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Graphical Analysis Windows

1. Y Axis Options Column Appearance More Graph Options This option brings up the following dialog box for the X axis Choose the X variable and select a scaling method for this axis Axis Setup Choose which columns to plot 3 AutoScale at 0 D Grains O Manual Scaling Left Limit oS B i Right Limit This option brings up the following dialog box for the Y axis Choose the Y variable and select a scaling method for this axis Y Axis Setup Choose which columns to plot 3 AutoScale at 0 Oo Manual Scaling Top Limit Bottom Limit This option brings up the Column Options dialog box which is described under the Data menu item below The following dialog box appears when you select this option A variety of graph options can be set with this box as well options that apply to each data column Graph Options LJ Error Bars LJ Connecting Lines O Bar Graph LJ Background Grid O Legend Column Appearance Y More lt Axis Options Cancel More Axis Options 39 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Data Sort Data Fill Column New Data Set Clear All Data Help dow Graph WIELE Analyze z sort Data Eill Column New Data Set Clear All Data Column Options New Column Edit Column Definition Use this option to sort the data in ascending order based on any column except those calculated with derivatives or delta functions This ope
2. f ates LIRE LIAERE EINI KONEX IES LASERE ee LINEEI EE EE IX WELIT IE AEE TATA OREERT 36 Aa a LON EEEE E T E E T A A A tans A T TA EE EE A A 36 ge 0 EE ASEE EEEE tere nent AEE EEE EE enn E EEEE EE E EE EEEE AE EEE EEEE EEEE EE EEE E ET 37 Ate ein neal arene RENERE RENE RI KENI NERL ATIE HENE Matis HRs HENE NE NERES HRs NENON ONENERA EAN 40 ARAN ZO e ante anna neanconsenntsenisanasiracnounseasnsseayansauresnouonssenssuasmncanossnouansunnexcnauscencascemoescesnciatcnmaanctae 42 POD aoar a E E E E E E E 43 Graphical Analysis WiIndOWSsictiniieniicriic ceteris cinrierieniiiii ie 45 VAD La AAA E tase senstaondacedene dd agalbahabdh A A A E A E E E 45 Data Table nih a aaa 46 EEN O aE E E E A nee ins E A E vas A E E EE A ET 46 MSO Mr aO eea e a a a T T E E EE EEES 47 ERE aE A A E T E A A E A AA AA A ET 47 Program DESIGN NOTES ios AAAA 48 Questions about Graphical Analysis ccsseseecesnseeecennssecesnnseececnnseseecnssssecnnssseesaassseeenseeesanes 48 APPENDIX A FILES ON THE GRAPHICAL ANALYSIS DISK asnsnnnnnnnnnnnnnnnnnnnnnnnnnnnn 49 APPENDIX B OTHER VERNIER SOFTWARE PRODUCTS ssnssnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 51 Graphical Analysis for Windows How to Use this Manual This manual is divided into three main sections the User s Manual the Teacher s Guide and the Reference Section The User s Manual includes a quick introduction to the most important features of the program The Teacher s Guide co
3. portability and ease of use at an affordable price Not only can you use LabPro with a computer but you can also use it with a Texas Instruments Graphing Calculator When you use LabPro with a computer you have a choice of Windows or Macintosh computers and a choice of connecting it to a serial port or USB port If you use LabPro with a graphing calculator the calculator programs you need are stored within LabPro Texas Instruments CBL 2 is perfect for anyone who wants to collect data with a TI Graphing Calculator Within the classroom you can use the CBL 2 and a graphing calculator as a low cost alternative to computers for collecting and analyzing real world data The CBL 2 System includes the CBL 2 interface a new stainless steel temperature probe light probe voltage probe calculator cradle short link cable use s guide and a TI Resource CD The calculator programs you need are stored within the CBL 2 For a complete listing of our products including over 40 sensors please check out our web site www vernier com Books Chemistry with Calculators by Dan Holmquist and Donald L Volz A collection of 35 experiments using LabPro CBL 2 with TI graphing calculators and Vernier sensors Included are the word processing files for the student handouts on disk 35 00 Physical Science with Calculators by Donald L Volz and Sandy Sapatka A collection of 40 physical science experiments using LabPro CBL 2 with the TI 82 or TI 83 and Vernier
4. the Control box Delete data pairs Select the rows and then choose Delete Data from the Edit menu Delete a column or data set Click the title of the column or data set and choose Delete Column or Delete Data Set from the Edit menu Sort the data Select the header of the column by which the data is to be sorted then choose Sort Data from the Data menu Insert data pairs into the table Enter the data at the bottom of the data table then select the Sort Data option in the Data menu Select the appropriate column to sort by Generate numbers automatically for the data table Select a cell in the Data Table and then choose Fill Column from the Data menu to fill from that cell down Change the way the numbers are rounded Select Column Options from the Data menu Calculate statistics for a column of data Click the data table and select Data Table Options from the Window menu then check the Show Statistics box in the pop up menu that appears Interpolate or extrapolate from the regression line or Choose Interpolate from the Analyze menu fitted curve of the data Copy the title bar and border with a window Hold down the lt Ctrl gt key while selecting the Copy Window option from the Edit menu Load Data from a TI 73 TI 82 TI 83 TI 83 Plus TI Connect the TI GRAPH LINK cable Choose Import from 85 TI 86 TI 89 TI 92 or TI 92 Plus graphing TI Calculator on the File menu Link the data using the calculator standard cal
5. 1941 issue of the Physical Review lt P Rate cts s C gt 40 60 80 100 120 140 lt gt Time min lt gt 26 Graphical Analysis for Windows lt D Distance cm C gt S w 7 3 lt lt D Speed m s c gt lt P Distance m C gt ho n oa Qo ho oOo oOo Qo 1500 k o o t 2 mn oOo o Graph Window Distance vs Time 2 5 Incline Distance 1 0 Incline Distance 0 5 Incline Distance Regression M 9 60 0 36 misis B 0 63 0 08 mis COR 0 994 30 0 15 0 20 0 25 lt 2 Time s Graph Window Distance vs Time 40 50 60 70 lt D Time mI H20 C gt Graph Window Distance vs Time mi D 0 30 0 35 TEACHER S MANUA DVST DAT d c t This set of data is the distance traveled from rest for a glider sliding down an inclined air track Three different data sets are included for different angles of tilt The data was taken from Project Physics Resource Book p 48 1981 FFT DAT Frequency Analysis You can use this file to show an example of a fast Fourier Transform The file contains a triangle wave The corresponding FFT shows the frequency components of the wave and can be used to determine the component frequencies FREEFALL DAT v c t This file contains speed and time data for a freely falling golf ball The data came from a high school lab report Cheryl Duyck and Shelee Moore 1981 A strobe photograph was
6. 20 0 0 cccccccccceeccceececeeeesee cece cece cece eesea cess eeseaeeseeeseeeseeeseueeseuseseeeseueeseeesseeeesans 16 Sample Data Files ciccccscciseniceuiceudtacesiansansseuideudbecsiensbanesecieeddecsieusdeileuideeideaienceeme a A 18 OMErODPEraNON Sania EA en cates enes 19 TEACHER S MANUAL cenna ea apes a enc a aaa 20 ES Ere ALE o EEE EE EN EAEE E A S E E A S AN ENEN 20 Computer Redurre mene aictp ice it tactchetcinctohdaateineisinchaichdacidachdadicachdiaidaciadiahdadidadidbaidictdichdadidaciabaldididiahdicidens 20 Loading Graphical Analysis Onto Your Hard Drive cccccseccceececeeeeeeeeceeeeseeeseeeseeeesaueesaeeesaeeesaaees 20 Using Graphical Analysis in Science ClaSSes cccccseccsseeeeseceeseeceseeeneeceaseeeaseceneesenseseneeseneeseneesens 20 Using Modified Data to Show the Relationship between Variables cccccceccseecseeeeeeseeeeeeeeeeseeeseees 20 Modeling Data with EQuations cccccccccsccceecceeeceeecneeeceeeceueceuecseecseeseeceuecsueesueesaeecsuessuesseeeseesseeesagss 21 Determining Relationships with Three or More Variables ccccceeccecceeeeeeceeeneeeeeeseeneeeeeeseeeneeeeeeees 22 Student Use During Labs cc ceccccecccsecceeeeeeeeeeeseeeeeeeeeseeeeeeeeeeeeeseeeesaeeeseeesseeeseaeesseeessueesaueeseneeseueesaes 23 Going Over Lab Results saceletetulat edu tecetuiedieteenculasuel cutee E E E A EA A 23 Plotting Graphs During Demonstration LADS cccccceeccseceeeee
7. Cc ha co Cc i E S 3 5 i a L 30 40 50 60 fall i 0 4 0 6 lt 2 Angle of Incidence C gt lt 2 sini lt gt Snell s law angle r vs angle i Snell s law sin r vs sin I Modeling Data with Equations Another powerful technique available with this program is the fitting of a mathematical equation to data The following three graphs of the Snell s law data contain different fitted curves The first graph shows the data with a linear model 21 Graphical Analysis for Windows TEACHER S MANUAL fitted to the data The second graph used a quadratic function and the last graph used a sine function Notice that the sine function produced the smallest mean squared error Graph Window Graph Window le of Refraction vs Angle of Incidence le of Refraction vs Angle of Incidence y htx B y i Bex Otxa M 0 49500 B 3 9500 A 1 4607 B 0 61964 C 0 0036071 Mean Sar Err 2 84 Mean Sgr Err 0 104 to mm mm b Se lt 3 Angle of Refraction C gt lt D Angle of Refraction C gt mm 30 40 50 G 70 0 E 30 70 0 40 50 R D Angle of Incidence gt lt Angle of Incidence C gt Snell s law data fitted with a linear curve Snell s law data fitted with a quadratic curve Graph Window le of Refraction vs Angle of Incidence y A sinfk x F A 42 560 K 0 93378 P 0 37815 Mean Sgr Err 0 0238 t g 5 a mh a v 30 4
8. DOS The mass of each of 100 U S pennies was collected The date stamped on each penny was noted during the weighing process A histogram of the data shows two peaks This is a result of the U S Mint changing the composition of metals in the penny after 1982 2 6 2 8 3 0 Mass g 0 010 g bin Pa oR POSTAL1 DAT Postal Rates 1958 1982 This table lists the cost of mailing a one ounce letter via the U S Postal Service The x axis is the time of each rate increase The data was collected by Albert Bartlett The Physics Teacher May 1982 For this time period the growth of the postal rate was nearly exponential The graph can lead to some interesting discussion of future rates lt D Cost oz cents C gt 10 30 20 lt D Time years C gt EEEN 1958 1 981 POSTAL2 DAT Postal Rates 1885 1991 This is the same data as in the last sample with the earlier and later years included The whole table does not fit a simple exponential curve as well as the previous file lt gt Costioz cents CY 10 30 20 lt gt Time years C gt The postal increases to 0 22 in 1983 to 0 25 in 1988 and to 029 in 1991 were added to Dr Bartlett s data 28 Graphical Analysis for Windows lt D Angle of Refraction 9 c gt o lt gt Period s C gt lt P Distance cm gt co Qo ho oOo Graph Window Period vs Diameter Data Set 1 30 40 50 60 lt gt Angle of Incidence lt C
9. THIS MANUAL vce tees ceca eeteca ces wetcetawaten Gusvesauitatensncdevesaeretaveaucncctenstentecaecestaez 5 USER S MANUAL seicirstiiewie acct Gees teenie dean ewctee vesiveuateaw eines cana ie eusebaansawnaiussanseusuenncneesmensenndetoune 7 General Description of the Program and Built in Help ccccceeseeeseeeseeeaesenseeeseeeeeseaeeeneeenseeeeeseaes 7 Fast Start If you don t read Manual cccceceeeeeeeeneeeneeeneeceeeceneeeaeeeasecasseeaseeaseeasecanseoasesenesenssoneeons 8 Using the Graphical Analysis Programm cccsseccssecceseeceseecessenceneeceseeceseseaseeoasseeasesoaseeoneesonsesonnesonaes 8 EPICA 5 lh ON inde aot at veh a a e a iceatice cis actise cist aie etic dis ctise cisatce obec erases ce eee eee eet eee 8 eal gitelal ace pes ace EGNING gl Brel kc mermemeermeecmerrmertn per N 9 Editing the Axis Labels Units and Graph Title ccccccccccceeceeeeesececeeeteeeceueeseeseeesseetsueeaueeseeeseeeaues 9 Giangin ie Bis o aug F eaire S Or EAr ai e een Caen a a E EMME Teun O Een Mtn E mance ener ere 10 Changing the Scale Of a Graph cccccccccccsecccseeeeeeeeeseeeeseeeeeeeeeseeeeseeeeseeeeseeeeseeeeseeeeseeeeseeesseeeeseeeeseeeeas 10 ZOOMING Nona ara Ol eee ananassae laa a eee 10 ANAYSSI MOO lSisiwevatosicstecovedistosciaaeuemsaemenensaegencuiaeslanauinamiatmiaemgnwansmecmanstaastancianienauenamenmbpouynoisanauqantmninl 11 Displaying a Range of the Graph ccccccccseccceeceeeeeecee
10. Window Pressure vs Volume ha nm ja So ha So Co So nm ja So Io g IE i E F ja io Using Examine Data The Examine option works on any graph window When you are finished examining the data click the Examine button or deselect the Examine option from the Analyze menu To see the tangent line click the Tangent Line button and move the mouse across the graph As you do a tangent line will be drawn at each data point A floating box will also display the numeric value of the slope at that point To turn off the tangent line click the Tangent Line button or deselect the Tangent Line option in the Analyze menu The number of points used to calculate the slope is controlled in the Preferences option in the File menu To determine the integral click and drag the mouse across the region of interest on the graph then click the Integral button The area under the curve will be shaded and a box will display the numeric results The integral is calculated using the trapezoid method To remove this information and the shading from the graph click the small box in the upper left corner of the floating box The Regression Line button is used to calculate the best fit line for a selected curve or region of a curve To fit a regression line to a set of data click and drag the mouse across the entire graph then click the Regression Line button A best fit line will be drawn on the graph and a floating box will display
