W 6 1 Getting Started 5 Outside of S PLUS select Start gt Programs gt S PLUS 6 0 Profes sional gt EnvironmentalStats or in the S PLUS program group double click the ENVIRONMENTALSTATS icon In the Table of Contents you will see the main help categories including Pull Down Menu Functions Datasets References and Glossary You can ac cess the help files for functions by category or alphabetically and you can ac cess data sets by source or alphabetically The help system for ENVIRONMENTALSTATS for S PLUS is a separate appli cation from the help system for S PLUS Words that are underlined and high lighted in
27. og scale We see in these plots that most of the observations in the Cleanup area are comparable to or even smaller than the observations in the Reference area but there are a few very large outliers in the Cleanup area Menu To produce the histograms and boxplots for the log transformed TcCB data us ing the S PLUS pull down menu it will simplify things if we first make a new data frame called new epa 94b tccb df to contain the original data and the log transformed TcCB observations To create the data frame new epa 94b tccb df follow these steps 10 Number of Observations Number of Observations Figure areas log TcCB ppb 1 Getting Started Histogram for Reference Area 2 o Histogram for Cleanup Area 7 Wikin h mE a m E t r r 2 0 2 log TcCB ppb 6 4 2 2 4 log TcCB ppb 6 4 2 1 1 Histograms comparing TcCB concentrations at Reference and Cleanup Boxplots for Log Transformed TcCB Data i o VA es Se Se Tash Cleanup Reference Area Figure 1 2 Boxplots comparing TcCB concentrations at Reference and Cleanup areas 1 11 A Tutorial 11 Highlight the shortcut epa 94b tccb df in the Object column of the Ob ject Explorer On the S PLUS menu bar make the following menu choices Data gt Transform This will bring up the Transform dialog box In the Target Column box type log TcCB In the Variable box choose TcCB In th
28. ous prediction intervals e Perform additional hypothesis tests not already part of S PLUS includ ing Chen s t test for skewed distributions Fisher s one sample ran domization test for location the quantile test to detect a shift in the tail of one population relative to another two sample linear rank tests the von Neumann rank test for serial correlation and Kendall s seasonal test for trend e Perform power and sample size computations and create associated plots e Perform calibration based on a machine signal to determine decision and detection limits and report estimated concentrations along with confidence intervals e Analyze singly and multiply censored less than detection limit data with empirical cdf and Q Q plots parameter quantile estimation and confidence intervals prediction and tolerance intervals goodness of fit tests optimal Box Cox transformations and two sample rank tests e Perform probabilistic risk assessment e Look up statistical methods in the environmental literature in a hyper text help system that explains the equations links the equations to the original reference includes abstracts of selected references and con tains a glossary of statistical and environmental terms e Reproduce specific examples in EPA guidance documents by using built in data sets from these documents 1 4 Intended Audience Users ENVIRONMENTALSTATS for S PLUS and this User s Manual are intended for any one who
29. percentile follow these steps 22 1 Getting Started 1 On the S PLUS menu bar make the following menu choices EnvironmentalStats gt Estimation gt Quantiles This will bring up the Estimate Distribution Quantiles dialog box 2 For Data to Use make sure the Pre Defined Data button is selected In the Data Set box select epa 94b tccb df In the Variable box select TcCB In the Subset Rows with box type Area Reference 3 Inthe Quantile s box select 0 90 4 Under the Distribution Estimation group for Type select the Para metric button In the Distribution box select Lognormal For Estima tion Method select qmle 5 Under the Confidence Interval group make sure the Confidence Inter val box is checked For CI Type select two sided For CI Method select exact For Confidence Level select 95 6 Click OK or Apply Command To estimate the 90 percentile and compute a two sided 95 confidence inter val for this percentile type this command gt eqlnorm TcCB Area Reference p 0 9 ci T Results of Distribution Parameter Estimation Assumed Distribution Estimated Parameter s Estimation Method Estimated Quantile s Quantile Estimation Method Data Sample Size Confidence Interval for Confidenc Confidence Interval Type Confidence Level Confidence Interval Interval Method Lognormal meanlog 0 6195712 sdlog 0 467953 mvue 90 th Sile 0 98
30. ronmental Statistics General References for a list of useful books and articles on this subject 1 5 System Requirements Because ENVIRONMENTALSTATS for S PLUS is an S PLUS module it runs under every operating system that S PLUS runs under including Windows and UNIX Currently only a Windows version is available Windows users must have S PLus 6 0 in order to run EnvironmentalStats for S PLUS Version 2 0 The module requires approximately 20 MB of space on your hard disk 1 6 Installing ENVIRONMENTALSTATS for S PLUS Before you install EnvironmentalStats for S PLUS you should make sure you are using S PLUS 6 0 or a later version To determine what version of S PLUS you are using start S PLUS and either choose Help gt About S PLUS on the menu or type version at the S PLUS prompt If you are using the Profes sional version of S PLUS for Windows you should see something like the fol lowing gt version Professional Edition Version 6 0 2 Release 2 for Microsoft Windows 2001 To install ENVIRONMENTALSTATS for S PLUS close all Windows applications and then simply run the Setup program included on the ENVIRONMENTALSTATS for S PLUs distribution CD To leave Setup before the setup is complete select Cancel from any Setup dialog box When you do this Setup displays an exit dialog box that warns you that you have not completed the setup procedure 1 7 Starting EnvironmentalStats for S Plus 5 1 7 Starting ENVIRONMENTALSTATS FOR
31. section in the Distribution box select Lognormal and for Estimation Method select mvue 4 Under the Confidence Interval section check the Confidence Interval box In the CI Type box select two sided In the CI Method box se lect exact In the Confidence Level box select 95 5 Click OK or Apply To compute the estimated mean and coefficient of variation for the original Reference area TcCB data follow the same steps above but in Step 3 for Distri bution select Lognormal Alternative and in Step 4 for CI Method select land Command To compute the estimated mean and standard deviation for the log transformed Reference area TcCB data type this command gt elnorm TcCB Area Reference ci T To compute the estimated mean and coefficient of variation for the original Ref erence area TcCB data type this command gt elnorm alt TcCB Area Reference cisT 1 11 7 Testing for Goodness of Fit ENVIRONMENTALSTATS for S PLUS contains several new or modified S PLUS menu items and functions for testing goodness of fit Here we will use the Shapiro Wilk test to test the adequacy of a lognormal model for the Reference area TcCB data 20 1 Getting Started Results of Goodness of Fit Test Test Method Shapiro Wilk GOF Hypothesized Distribution Lognormal Estimated Parameter s meanlog 0 6195712 sdlog 0 467953 Estimation Method mvue Data TcCB ref Sample Size 47 Test Statistic W
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