11. appears 34 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Save Save As Print Printer Setup Preferences Exit Use this option to save all current data sets and graphs together in one file This option will use the current file name and replace the previously saved file with the new file Use this option to save all current data sets and graphs together in a new file This option prompts you for a file name You can also choose the folder and disk where the file will be stored From this option you can choose to print the Data Table Selected Display or the Entire Screen The Data Table option will print the entire data table including rows not displayed in the window This option may produce many pages of paper The Selected Display option only prints that portion of a window displayed on the screen It can be used to print graphs data tables and other windows If you select this option for a large data table the entire data table may not appear To print a graph first select the graph by clicking it then select the Selected Display option To print the entire screen including all windows select the Whole Screen option If you have a Text window that contains more text than can fit in the window a scroll bar will appear on the right hand side of the window To print all the text you will need to click the Text window and select Copy Text from the Edit menu Paste the text in a word processor and print the tex
12. as educational to show that other modified graphs do not produce straight lines When you suspect the relationship to be of the general form Y c X an alternative way to find the relationship between variables is to use a log log graph Plot the natural log In of Y vs the natural log In of X by creating two new calculated columns of data This is useful because taking the natural log of both sides of the above equation produces In Y Inc ndinX This equation is in the general form y M x B if we treat In Y as y and In X as x Therefore if In Y is graphed vs In X the result will be a straight line with a slope of n and a y intercept of In c provided the relationship 1s of the general type that we are discussing Notice that this general type of equation includes many of the important relationships in science A In In graph of an inverse square relationship will produce a straight line with a slope of 2 A In In graph of Y x will produce a straight line with a slope of 0 5 It 1s interesting to determine the slope of the In In graph line by plotting the graph and including the linear regression line You and your students can experiment with several sample files on this disk e g GALILEO DAT DVST DAT COULOMB DAT TVSH DAT Exponential relationships of the form Y c e are also important in science and may be studied with the modified column technique If the constant k is positive the equation represents expone
13. ease of use at an affordable price Not only can you use LabPro with a computer but you can also use it with a Texas Instruments Graphing Calculator When you use LabPro with a computer you have a choice of Windows or Macintosh computers and a choice of connecting it to a serial port or USB port If you use LabPro with a graphing calculator the calculator programs you need are stored within LabPro Serial Box Interface Our Serial Box Interface is the low cost way to take data with your PC computer Plug the Serial Box Interface into the serial port of the PC computer connect your sensor s and graph temperature pH pressure heart rate light intensity voltage and more Use with any of the standard Vernier Software sensors with 5 pin DIN connectors May be powered by a battery pack mounted inside the box sold separately Serial Box Interface is 99 00 Software sold separately Universal Lab Interface The Universal Lab Interface for PC computers allows a wide variety of sensors and probes to be interfaced to PC computers Available sensors include motion detectors force sensors radiation monitors pH probes pressure sensors light sensors magnetic field sensors and microphones 220 Software sold separately For a complete listing of our products including over 40 sensors please check out our web site www vernier com Software Logger Pro is our all purpose data collection and analysis program It combines the features of most
14. functions to paste e are an equation into the field however you can enter any ner Ae Po asa f i ks Inverse equation you want using the variable X and any functions nMZ ileal ns B ower coefficients constants or exponents In the example to exp K x Exponential fl axpi E x Rewerse Exp the right the equation y A x42 1 x B has been entered If you enter your own equation the program determines the curve fit by trial and error It tries various values calculates the mean square error adjusts the values slightly and repeats the process You can watch the process as the program tries different values You may find it interesting to see how the curve moves gradually to the best possible fit As you experiment with curve fitting you might select the reverse exponential sine or Gaussian model These models do not have single closed forms In each case the best solution is calculated by trial and error This may take a considerable amount of time especially on a slow computer While the curve fitting calculations are being performed you can also click on any of the coefficients or exponents to suggest a better value This can speed up the curve fitting process and in a few cases may be necessary to help the curve fitting routine find a solution Throughout this process you will be able to watch the fitted curve as it is modified to fit the data Sample Data Files There are a number of sample data fil
15. graph to add features to the graph Click on the numbers at the ends of the axes to change the scaling Experiment with the Zoom buttons the Analyze button and the Tangent button Click and drag through a section of the graph to use the Integrate and Linear Regression button Choose New Window or Replace Window from the Window menu item to add new windows Choose Arrange Windows from the Window menu to rearrange the window layout Try the various menus Have fun experimenting If you have questions check the Built in help If all else fails remember there is a manual Using the Graphical Analysis Program Typical Screen Start up the program by double clicking on the Graphical Analysis icon Click the OK button in the About box to continue You will be presented with a blank data table and graph A typical Graphical Analysis screen is shown below The data and graph was taken from the STROBE DAT file included with this program This screen includes three different windows with a menu and a toolbar at the top Important features of the window have been identified on this figure Graphical Analysis c win_ga decay dat Menu Bar f File ac Window Graph Data Analyze aa Tool Bar gt RATATI Soa Window Control Box i ata T Graph Window Title Bar Data Set Title i Row y Rate vs Time Rate Column Title E min cts s 4 000 392 200 12 000 315 100 20 000 Cell Being Edited Graph Window Floating Box lt
16. of our older programs Data Logger Motion Sound Rotary Motion and ULI Timer into one easy to use full color program It is our newest software works with all of our sensors and has been very popular since we began shipping it in 1997 Books Chemistry with Computers by Dan D Holmquist and Donald L Volz A collection of 30 chemistry experiments using Vernier programs and sensors 35 00 Physical Science with Computers by Donald L Volz and Sandy Sapatka A collection of 41 physical science experiments using Vernier programs and sensors 35 00 Biology with Computers by Dave Masterman and Scott Holman A collection of 30 biology experiments using LabPro Serial Box Interface or ULI for Macintosh or PC computers 35 00 51 Physics with Computers by Ken Appel John Gastineau Clarence Bakken David Vernier and Richard Sorensen A collection of 34 physics experiments using LabPro or ULI for Macintosh or PC computers 35 00 Water Quality with Computers by Robyn L Johnson Scott Holman and Dan D Holmquist A 250 page manual and accompanying CD for using your computer and Vernier sensors to determine the water quality of streams lakes and seawater 35 00 Middle School with Computers by Donald L Volz and Sandy Sapatka This lab manual provides 38 ready to use experiments for science classes in middle school 35 Hardware and Books for Calculator Data Collection Hardware LabPro LabPro offers unparalleled flexibility power
17. option displays a brief hint or tip about Graphical Analysis These hints highlight some of the more obscure features of the program which you may find useful If the Display Hints on Startup checkbox is selected the hint dialog box appears while the program is first loading You may want to deselect it after you have been using the software for a while This option provides a pop up screen with information about this software including the version date At the bottom of the screen you will find a short description of your computer s hardware This includes the type of CPU in the computer and the amount of remaining free memory 44 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Graphical Analysis Windows Each of the types of the windows used in Graphical Analysis for Windows has its own features and controls Graph This general purpose graph window is used to plot any data column You can change the axes by clicking on their labels The title of the graph can be customized by double clicking on it and entering the desired text The scales can be changed by clicking on the tick mark labels at either end of the axis Type in a new value and the limits of the graph will be changed For example on the sample graph if you clicked on the top tick mark label on the vertical axis and typed in 3000 you could change the scale so that it runs from 0 to 3000 Grains Graph Window Grains vs Time h b ho ho oa nn oa nn oa oa
18. the mouse moves over the data table the entire row will be highlighted If you have a graph displayed with a data table a cursor line on the graph will scroll across the graph along with the highlighted row in the data table This also works the other direction If the mouse moves over any graph the row corresponding to the point on the graph will be highlighted in the data table Data Table Data Table Window Data Set 1 Data Days S000 eo 2773 OOO BOO 4 159 C aces Oy ee lo Ro co 4 ay Co ba To select the entire data table click the gray Control box in the top left corner of the window An entire data set can be selected by clicking on the data set header Data columns can be selected by clicking on the column header Similarly entire rows of data can be selected by clicking the row number FFT Graph When you double click a data table a dialog box appears showing all the columns that can be active in the data table You can use this to hide columns in the data table You can also display statistics for each column in the data table by checking the Show Statistics box The statistics for each data set are placed at the bottom of each column The FFI Graph window displays a Fast Fourier Transform of the data set An FFT is a bar graph showing the frequencies that make up a periodic signal such as sound waves For example if you are given waveform data
19. to use them to demonstrate the use of graphs as tools to find the relationship between variables Graph Window BOYLE DAT Pressure vs Volume ou in m v c 1 p 32000 This historical data was gathered by Boyle in studying the relationship between the volume and pressure of a gas at a constant temperature The experiment used a J shaped tube filled with mercury Reference Morris H Shamos Great Experiments in Physics 1959 The data was converted to metric units ho ao oOo lt D Pressure mm n co 15 20 25 lt gt Volume cm Cc gt Graph Window COULOMB DAT Force vs Distance f c 1 r2 Use this file to see the relationship between distance and electrical force The data in this file are student results West Starr and Bob Faber 1978 from the Project Physics version of the Coulomb s law experiment lt gt Force Hooks C gt 10 15 20 25 30 35 lt gt Distance cm lt gt Graph Window DAMP_SHM DAT Potential A vs Time Damped Simple Harmonic Motion The data in this file was imported from the MultiPurpose Lab Interface Program A strain gage was attached to horizontal hacksaw blade The hacksaw blade was displaced from the horizontal and allowed to undergo simple harmonic motion Q 3 D B a 2 Rate ve Time DECAY DAT In d c t This file contains data showing the decay rate counts sec of a radioactive sample The data was taken from a
20. when you want to read the values from a graph The check mark next to the Examine option indicates that it 1s active Graph Window i dh D E D D D a z A Time 0 130 Y Speed 2 000 mis 0 10 0 15 0 20 0 25 0 30 0 35 Time s Using Examine This option is used to read values from a fitted curve or linear regression line With Interpolate on a small set of vertical and horizontal lines will follow the curve as you move the mouse across the graph The X and Y values for that point on the curve will be displayed below the floating box Graph Window J Regression M 9 5963 mis s B 0 6331 m s COR 0 994 z a amp Q 0 2 0 3 lt P Time s This feature adds statistical information to a graph When a region of a figure is selected the minimum maximum mean and standard deviation of the selected data are calculated A solid horizontal line shows the mean and dashed lines mark one standard deviation above and below the mean A floating box which contains the statistics is also added to the graph 42 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Regression Integral Manual Curve Fit Automatic Curve Fit Floating Box Options Help Help Contents Graph Window This option causes the best fit linear PEETA Time regression line to be drawn through all Regression f M 9 5963 misis B 0 6331 mis or part of the data The line is calcula
21. you want to zoom in click and drag the mouse over the region and click the Zoom In button 1m on the toolbar or choose Zoom In from the Graph menu The program will then adjust the scales of the graph so that only the region included in the rectangle is graphed For example a small section of the graph on this graph has been selected with the mouse 10 15 20 25 lt P Volume NaOH mL C gt After selecting Zoom In this region is expanded to yield the graph to the right 24 26 2 lt P Volume NaOH mL gt 2Tf the numbers to be graphed are all positive the axis will start with zero If the numbers to be graphed are all negative the graph will end with zero If both positive and negative numbers are to be graphed the scale will be adjusted to include both positive and negative values 10 Graphical Analysis for Windows USER S MANUAL Analysis Tools Five very useful analysis tools can be found on the toolbar Those tools are available by clicking any of the following buttons Examine i Tangent Line rl Integrate Ad Regression Line eee or Curve Fit te Note that these tools can also be found in the Analyze menu The Examine feature of the program will display the values of an individual data point Click the Examine button on the toolbar and move the cursor across the graph A vertical line will be drawn through the data point closest to the cursor and a box will display the values that correspond to that point Graph
22. 0 50 an 70 0 lt 2 Angle of Incidence lt gt Snell s law data fitted with a sine curve The above fitted curves were made using the Automatic Curve Fitting option in the Analysis menu Students can easily experiment with various models to determine a best fit for their data Of course it 1s important to realize that the model is only as good as the data For example in the above experiment if the angle of incidence were limited to a range of 30 to 50 degrees a linear model would fit the data You can also have students use the Manual Curve Fitting option in the Analysis menu To use this option the students would have to make educated guesses concerning the curve s coefficients and exponents and it might require more work to obtain a fit The sample files included on this disk can be used to investigate a variety of mathematical relationships Determining Relationships with Three or More Variables The previous examples investigated the relationship between two variables In some case three or more variables many be involved Consider the example below where you have temperature electricity usage and time The graph on the left shows average temperature over time while the graph on right shows electric usage over the same time 22 Graphical Analysis for Windows TEACHER S MANUAL Graph Window Graph Window LA co Oo J o ao Oo mn Oo t o a g 5 j E 2 Q uw Oo Each of these variabl
23. 804 0 028345 mists B 6 3510 0 050506 mis COR 1 000 i 5 z i g d Distanceydt ms gt LW 1 0 1 5 2 0 i 1 0 1 5 2 0 lt gt Timeis lt gt Time s gt Timing Graph Distance vs Time Timing Graph Delta Distance Delta Time vs Time 25 Graphical Analysis for Windows TEACHER S MANUAL Using Data Collected with Other Programs Because Graphical Analysis is a Windows program data transfer to other programs is easy For numeric data simply drag across the part of the data table you want and choose Copy Data from the Edit menu Go to the Program Manager by simultaneously pressing the lt Alt gt and lt Tab gt keys and launching the application into which you want to paste the data Go to the appropriate part of the application and choose Paste from its Edit menu This works with both word processing and spreadsheet programs Graphs and other windows can be transferred in the same way Select the window you want to copy and choose Copy Window from the Edit menu If you need the Graphical Analysis Program data in a simple text file format for any reason follow the instructions above using the Notepad application included with Windows and paste in the data Then save the data after choosing Text as the type of file in the Save dialog box Sample Data Files Several sample data files are included on the Graphical Analysis disk Use them to explore the features of this program Later you may want
24. D Rate cts s C gt 105 000 21 500 116 000 17 600 124 000 14 000 ee nae aes as eee i ae ee ees 60 M O S lt 2 Time minj C gt Label Axis meN eN nd N N ed rN ed dd rm Ema aaa On Sioa O a Ea wn OI ho Data Table re y Pe Text Window og Data on the decay rate counts sec of a radioactive sample taken from a 1941 issue of the Physical Review E Text Window Wiw ed ed ed ed ed ed ed OOO Och Sco ho 1S Help Bar A Typical Graphical Analysis Screen Graphical Analysis for Windows USER S MANUAL As you work with the Graphical Analysis program you can choose from five types of windows Data Table windows use a table to display data in the same way a spreadsheet does Graph windows plot data on a scatter graph Histogram windows plot the number of occurrences of the various data values Fast Fourier Transform FFT Graph windows plot the frequency components of a column of data Text windows display notes about the data or graphs When the program starts the screen will have a Data Table window on the left and a Graph window on the right A small Text window will be displayed in the lower left Only one window can be active at a time and it will have the same color or shading as the Graphical Analysis Title Bar You can make a window active by simply clicking it with the mouse Entering and Editing Data The first step in using Graphical Analysis is usually entering a table
25. Graphical Analysis for Windows COPYRIGHT 1995 Vernier Software ISBN 0 918731 81 X User s Manual Teacher s Guide Reference Section Graphical Analysis c win_ga decay dat Data Table Window Graph Window Data Set 1 Data Rate vs Time i Rate Rate min 4 000 5 972 12 000 20 000 5 526 28 000 gt x 5 Cam cnfen on tofin gt a SIR en waa l oO gt 36 000 161 400 O00 128 300 g x ab a a Q A 438 28 K 0 027856 60 000 82 100 Mean Sqr Err 0 453 63 000 65 500 76 000 52 600 84 000 41 600 92 000 33 900 y A exp K x wiwe kar Lomi Gad Ea MIO 00 Oo ho co 3523 3 288 700 000 26 800 ah ah 108 000 21 500 l 116 00 17 600 i lt D Time min gt 124 00 14 000 2 639 100 Regression M 0 0279 min B 6 0629 COR 1 000 holo oo DiD co co lt P In Rate gt 4000 12 000 20 000 28000 __ 36 000 44000 52 000 __ 60 000 _ 68 000 __ 76 000 84 000 92 000 100 000 _ 108 000 pe aes ae as SS Text Window Data on the decay rate counts sec of a radioactive sample taken from a 1941 issue of the Physical Review 40 60 80 lt gt Time min lt gt Vernier Software amp Technology 13979 SW Millikan Way Beaverton Oregon 97005 2886 Phone 503 277 2299 FAX 503 277 2440 www vernier com info vernier com Version 12 6 00 Graphical Analysis for Windows TABLE OF CONTENTS HOW TOS
26. In y vs x gives a straight line with a slope of 2 This file consists of data on the mean periods and radii of the nine planets The radius units were converted to earth radii Graphing R43 vs T 2 verifies Kepler s third law This data file from the Mass Plotter program shows a histogram for the mass of 100 U S pennies A change in the composition of the penny in 1982 is the cause of the bimodal histogram This table lists the cost of mailing a one ounce letter via the U S Postal Service from 1858 1995 The period of oscillation of metal rings of various diameters as they rock back and forth This data was collected for a beam of light traveling through air and entering glass All of the angles are in degrees Distance traveled from rest for a nearly frictionless puck being pulled by a constant force along a level table This is a plot of temperature in Celsius vs temperature in Fahrenheit This is a sample file showing pH vs mL of base added during a titration experiment 49 Os IVSH VO WIRE CBLASPROBES DAT CBL ACC DAT CBL BALLOON DAT CBL BUNGEE DAT CBL DROPZONE DAT CBL LAKE DAT CBL RUNNING DAT CBL SPACEN DAT CBL STORM DAT DAT DAT DAT DAT The time taken to empty a can of water through holes of different diameters Four different sets of data are included Each set is for a different starting height of the water The time taken to empty a can of water through a hole i
27. ables to be graphed Changes can be made to this new graph as they were with the first graph The second graph can be used to display different columns of data or the same data with different scales and graph styles Additional graph windows can be created but the screen can only have ten windows open at one time Multiple Data Sets As you have seen Graphical Analysis data are stored in columns Data Table Window 2 and rows but data can also be stored in additional data sets The Row pd Time Distance Time Distance use of different sets of data is a good way to compare various l l M 1 2 700 20 000 1 900 20 000 experimental results when an experiment is being repeated under 3 500 30 000 3 500 30 000 r gt 3 700 40 000 2 600 40 000 different conditions or for different experiment runs For a reat ena FN T example the figure to the right shows time and distance data for 4 500 60 000 3 500 60 000 6 4 500 70 000 3800 70 000 a ball rolling down a ramp in two different runs The data set on the left was collected when the ramp was inclined at 2 5 while f ea i a the ramp was inclined at 1 for the second data set Each data set in a Data Table window contains the same set of columns and each can be graphed separately When several data sets are combined on a graph every set has a different shape point protector a separate point to point line and separate curve fit lines Graphing the various data sets on the same graph
28. al Curve Fit option however the program calculates the coefficients constants and exponents used in the mathematical model The list of mathematical functions includes linear exponential polynomial etc Choose the type of function you want and the program will determine the best fit Refer to the Built in help or the User s Manual for more information This option is used to change the appearance of floating boxes which are associated with fitted curves regression lines integrals etc Analyze How to Use Help search for Help On Hint About GA Use this option to access a table of contents for the Help system From there you can get information on getting started with Graphical Analysis for Windows tips on performing common tasks menu descriptions and descriptions of windows 43 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION How to Use Help Search for Help On Hint About GA This option is used to access extensive information on the Help functions available in the Windows environment Use this option to search for a specific topic When you select this option the Search dialog box will automatically open Type in a key word and then click the Show Topics button or press lt enter gt A list of topics then appears at the bottom of the screen Select the appropriate topic and click the Go To button You can also double click the topic for quicker access to the Help This
29. am calculate the statistics of the best fit line through the two points can be instructional The slope is 9 5 and the intercept is 32 These are the numbers used to convert Fahrenheit to Celsius temperatures The Interpolate item on the Graph menu can be used with this sample file for converting temperature units This idea comes from an article by M Bucher and Hugh A Williamson in the May 1986 issue of The Physics Teacher 29 L Graphical Analysis for Windows TEACHER S MANUAL Graph Window TITRATE DAT DH vs Volume NaOH Titration Use this file to investigate a sample titration Take the derivative of pH vs volume to determine the equivalence point Vincent J Sollimo Burlington County College NJ provided the data for this graph 30 35 10 15 20 25 lt gt Volume NaOH mL C gt Graph ast TVSD DAT 30 cm height Time 410 cm height Time 2 tr4 0 crn height Time t a 1 d 1 0 cm height Time Here the time taken to empty a can of water through holes of different diameter is studied Four different sets of data are included Each set is for a different starting height of the water Data taken from Appendix 2 of the PSSC Lab Guide Fifth Edition lt P Time s c gt De se EErEE rr 2 5 3 0 3 5 40 4 5 5 0 lt P Diameter cm amp gt Graph Window TVSH DAT Time vs Heigh 5 0 cm hole Time Somme tme t Vh 1 5 cm hole Time _ This file contains the time taken to empty th
30. an search for the graph that gives the best straight line In this way you can often find the relationship that best fits the experimental data The bottom graph at the right shows that in this case Y is indeed proportional to X 15 Graphical Analysis for Windows Example 2 The top graph on the screen to the right shows a different kind of relationship What is it Clearly Y decreases as X increases so you might try an inverse relationship Y 1 X The middle graph plots Y vs 1 X but it is not linear The bottom graph plots Y vs X and this is linear therefore Y is proportional to the 1 X This procedure is summarized below USER S MANUAL Graphical Analysis File Edit Window lt Wind ow Graph Window Data Set 1 Data 0 48200 0 96600 4 304 1 072 amp o ojejn ojo Ojj fja al wje oo i En 5o ojo Nje i CO ma Ao ojoj on i ico 2 41000 0172 E 1 2 3 4l 6l 8l 9 10 14 12 20 21 22 Double click for Data Table Options or click amp drag the mouse to select data 1 Decide on a possible relationship between the two variables Usually you can do this by looking at the data table or by looking at the original graph Other times the relationship to test will be suggested by a teacher lab manual etc Since it does not take very long to produce a graph using Graphical Analysis do not worry a
31. anual curve fitting When selecting the automatic curve fitting option you choose an appropriate model and the program will use standard statistical formulas to calculate the coefficients constants and or exponents of the model For example open the DECAY DAT file and select the Automatic Curve Fit option in the Analyze menu Select the Linear model from the Stock Functions list The screen to the left will appear It is obvious that this model does not provide a good fit to this data As a matter of fact the mean square error of 2020 is very large 3The Teacher s Guide has more information on how to use Graphical Analysis to find the relationship between variables 16 Graphical Analysis for Windows USER S MANUAL a E A File Edit Window Data Analyze Help Data Table Text Window Equation y 4 amp x amp 2076 8 Mean Sqr Err 6280 i Create Column OK Keep Fit Try Hew Fit Is this fit OK If you are satisfied with this fit press the OK Keep Fit button Press Modify Fit to edit the parameters in the above equation Press OK to keep the fit displayed on the screen aS File Edit Window Data Analyze Help Graph Window Rate vs Time Data Table 60 80 lt P Time min gt Text Window Equation y A exp K x amp 438 28 K 0 027856 Mean Sqr Err 0 463 Cl Create Column Try New Fit Is this fit OK If you are satisfied with this fit press the OK Keep Fit button Pre
32. at the automatic curve fit features have been disabled Data files have been included on this disk for use with Graphical Analysis for Windows and have the extension DAT These files are described in the Teacher s Guide File BOYLE DAT COULOMB DAT DAMP_SHM DAT DECAY DAT DVSI DAT PFL DAIL FREEFALL DAT GALILEO DAT GRAINS DAT KREPLER DAT PENNY DAT POSTAL DAT RINGS DAT SNELL DAT STROBE DAT TEMP DAT TITRATE DAT Description Historical data gathered by Boyle in studying the relationship between the volume and pressure of a gas at a constant temperature Student results West Starr and Bob Faber 1978 from the Project Physics version of the Coulomb s Law experiment This MPLI experiment file shows damped harmonic oscillator data The intended use of this file is to demonstrate the Manual Curve Fit feature Data on the decay rate counts sec of a radioactive sample Distance traveled from rest for a glider sliding down an inclined air track Triangle wave and corresponding FFT showing the frequency components Speed vs time for a freely falling golf ball The slope of a linear regression line is a measure of the acceleration due to gravity Distance traveled from rest for a ball rolling down an inclined plane The timing was done using a waterclock in an attempt to duplicate the work of Galileo The file is intended for demonstrations of the exponential function A semi log graph
33. ave As commands To save a file in text format choose the Save As command in the File menu Next pull down the Save As Type list found at the bottom of the dialog box and select the Text File TXT option Files saved in text format can be opened by word processing and spreadsheet programs Note however that only the data is saved in a text file Data saved in either format can be opened by Graphical Analysis 14 Graphical Analysis for Windows USER S MANUAL Quit If you want to quit the Graphical Analysis program choose Quit from the File menu If you are working with an unsaved file or have entered new data you will be asked if you want to save this information on disk before quitting Finding a Mathematical Relationship between Variables An important goal of data analysis is to determine the mathematical relationship between different variables Graphical Analysis provides two methods to achieve this goal One method described in the following section involves the graphing of modified data to find linear relationships The other method described later applies mathematical models to automatically or manually fit a curve to the data Graphing Modified Data This method of analysis is performed with columns of modified data This concept is based on the idea that if a graph produces data along a straight line then whatever you whatever you the vertical graphed on the graphed on the X ea axis i vertical axis horizontal a
34. ave their data so you can reload and use it as you discuss the lab 23 Graphical Analysis for Windows TEACHER S MANUAL Graphing Data Collected with LabPro CBL 2 and CBL The LabPro CBL 2 and CBL systems provide a method of collecting and analyzing data with TI Graphing Calculators Sometimes though you will want to transfer this data to your Windows computer for further analysis or to print higher quality graphs Such transfer is possible with this program and a TI GRAPH LINK cable part of the TI GRAPH LINK package which is sold by Vernier Software and other Texas Instruments dealers This cable connects the TI Graphing Calculator to the serial port of your PC computer Perform the following steps to import data from the calculator into Graphical Analysis e Connect the TI GRAPH LINK cable between the serial port of your PC computer and TI Graphing Calculator Link port e With Graphical Analysis running and a blank data table displayed select the column where you want the data imported e Choose the Import from TI Calculator option in the File menu e On the calculator follow the same procedure you would if you were sending Linking lists from your calculator to another calculator e When transferred to Graphical Analysis the lists will appear in columns of the data table They will be labeled with the simple list names from the calculator If you want to rename them or add units double click the column heading an
35. bled File is 1 Edit is 2 etc and y is the number of the item in the menu the first item is 1 the second item is 2 etc The separator lines in the menus also count as items To disable toolbar buttons x should be zero and y should be the number of the button counting from the left with the first button being 1 You can disable any number of items When you are finished editing the file save it and reload the program Included on the distribution disk is a file called STUDENT DAT This data file contains the commands that will disable the Automatic curve fitting button and menu item If you would rather your students did not use automatic curve fitting rename the STARTUP DAT file as STARTUP OLD and rename STUDENT DAT to STARTUP DAT If you are experienced with a resource editor such as Borland s Resource Workshop you can make minor changes to the Graphical Analysis program These changes could include changing the text of menu items dialog boxes and help text or adding keystroke equivalents for menu items Only modify a back up copy of Graphical Analysis You could accidentally make changes that make the program unusable Refer to a statistics text for more information for example An Introduction to Error Analysis by John R Taylor Oxford University Press 1982 32 Graphical Analysis for Windows TEACHER S MANUAL Questions about Graphical Analysis Graphical Analysis is the fourth version of a program first written in 1982
36. bout this choice If it does not work out you can always try another graph 2 Pull down the Data menu and choose the New Column option Select Calculated from the pop up menu that appears Enter the appropriate information in the New Column dialog box Refer to the Creating a New Column of Data section for further information 3 Click the Y axis label of a graph to select the appropriate variable to be graphed 4 Check the graph to see how linear it is If it seems linear determine its slope and intercept The easiest way to do this is to click and drag through the data then click the Regression Line button Refer to the Analysis Tools section 5 If that graph does not seem linear try a different relationship Even if the graph you made appears to be a straight line it is a good idea to try other relationships to verify that they are not as linear Automatic Curve Fitting Graphical Analysis ae File Edit Window Data Analyze Help Data Table Text Window Equation y M x B M 2 7838 B 297 49 Mean Sqr Err 2020 O Create Column OK Keep Fit Is this fit OK If you are satisfied with this fit press the OK Keep Fit button Press Modify Fit to edit the parameters in the above equation Another way to explore the relationship between variables with this program is to fit mathematical models or curves to data Within the program you have two options for curve fitting automatic curve fitting and m
37. cal Analysis Select a new column in the Graphical Analysis data table and repeat this process to retrieve additional data groups from the CBL Refer to the Retrieving Collected Data from the CBL section of the CBL System Guidebook p 24 for information on the order in which data groups are sent from the CBL Demonstrating the Shape of Various Mathematical Functions You can use Graphical Analysis to produce graphs of mathematical functions For example open a new data file by choosing the New option from the File menu From the File Menu choose Preferences and click the degrees radio button then click OK Click the X label in the data table and use the Fill Column option in the Data menu to create a sequence of numbers from 0 to 359 with a step of 1 Now double click on the column labeled Y and click on the Definition button If you want to graph a sine function for example enter a column name Press the lt Tab gt key twice to move to the Column Definition Box and click the Sine button on the calculator Next choose the X column from the Columns drop down list When you click the OK button the sine of each X value is shown in the Y column and graphed on the graph You can change and edit the column definition to show graphs of various functions The graphs below show sine and tangent functions 24 Graphical Analysis for Windows TEACHER S MANUAL Graph Window Graph Window lt 3 Tan Angle gt
38. columns labeled pressure and volume A sample set of data can be found in the BOYLES DAT file included with this program In addition to a graph of pressure vs volume you might want to graph pressure vs the reciprocal of volume Start by adding a new calculated column to obtain the above New Column dialog box After entering reciprocal volume for the new column name and reciprocal mL for the new column unit click the New Column Definition box Next click the 1 key on the calculator followed by the divide key Click the Columns button to pull down a list of columns Choose the volume column The column definition will now read 1 volume Click OK to save this new column The new column will appear in the data table and will be available for graphing by clicking on any axis label Modifying Data and Its Display To modify a column of data double click on the column heading of the data to be modified This will bring up the Column Options dialog box from which you Speen can change the label units and definition of the column The precision of the wwie Tica lt 1 data can be specified by choosing either decimal places or significant figures and entering the number of digits that will be displayed in both the data table 71S a and graphs In addition the point protector symbol the column color and the Po Protector et aahi a EEEE EET Col Color size of the error bars can be ch
39. culator keystrokes 19 Graphical Analysis Program for Windows TEACHER S MANUAL Getting Started Computer Requirements The Graphical Analysis Program for Windows requires a a 386DX or newer computer b Windows 3 1 95 98 2000 2000ME NT 4 0 operating system c at least 4 MB of RAM d a hard disk with approximately 2MB available for the program and related files e a PC VGA graphics compatible display f a mouse or Windows compatible pointing device g If you want to print graphs or data tables you need a Windows compatible printer and a properly installed print driver See the Windows 3 1 manual for this information Loading Graphical Analysis onto Your Hard Drive Windows Software installation To install Graphical Analysis on a computer running Windows 3 1 95 98 2000 2000ME NT 4 0 follow these steps e Place the Graphical Analysis CD in the CD ROM drive of your computer e If you have Autorun enabled the installation will launch automatically otherwise choose Settings gt Control Panel from the Start menu Double click on Add Remove Programs Click on the Install button in the resulting dialog box e The Graphical Analysis installer will launch and a series of dialog boxes will step you through the installation of the Graphical Analysis software You will be given the opportunity to either accept the default directory or enter a different directory Using Graphical Analysis in Science Classes Students s
40. d enter new names on the pop up menu that appears If you have problems importing data from the TI calculator perform the following checks e If you have transmission error problems with the calculator make sure the cable is connected to the correct serial port on the computer and that you have selected the correct serial port in the Graphical Analysis program Also make sure the plug on the GRAPH LINK cable is completely pushed into the calculator link port connection e Make sure you select the Import from TI Calculator option before you transmit the data from the calculator e Check to be sure you are only sending lists to the computer and not matrices programs etc An interesting variation of this procedure is to import data directly from the CBL unit This procedure is useful when using a TI 82 because the TI 82 lists are limited to 99 elements You can program the TI 82 to collect more than 99 points per channel and then send the data directly from the CBL to the computer To perform this procedure after the CBL has collected the data connect the TI GRAPH LINK cable between the serial port of your PC computer and the CBL Have the Graphical Analysis program open with a blank data table Select the column where you want the data imported Choose the Import from TI Calculator option in the File menu With data stored in the CBL press the lt 2 gt and lt XMIT 85 gt keys on the CBL The first data group from the CBL will be sent to Graphi
41. e information The text window below is taken from the BOYLES DAT file Spe Window Historical data gathered by Boyle in studying the relationship between the volume and pressure of a gas al at a constant temperature The experiment used a Jishaped tube filled with mercury Reference Morris H Shamos Great Experiments in Physics 1959 The data was converted to metric units 47 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Program Design Notes The main portions of this program were written using Borland Pascal for Windows a powerful Pascal compiler developed by Borland International 1800 Green Hills Road P O Box 660001 Scotts Valley CA 95066 0001 Graphical Analysis for Windows was programmed by Mark Topinka and Chris Chamberlin The Built in help was written by Chris Chamberlin David Gardner and Rick Sorensen Questions about Graphical Analysis If you have any problems or questions about this program please contact us at Vernier Software amp Technology 13979 SW Millikan Way Beaverton Oregon 97005 2886 Phone 503 277 2299 FAX 503 277 2440 www vernier com info vernier com 48 Appendix A Files on the Graphical Analysis CD GAX EXE The executable file for Graphical Analysis for Windows compiled with Borland Pascal for Windows STARTUP DAT The data file used when the program starts This file sets the window layout etc STUDENT DAT This is the same as the file STARTUP DAT except th
42. e it choose Help Contents from the Help menu You will be provided with a list of four general help topics These topics include Getting Started How to perform certain operations Menus and Windows You also have access to the Search feature of the Help system Click on the Search button found in the toolbar of the Help program A dialog box will appear from which you can type in a key word As you type in a word the search list will automatically scroll through an alphabetical list of topics The Graphical Analysis Program for Windows version is designed to operate on a PC computer running Windows version 3 1 or Windows 95 98 2000 2000ME NT 4 0 An MS DOS version of this program has been available for several years It includes most of the features of the Windows version It is a menu driven program and does not require a mouse It works on any PC computer with 640K of memory If your computer is not capable of running the Windows version contact us about exchanging for the MS DOS version Macintosh and Apple II versions of Graphical Analysis are also available Graphical Analysis for Windows USER S MANUAL Fast Start If you don t read manuals Many computer users do not believe in manuals If you are one of them we offer this information to get you started with Graphical Analysis Double click the Graphical Analysis icon Click the OK button in the About box to continue Enter data into the data table Double click on the
43. e water through a hole in a can The can was filled to various heights Four different sets of data are included Each set is the result of experiments done with a hole of different diameter Data taken from Appendix 2 of the PSSC Lab Guide Fifth Edition lt P Time s c gt 10 15 20 lt gt Height cm cC gt Mace verLenath WIRE DAT M ek ce L This file contains a set of sample data taken from the article Demonstrating the Role of Mathematics in Science by D W Turner from the book Best of Physics from Science Teacher s Workshop A pan balance was secretly weighted The students took data on the mass of 1 1 various lengths of wire They then determine the mass of another length lt 2 Length cm o gt 3 12 cm of the same wire by using their graph lt P Mass 9 gt 30 Graphical Analysis for Windows TEACHER S MANUAL General Notes Statistics The standard deviation used in statistical calculations is Ve ai ee std dev n i where Xm mean n number of data points This is sometimes referred to as the sample standard deviation The program calculates the best fit line using linear regression by the method of least squares The equations used are slope M m Exiy Ex Ey n x xi n x Ex intercept B EAE EER correlation coefficient aoa ea es Exi n x Ly n y gt std dev of slope std dev of y interc
44. eeese cess eeeeeeeesaeessaeesseeeesaeessaeesaaeessaeessneessaeesaaess 11 Greating a NeW Column Or Dala istassiaissoisoiatosslaneiaioiala N 12 Modifying Data and Its DISDIAY ccc cccceccseeceeeceeeneeeeeeseeeneeeeeesaeeseeeeeetaeeseeeeueeeeeseeeeueseeeseesaueneeeseeeaeees 12 Ghanging What Is Graphed on An AXIS aiina aaa aaa A A A A E a 12 Creating a New Graph cccccccccecccseeeeseeeeee cece cece eeeee sees eeeseeeeseeeeseeeeseeeeseeeeseeeeseeeesaeeeseeeeseeeseueenseeess 13 AMMAN AES SS tech hse ah gah ac gach allah eal al ee steamed 13 Renaming Data eb ote age Sanaa Sane Gene jane aastanssana sane sand danscianesnna dene Gand ora are ani Gand Gand ana ananena AEA 13 Ponin erap ORDA tc Anette ann ne ere er ee ee ee reer rent 13 Transferring Graphs and Data to Other Applications ccccccccceececeeeeceeeeeeeeeseeeseeeeseeeeseeeeseeeesaeeesaes 14 Transferring Data from Other Applications cccccccccceeccceeeeceeeeeeeeeseceseeeeseueeseeeeseeeeseueeseeeeseeeesaeeeaees 14 SAWING TOMATO keena scree ccietasartec Se geese eecasnnal sanceane ent eeteanttan taunts ant ben shart tanitentiantbeeenartiaettancassteneteienonate 14 O iatatedsintaieneananiaynananieiminanaennianasnnianeasantannd sang iainaninbsiainanaeanieineeetonnaninaateaniaiatene 15 Finding a Mathematical Relationship between Variables ccsccsescseeeeeeeseeeeeeeseeneeeaeenseeneeeaeeneeoaes 15 Graphing Modmied Dalase eaaa a A ARA 15 Automatic Curve Fitting
45. ept where n number of data pairs Xm mean of x values Ym mean of y values o2 y B M x When Graphical Analysis performs automatic or manual curve fits it calculates and reports the mean square error which is mean square error where y the y value of each data point yr the y value of the curve fit n number of data points 31 Graphical Analysis for Windows TEACHER S MANUAL These are fairly standard formulas The coefficient of regression is a useful measure of how well the data fit a straight line but it should not be overused Always examine the graph The coefficient is greatly affected by a few extreme points Smoothing When smoothing is used in a calculated column the column data z is a weighted average of the number of points selected by the user to use in smoothing m i n X wie yg __ n Zj i n Wi i n i n2Z2l2 n wi lt n n int m 2 1 Modifying Graphical Analysis If you do not want your students to use certain features of this program we have provided a method for disabling menu items or toolbar items You might use this feature to disable the Automatic Curve Fit option so that students are required to use Manual Curve Fit to find a fit To do so use a text editor such as Notepad to load the STARTUP DAT file In the section marked System Settings add a line like this Disable x y where x should be the number of the menu you want disa
46. es is a function of change with time but is there a relationship between electric usage and temperature Since Graphical Analysis allows you to quickly change the variable plotted on each axis you can easily plot energy vs temperature as in the graph below Graph Window M 62 343 B 4608 6 Mean Sqr Err 68300 ho ho oo i Si o nn Si o o o Oo Oo o o o oOo M 57 960 B 4485 1 Mean Sqr Err 105000 lt D Energy KWH c gt 50 lt gt Temperature C F lt gt Student Use During Labs Graphical Analysis can be very useful for students trying to analyze the results of a lab They can use the program to search for straight line graphs or to model equations to the data Certainly students need to know how to plot a graph by hand but after they have demonstrated this ability they can create and analyze graphs much faster using the program The User s Manual is designed to give students enough information to enter data and plot a few graphs without confusing them with all the other features of the program Going Over Lab Results One way to review a recently completed lab investigation is to use a large monitor or projection panel to plot a typical group s data using Graphical Analysis In fact the results of several different lab groups can be entered as separate data sets The different results can be compared on the same graph Using modified graphs or curve fitting features you can demonstrate the relatio
47. es on the Graphical Analysis disk that you can open and graph Try finding the relationship between the variables for some of them You can use the modified data method or the curve fit method to find the relationship between variables All these sample data files are described in the Teacher s Guide 18 Graphical Analysis for Windows USER S MANUAL Other Operations The previous description of the manual has covered only the essential features of the program This program has many other features Here is a quick summary of other operations you might want to perform For more information on any feature of the program consult the Reference Section of this manual or the Help system built into the program Select the New Data Set option from the Data menu Resize a window When two or more windows appear on the screen it 1s possible to resize them Move the mouse pointer over the space between the windows It will turn into a double headed arrow pointing in the directions that the window edge can be moved Click and drag the edge of the windows until they are sized as you want them Release the mouse Swap windows It is very easy to swap two windows using the mouse To do this click and drag the title bar of one window into the other The mouse pointer will change notifying you of the swap Note you can also Choose Arrange Windows from the Window menu Remove a window Select Close Window from the Window menu or double click
48. for the Apple II Many of the features of the program are the result of suggestions made by users of earlier versions of the program We thank all of them for their support and suggestions If you have any problems or questions about this program or if you are not on our mailing list please contact us We publish a periodic newsletter containing program improvements and new ideas for using this and other Vernier Software programs Vernier Software amp Technology 13979 SW Millikan Way Beaverton Oregon 97005 2886 Phone 503 277 2299 FAX 503 277 2440 www vernier com info vernier com 33 Graphical Analysis for Windows REFERENCE SECTION Graphical Analysis Menus File New Open Import from TI Calculator Graphical Analysis untitled dat gem Edt Window bGraph Data Analyze New Oper Import from TI Calculator Save Jave AS Print Printer Setup Preferences Exit This option opens up a new blank data window and graph The data and graph options will be the same as the STARTUP DAT file This option can be used to load a previously saved file Graphical Analysis will only allow you to have one file open at a time If you wish to view a previously saved file or create a new file you must first close the currently open file You can also load files saved with several other programs including any spreadsheet when the file was saved as text Vernier Software MS DOS applica
49. from several different musical instruments you can display an FFT Graph to show that each of the instruments produces a different set of frequencies harmonics The graph below shows the frequency components of a 500 Hz square wave This example shows the fundamental frequency of 500 Hz as well as the odd harmonics 46 Data Table Options Columns visible in data tables J Time EJ Grains In Grains Ll Show Statistics GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Histogram Graph Text You can double click the FFT Graph to set several options The dialog box displayed saume to Plot O AutoScale at 0 lets you select the column on which to 5 apply the FFT You can also set the frequency axis scaling and other options of tof pts o8 E the FFT calculation and display Ed Spike Enhancement gt Show Peak Freq A Histogram window displays a bar graph showing the distribution of readings It is useful in studying noise levels Double click on the Histogram window to change what data are analyzed on the histogram or to change the bin setting used in the calculation You can enter text in a Text window and save it as part of an experiment Examples include teacher notes to students descriptions of where the data came from questions for students to answer and summaries of results If you add more text than will fit in the text window you can use the scroll bar on the right side of the window to access all th
50. graph Graph Window Both horizontal and vertical error bars can be added to the graph To control the size of the bars double click the column label for the data of interest A Column Option dialog box will appear Enter the amount of the error bar and choose whether or not the error 1s a percent of the data point 0 15 0 20 lt P Time s 37 GRAPHICAL ANALYSIS for Windows Connecting Lines Bar Graph Background Grid Legend Zoom In Zoom Out Auto Scale This option will cause a point to point line to be drawn connecting the data points The line will be drawn from point to point in the order in which the data appear in the data table If the data in the table are not listed in order by the column graphed on the horizontal axis you should sort the data by using the Sort command on the Data menu If more than one set of data is being graphed a separate line will be drawn for each set This option drastically changes the appearance of the graph by producing a bar graph If you choose this option you will probably want to turn off the other options except perhaps the grid The bar graph style 1s not very useful if several data sets are plotted This option produces a background grid of dots on the graph so that it looks more like graph paper If you activate this option you will probably want to use point protectors to make the data points distinguishable from the grid dots A legend helps you
51. gt Graph Window Distance vs Time 1 0 1 5 2 0 lt gt Time s Graph Window Temp 1 vs Temp 2 50 100 lt gt Temp 2 Centigrade C gt TEACHER S MANUA RINGS DAT T k dq This file contains the period of oscillation of metal rings with different diameters as they rock back and forth It was assumed that the equation for the period was likely to in the form T k d but the value for n was unknown Graphing the In In graph with the regression line included yields the numerical value of n The value of k may also be determined from the fact that the y intercept of the In In graph 1s In k This data file consists of two different runs with two different data sets SNELL DAT sin I n sin r Data in this file compares the angle of incidence to the angle of refraction as a beam of light traveled through air and entered glass All the angles are in degrees This data is from PSSC Physics Fifth Edition p 397 STROBE DAT d c t2 A strobe photograph provided the distance and time data for this file The data was collected as a nearly frictionless puck was pulled along a level table by a constant force The data table was taken from PSSC Physics Fifth Edition p 32 TEMP DAT T1 c T2 k This is a plot of temperature in Celsius vs temperature in Fahrenheit The only two data pairs are the freezing and boiling points of water Plotting the non modified graph of these two points and having the progr
52. hen choose Copy Window from the Edit menu This places a bitmap of the graph in the Windows clipboard If necessary you can store the graph to a file Later you can paste the graph into another application You may also want to transfer data from a Graphical Analysis data table into another application such as a spreadsheet The easiest way to make this transfer is to copy the data from the Graphical Analysis data table window to the Windows clipboard You can then paste it into the other application If necessary you can store the data temporarily in a clipboard file To copy a whole data table make sure the data window is active choose Select All from the Edit menu then choose Copy Data Set from the Edit menu If you want to get only part of a data table drag the cursor across the data table until all the data you want is highlighted then choose Copy from the Edit menu Once the data has been copied to the clipboard open the new file and paste in the data Graphical Analysis can also create text files that can be opened by other applications This procedure is explained in the section Saving Information Transferring Data from Other Applications You may also want to transfer data from another application such as a spreadsheet into a Graphical Analysis data table The easiest way to make this transfer is to copy the data from the other application to the Windows clipboard You can then paste it into the Graphical Analysis Data Table To cop
53. hould learn in a science class that graphs are useful tools for determining the relationship between variables Usually this concept is discussed in class and examples of various graphs are shown to the students Later students are expected to use graphs to analyze lab results This program may be used to give the students more practice with graphically analyzing data A number of sample data files have been included with this program for this purpose You can use this program in two ways to see the relationship between two variables 1 You can analyze the graph by looking for a linear relationship between two variables If a linear relationship does not exist you can perform calculations on the variables to find a linear relationship 2 You can use various mathematical models to fit a curve to the data Each of these methods is described below Using Modified Data to Show the Relationship between Variables Students can investigate the relationship between variables by performing calculations on data and graphing this modified data For most of the mathematical relationships that show up in science a modified graph may be made to linearize the data For example to test for an inverse square relationship between x and y plot y vs x You can 20 Graphical Analysis for Windows TEACHER S MANUAL quickly see whether the data fit an inverse square relationship by checking whether the modified graph produced is a straight line It may be just
54. identify the data points by point protector shape It is a small table listing the name of each data set and showing the point protector shape associated with it Use the legend when you have more than one set of data on a graph vp N WS co Mm o a in lt D Speed mis c gt lt P Time s c gt REFERENCE SECTION Graph Window 005 O10 O15 O20 O25 O30 0 35 lt 2 Time s Graph Window Speed vs Time 005 O10 O16 O20 O25 O30 0 35 lt 2 Time s Graph Window Speed vs Time 0 05 0 10 0 146 0 20 0 26 0 30 0 36 lt P Time s Graph Window Time vs Diameter 30 cm height Time 410 cm height Time 4 0 cm height Time 1 0 cm height Time 2 5 3 0 3 5 4 4 5 5 0 lt D Diameter cm lt gt Use this option to examine a portion of a graph more closely Before using Zoom In you must select a region by clicking and dragging through it Choosing this option causes the region selected to expand to fill the entire graph You can repeat the Zoom In several times You can undo the most recent Zoom In operation by choosing Undo Zoom In from the Edit menu You can restore the graph to a more standard scale by selecting AutoScale from the Graph menu When you use the Zoom Out command the range of the axes will be increased by 200 Use this option to automatically set the range of the axes so that the data just fits in the graph 38 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION X Axis Options
55. is command is used to cut sections of text and is available only in text windows The Copy Data command is used to copy selected regions of a data table or a text window to the clipboard The command will not be accessible until you highlight the data or text This command is used to paste data into a data table or text into a text window The use of Cut or Copy along with Paste provides a convenient way of moving data around in the data table This option deletes all data from the selected cells Use this option to quickly select all the data This command selects data only not column labels and units File Edit Bunt Data Analyze ou Arrange Windows Close Window Graph Options Replace Window New Vfindow L QU Hel New Window O gt If more than one window is open choose this item to bring up a dialog box showing all of the possible layouts for these windows Sometimes so many windows are open that not all layouts can be shown In these cases the basic layouts are shown and a Rotate button is available allowing you to select other layouts To choose a layout click one of the diagrams and select OK This item will close the currently selected window This item displays a dialog box containing the options available for the currently selected window which may be a graph a data table or a text box 36 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Replace Window New Windows L UL Ne
56. l examples showing the use of this concept To create a new column click the Eg button for a calculated column or the button for a manually entered column Alternatively choose New Column from the Hew Column Hame Hew Column Units Eoo o Data menu and choose between a calculated column and a manually entered PEOS AOO column If you choose a manually entered column enter the name and units for the new column and click OK If you choose to add a calculated column the pop up screen to the left will appear Enter the name and units for the new column and EEE move to the New Columns Definition box Define the new column in this box by eeraa either typing in a formula or by clicking the various buttons provided If you choose E A e ee to type in the formula you must include the name of any column in double quotes GIbIGIL The easiest method is to use the mouse and click the various buttons in the dialog LeJis JL box These buttons include a calculator keypad with standard mathematical ae el ee ed functions a button labeled Columns that provides a list of all existing columns that can be used and a button labeled Other Functions that provides a list of various functions to apply to the columns functions such as derivative integral smoothing and absolute value ee J Lin 10 Lios J To demonstrate this process consider the example where you have pressure and volume data from an experiment and it is stored in
57. lt 3 Sin Angle 700 300 lt Angle gt Using the Derivative Function to Analyze Data The Derivative function can be used to study the rate of change of a variable Choose New Column from the Data menu and create a calculated column When entering the column formula in the New Column Formula box choose the derivative function in the Functions pull down list The derivative can then be plotted just like any other column There are many uses for this kind of data analysis For example if you have several distance figures taken at equal time intervals the derivative column becomes a table of velocities Use this approach to analyze strobe photographs videotaped data or ticker tape timer data The example below shows the derivative being used on data from a titration experiment to find the maximum rate of change in the pH Graph Window Graph Window oH vs Volume NaQH gt di pH ydy 15 20 25 30 35 lt 2 Volume NaOH mL C gt lt gt Volume NaOH mL gt Titration Graph pH vs mL Added Titration Graph Delta pH Delta Volume vs mL Added As another example here are two graphs of data from a strobe photograph of an accelerating object The first graph 1s the raw data the second one is the derivative of distance with respect to time The acceleration can be determined from the slope of the linear regression line Graph Window d Distance fdt vs Time Graph Window Distance vs Time Regression M 13
58. nclosed in double quotes The Columns button is a pull down menu listing all existing columns that can be used in defining your new column The Other Functions button is a pull down menu that allows you to choose various functions to apply to the columns functions such as derivative integral smoothing and absolute value The part of the dialog box that looks like a calculator provides standard mathematical functions that can also be used in defining the New Column As you click on the buttons and use the pull down menus in this dialog box the new column definition will be updated New Column Hew Column Hame Hew Column Units Hew Column Definition exe J Cin 10 Lios sin cos tan 2 LALJI L sart E ee ee LJAL JLL E esis oe E E Edit Column Definition If the currently selected column is a calculated column this item can be used to change the column definition When this option is selected the above dialog box will be displayed 4 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Analyze Tangent Line Examine Interpolate Statistics aph Data BRE td cr Tangent Line Examine interpolate Statistics Regression Integral Manual Curve Fit Automatic Curve Fit Floating Box Options You can use this option to see the tangent line on the data or fitted curve The tangent line is only effective on a graph not FFT graphs or histograms This option is useful
59. nship between variables discuss problems with the results and sometimes come up with meaningful constants from the slopes intercepts and areas The same strategy is useful in going over homework problems that involve graphing Plotting Graphs During Demonstration Labs This program can help you present and analyze data collected during demonstration labs collected in front of the class When you finish gathering the data it is awkward to stop and take extra time to make a graph on a chalkboard or overhead projector This program provides a quick method to produce quality well labeled graphs on a large monitor or projection panel Graphing Data Collected on Windows Computers A feature of Graphical Analysis is the ability to graph data collected with Windows computers Many schools use Vernier Software programs and hardware to collect data from temperature probes photogates pH probes etc After data is collected use the File menu of the data collection program to save the data as a text file In Graphical Analysis for Windows choose the Open option in the File menu and change file type to TXT in the pull down box found in the bottom of the dialog box Change to the correct directory and select the appropriate file The data will then be loaded into the Graphical Analysis data table window gt One efficient way to do this is to have the first few lab groups that complete a lab enter their results into Graphical Analysis Have them s
60. ntains suggestions on how this program can be used in the classroom It also gives information on all the sample files on the disk The Reference Section explains all the features and menus of the program in some detail Refer to the Reference Section if you have questions about the program Some familiarity with the use of Windows and a mouse is assumed in this manual If this is the first time you are using the Graphical Analysis program look over the User s Manual Refer to the Built in help when you want to learn more about other features of the program If you want to learn how to install Graphical Analysis on your computer read Getting Started at the beginning of the Teacher s Guide This section explains how to install the Graphical Analysis for Windows software If you have a particular question about program operation Graphical Analysis for Windows has extensive Built in help describing every menu item every dialog box and every type of window To use the Built in help highlight the item of interest and press the lt F1 gt key You can also get help when you press the key combination lt shift gt lt FI gt move to the item of interest and click the mouse The Reference Section of this manual contains answers to specific questions Graphical Analysis for Windows is a copyrighted program by Vernier Software The program disk does not have any copy protection and back up copies may be made using standard procedures Purchaser
61. ntial growth population compound interest a charging capacitor etc If k is negative the equation represents exponential decay radioactivity a discharging capacitor etc In either case plot the In of the Y axis data vs the X axis data This is sometimes called a semi log graph If you take the log base e of both sides of the general exponential equation above you get In Y Inc kX Ine or In Y Inc kX Thus if In Y is plotted vs X exponential data will produce a straight line with a slope equal to k and a y intercept of In c You might want to try this with the data files GRAINS DAT POSTALI DAT or POSTAL2 DAT For more information about the exponential function see the series of articles by Albert A Bartlett in The Physics Teacher beginning in October 1976 Many other mathematical relationships can be discovered using this technique Physics teachers often have students investigate the relationship between the angle of incidence and the angle of refraction for a beam of light striking and passing into a different medium Graphical Analysis can be used to plot sin 1 vs sin r to show Snell s law The graph on the left shows some Snell s law data plotted with no modification The graph on the right is a sin r vs sin 1 graph Graph Window Graph Window Angle of Refraction vs Angle of Incidence sin r vs sini Regression Wi 0 65910 00022932 J B 0 0038655 00 0016215 COR 1 000 i co 40 DI
62. oa Co Oo Oo Oo o lt gt Grains c gt mn oa o g lt 2 Time Days gt The arrows near the graph axis labels provide another way to change what is graphed These arrows allow you to scroll the graph by one minor division in the direction chosen for the respective axis For example if you click on the right arrow of the sample graph the entire graph would scroll to the left by 0 5 days Double click on the graph if you want to make other changes to the graph A dialog box will appear The top AE section of the dialog allows you choose what should f O sackgrouna cria appear on the graph a grid lines between data points Sie ees point protectors and frequency of the symbols bars C Bar Graph legend and error bars The button labeled Column 5 0O Error Bars Appearance lets you change the appearance of the data olumn Appearance Yv points in several ways You can choose the color used the point protector symbol the error bar size or even the label used for the column The bottom two buttons provide ways to adjust what is graphed on each axis and to change the scale used on each axis 45 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION The Data Table window displays columns of raw and calculated data A data table can also contain histogram FFT and curve fit data In the figure below the data for the graph shown above are displayed along with a new column defined as the natural log of Grains As
63. odify their data with mathematical operations They would then create and analyze graphs looking for linear relationships This approach 1s still supported in this program and explained in the Graphing Modified Data section of the User s Guide In addition we have added curve fitting to this version Students can easily fit a curve to data and quickly test various mathematical models Curve fitting is discussed in the Automatic Curve Fitting section of the User s Guide Built in Help This manual will give you an introduction to Graphical Analysis for Windows Much more information about this program is included in the Built in help You can access the Built in help in several ways e To get a brief description of a part of the screen move the mouse over that part and read the short message displayed in the help bar at the bottom of the Graphical Analysis window To obtain help information simultaneously press the lt shift gt lt F1 gt keys The cursor turns into a question mark To get help on a button or a window click on the object To get help with a menu option while the cursor is a question mark click the menu and hold the mouse button down drag down to the option of interest and release the mouse Help information will be displayed for each item you access To get help on a specific item or dialog box press F1 while you are accessing the item A Table of Contents for the Help program is available from the Help menu To us
64. of data Most data tables will have two manually entered columns The blank data table to the right has been set up so that Time X axis and Distance Y axis can be manually entered into the first two columns To enter the time and distance data simply click a cell and start typing When you have completed an entry press the lt tab gt or lt enter gt key to move to the next available blank data cell in the table For example after entering data in the first row press lt tab gt to move the cursor to the first cell in the next row After each data pair has been entered the corresponding data point will be graphed As you make entries the program will check to make sure that you have entered a valid number If your entry is not valid the cell will not be updated Data Table Window a 2 9 Incline Data cm D cn Lo ha The figure to the right shows a completed data table Editing a cell is easy Use the mouse or keyboard to select the cell you want to change To move horizontally with the keyboard use the lt tab gt or lt enter gt keys To move vertically within the data table use the up or down arrow keys Once the cell is selected edit the cell by either typing in a new value or using the left and right arrow keys and the delete keys to change a limited number of digits in the entry To accept the changes and automatically adjust the graph press lt enter gt lt tab gt or either the up or do
65. osen aai ai ieie ajala Rounding Dec Places s O Sig Figs the Edit Column Definition dialog box will appear allowing the definition of ee oe the column to be changed The column will be updated after you redefine the column When the definition button is clicked and the column is a calculated column Definition Raw Data Column Changing What Is Graphed on an Axis To change which columns are plotted on a graph simply click on the axis label A pop up menu listing all the columns in the data table will be displayed You can choose what you want graphed on the axis from this menu Any number of columns can be plotted on the Y axis but only one column may be plotted on the X axis 12 Graphical Analysis for Windows USER S MANUAL Creating a New Graph To create a new graph select either of the last two options in the Window menu Since all windows on the screen are non overlapping windows the New Windows option divides the area held by the currently selected window into two equal areas The original window remains and a pop up menu appears from which you select the style of the new window To create a new graph choose the Graph option The New Window LI UU option adds the new graph by splitting the current region of the display vertically into non overlapping windows The New Window option splits the old window horizontally The new graph will contain no data and blank axes Click on each axis to select the vari
66. provides a convenient way to compare results To create a new data window select New Data Set from the Data menu The new table will appear in the data table Numbers can be entered into these new data set columns as they were in the original data columns You can control which data sets appear on a graph by clicking the Y axis label and checking or unchecking the box for each data set Any one Graphical Analysis file can have up to nine data sets Each data set can have up to twenty columns and as many as 8000 rows of data Renaming Data Sets You may want to rename the data sets you create so they have meaningful names such as Joe s data or Run 2 with 5 gram mass The name of the data set appears in the title of the data set column and it can also appear in the legend on the graph if you activate the legend option To rename a data set double click the data set name and enter a new name or modify the existing name that appears in the pop up dialog box Printing Graphs or Data To print a graph or data table select the Print option in the File menu A pop up menu displays three options Data Table Selected Display and Whole Screen The Data Table option will print the entire data table including rows not displayed in the window This option may produce many pages of paper The Selected Display option only prints the active window on the screen It can be used to print graphs data tables and other windows If you select this o
67. ption for a large data table the entire data table may not appear To print a graph first select the graph by clicking it then select the Selected Display option To print the entire screen including all windows select the Whole Screen option If you have a Text window that contains more text than can fit in the window a scroll bar will appear on the right hand side of the window To print all the text you will need to click the Text window and select Copy Text from the Edit menu Paste the text in a word processor and print the text from the word processor If you want to quickly print the active window click the button on the toolbar Make sure the correct window is active before you start printing 13 Graphical Analysis for Windows USER S MANUAL In printing with a network it is useful to attach an identifying header To do so select the Printer Setup option from the File menu A pop up menu will appear If you check the Name checkbox you can enter your name and it will appear in the upper left corner of the printout If you check the Date checkbox the date will appear in the upper right corner of the printout Transferring Graphs and Data to Other Applications In many cases it can be useful to transfer graphs created in Graphical Analysis to another Windows program For example you may want to include the graphs in a report being written with a word processing program To copy a graph make sure the graph window is active and t
68. ptions Time s Options protector and to specify the column color You can also control the rounding of the numbers as they appear in the data tables graphs and statistics You can choose either to specify the number of significant digits or to enter the AREE number of digits to the right of the decimal point The allowable range is 1 to 9 significant digits or 0 to 9 digits to the right of the decimal point If you have chosen to display error bars use this screen to control their display If this column is a calculated column you can display and edit the definition Point Protector foJO 4x o ema Bee eeeeo Di Timi Timm Dec Places B Sig Figs Error Bars 0 000 gt Percent Definition Raw Data Column Column Options Dialog Box Column Color New Column This item is used to create a new column in which the data are either manually entered or calculated from a formula If you choose the manually entered data column you will need to type in the label and units of the column A blank column will be added to the data set so that you can enter new data If you choose the calculated data column you will be presented with the following dialog box Enter the name and units for the new column and move to the New Columns Definition box Define the new column in the box provided by typing or clicking the various buttons provided If you type in the name of a column in the definition it must be e
69. ration can be used to make it easier in analyzing data It may be desirable to use the option when you plan to include a point to point line on the graphs The line drawn between points is always drawn in the order in which the data appears in the data table If the data table is not in order the point to point line may not be useful Sorting by the column used on the horizontal axis is sometimes necessary before integration can be carried out on the graph If the data table includes more than one set of data the data will be sorted separately within each set The Fill Column option can be used to quickly fill in a data table when there is a simple pattern to the numbers To use this option click on the top cell to be filled or select the column header Select the Fill Data option in the Data menu The dialog box shown below will appear Specify the starting value ending value and increment Fill Data Fill Column Time Start Value End value Increment Increment Dialog Box The New Data Set item creates a blank data set with the same columns as the previous data sets Clear All Data deletes all data stored in all data sets This is different from New option in the File menu which creates a new file with a blank data set and default screen layout 40 GRAPHICAL ANALYSIS for Windows Column Options Use this option to enter the name and unit of a column to select a point REFERENCE SECTION Column O
70. rs marks that can indicate the uncertainty in the data Connecting Lines straight line segments from point to point Bar Graph bars extending from the bottom of the graph to the top for each data point Background Grid a pattern of background dots on the graph Legend small box matching point protectors data columns and data sets Changing the Scale of a Graph In most circumstances the axis scales of the graph are automatically adjusted by the program but you may want to change them To change gt EE pena the scale of a graph move the mouse to the graph and click either axis label A dialog box like the one to the right will appear Left Limit j j enw You have three different choices for the scaling of each axis If you siete select Manual Scaling you can enter the minimum and maximum values to be used on the axis Enter the appropriate value in each box If you choose Autoscale the program will automatically calculate a scale for the graph just fitting all the points on the graph If you choose Autoscale at Zero the program will automatically choose the axis scale but it will always include zero on the axis There is another way to quickly adjust the axis limits from the graph itself You can change each limit by clicking on that limit entering a new value in the small box that appears and pressing lt enter gt Zooming In on a Graph You can zoom in on any region of a graph to examine it more carefully When
71. s of Graphical Analysis are permitted to make as many copies of the program as they wish for use within their own high school or college department Making copies for any other purpose is prohibited Graphical Analysis for Windows was programmed by Mark Topinka and Chris Chamberlin and is copyrighted 1995 by Vernier Software The program was designed by David L Vernier Mark Topinka and Chris Chamberlain The Help system was written by Chris Chamberlin David Gardner and Rick Sorensen This manual was written by David L Vernier Rick Sorensen and David Gardner It is copyrighted 1995 by Vernier Software Vernier LabPro is trademarked by Vernier Software and Technology Microsoft Windows and MS DOS are registered trademarks of Microsoft Corporation Calculator Based Laboratory CBL 2 CBL and TI GRAPH LINK are trademarks of Texas Instruments Inc Hewlett Packard HP and LaserJet are registered trademarks and DeskJet is a trademark of Hewlett Packard Company Macintosh and Apple are registered trademarks of the Apple Computer Inc Turbo Pascal is a registered trademark of Borland International Inc Vernier Software amp Technology 13979 SW Millikan Way Beaverton Oregon 97005 2886 Phone 503 277 2299 FAX 503 277 2440 www vernier com info vernier com Graphical Analysis for Windows USER S MANUAL General Description of the Program and Built in Help Graphical Analysis for Windows is a user friendly program tha
72. s studied The can is filled to various heights Four different sets of data are included Each set is the result of experiments done with a hole of different diameter These data are from a ticker tape experiment in which a cart was accelerated by a weight hanging over a pulley There are four separate runs as four separate data sets using masses of 50 100 150 and 200 g as the weight hanging over the pulley A pan balance has been secretly weighted The students took data on the mass of various lengths of wire They then determine the mass of another length 3 12 cm of the same wire by using their graph CBL data showing temperature air pressure and relative humidity as a car drives from Portland Oregon to Madras Oregon over the Cascade range A Low g Accelerometer in a Toyota Celica manual shift going from 0 to 95 km hr which is 26 4 m s Data showing CBL readings during a hot air balloon ride on 7 25 95 over Newburg Oregon Data showing CBL readings during a bungee jump using three Low g Accelerometers Low g Accelerometer data from the Drop Zone at Great America Santa Clara CA According to the Great America literature free fall is 129 feet 39 1 tower height is 224 feet 67 9 m braking acceleration is 4 0g s Our free fall time is about 2 8 seconds which yields D 1 2 a t 2 125 ft 38 0 m Water sample data collected from Hagg Lake OR on 8 Oct 96 by Scott Holman and Dan Holmquist Water collected u
73. seeeseeeceeeeseeeseeeseueeeueeseeeseeeseeeeeueeaeeenes 23 Graphing Data Collected On PG COO uners icc esc oo i I ol ot 23 Graphing Data Collected with the Calculator Based Laboratory System cscccseseeeeeeeeeeeeeeeeeeees 24 Demonstrating the Shape of Various Mathematical FUNCTIONS ccccecceecceceeeeeeeeceeeseeeseeeeeeseeeseees 24 Using the Derivative Function to Analyze Data ccccccccccceecceeeceeeceeeeseeesaeeseeeeaeeseeeseeeseueeseeeseeeseeeees 25 Using Data Collected with Other Programs cccccccceeccceeeeceeeeceeeeseeeeeeeeseeeeeaeesseesseesaeeesseeesaeeesaaees 26 Salnple Data Files vatsctiictsicteigieictoiclescstscieacieac ites tisciiscieagleseitecdincalanstagieaaitocsiwoadaaetanieaastoasiuciwuyvenen eur ee 26 General NOLES caer crsetca ees eee aes aes ewes seca E E a cee eee mneemteens 31 SIL US eee asia eh ahaa ATA IAI AA A a ok A ca genta a A ams E E N uaa E T 31 SIM OO FM Gl Toara ea dene dacacanasamadene daca acscanacenatena dane dauacanscenatanadanedauscanscanatsaa E 32 Modifying Graphical Analysis c cccccccccececeeeceeeeeeeeneeeseeeseueseueeseeeseeeseeeeeueeeeeeseesaeeseeesaueeseeeseeeseeesanss 32 Questions about Graphical Analysis ccccceeeseeeeeeeeneeeeeeeneeeseeaseeeseeaaeesceaaeeeseeaseeseoaseeseoaaeeesonaas 33 REFERENCE SECHON rririk aE ari 34 Graphical Analysis Men s sensasie a a 34 E AEE E E E E N E bua eye E E E soe ose E E E A E E E E E ee aes T 34
74. sensors 35 00 Biology with Calculators by Dave Masterman and Scott Holman A collection of 30 biology experiments using LabPro CBL 2 with the TI graphing calculators and Vernier sensors Included are the word processing files for the student handouts on disk 35 00 Physics with Calculators by Ken Appel John Gastineau Clarence Bakken David Vernier and Richard Sorensen A collection of 34 physics experiments using LabPro CBL 2 with TI graphing calculators and Vernier sensors Included are the word processing files for the student handouts on disk 35 00 Water Quality with Calculators by Robyn L Johnson Scott Holman and Dan D Holmquist A 250 page manual and accompanying CD for using your LabPro CBL 2 and Vernier sensors to determine the water quality of streams lakes and seawater 35 00 Middle School with Calculators by Don L Volz and Sandy Sapatka This lab manual provides 38 ready to use experiments for science classes in middle school 35 32
75. sing the Vernier Water Depth Sampler D O pH and TDS readings were taken from raised samples Temperature taken using the Vernier Extra Long Temperature Probe 50 year old male running on hilly terrain 0 4 min getting ready to run 0 13 min rolling hills neighborhood 13 32 5 hills including Hamilton 32 5 37 5 walk on uphill 37 5 44 5 climb to summit 44 4 48 5 down 48 5 short water break 48 5 58 mostly down with final hill 58 62 walk downhill 62 sitting down Acceleration and air pressure data taken during a ride up the Seattle Space Needle Pressure in Portland OR for the storm on 12 11 95 Data was collected in four parts using a CBL The data was added in with the time adjusted for the start of the each new run 50 Appendix B Other Vernier Software Products Vernier Software has been publishing science software since 1981 We have software and hardware for Macintosh Windows MS DOS and Apple II computers as well as Texas Instruments Graphing Calculators The following is a list of some of our other products If you would like to receive a complete catalog of Vernier Software products please contact us at Vernier Software amp Technology 13979 SW Millikan Way Beaverton Oregon 97005 2886 Phone 503 277 2299 FAX 503 277 2440 www vernier com info vernier com Hardware Software and Books for Computer Data Collection Hardware LabPro LabPro offers unparalleled flexibility power portability and
76. ss Modify Fit to edit the parameters in the above equation Rate vs Time y A explk x A 4365 26 K 0 027856 Mean Sqr Err 0 453 Rate cts s 20 40 BO 20 Time min 17 We should try another model Click the Try New Fit button and select the Inverse model from the Stock Functions list Again the model does not provide a good fit The mean square error 6280 is even larger Click the Try New Fit button and select the Exponential model This choice has provided a very good fit with a very small mean square error 0 453 If you click the OK Keep Fit button you will return to the main screen The graph window will now look like the screen to the left The raw data will be graphed along with the exponential model A floating box will be displayed on the graph This box will contain the model the calculated coefficients constants and or exponents and the mean square error Graphical Analysis for Windows USER S MANUAL Each of the above examples uses one of the stock equations built into the program An extremely powerful feature of the curve fitting options is the ability to enter your own custom equation To do that select the Perform fit on Automatic Curve Fit option from the Analyze menu The LI sise origin pop up box to the right will appear with a field labeled y in the top portion of the box In the examples Stock functions R B Li above you clicked on one of the Stock
77. t allows you to easily graph and analyze data Data may be manually entered from the keyboard pasted from the clipboard or retrieved from a file saved on disk You can even import data from Texas Instruments TI 73 TI 82 TI 83 TI 83 Plus TI 85 TI 86 TI 89 TI 92 and TI 92 Plus graphing calculators and LabPro or Calculator Based Laboratory CBL CBL 2 interfaces Data can be displayed in spreadsheet form and as a graph You have several options on the scaling and style of graphs Powerful data analysis tools are provided including curve fits derivatives tangent lines integrals smoothing FFTs and histograms Graphical Analysis allows you to create new columns that are based on other data much as you might do with a spreadsheet program Since this is a Windows program you can easily copy your data and graph to a word processing or spreadsheet program via the clipboard Several sample files are included for your experimentation The Graphical Analysis program has been designed with non overlapping windows We chose this approach because overlapping windows often cause confusion As you create new windows the screen will be subdivided among all the windows without overlapping You can adjust the size of windows by dragging the horizontal and vertical dividers that separate them You can set up the screen with up to ten windows open at one time In previous versions of Graphical Analysis the emphasis has been on teaching students to m
78. t from the word processor The Printer Setup option is used to include header information to be used in the print out You can enter your name and check the box next to your name to print it as part of the header You can also select the date as part of the header by checking the box next to the date This option is also used to choose the printer This option controls a number of settings saved with each file The Preferences dialog box is shown below The derivative and smoothing pull down options control the number of points used in each calculation for those columns using these functions Set the appropriate options according to your preference then click OK Preferences A Borders between windows Derivatives 3 Smoothing a a Angles measured in Radians OO Degrees Preferences Dialog Box Closes the Graphical Analysis program 35 GRAPHICAL ANALYSIS for Windows REFERENCE SECTION Edit Undo Copy Window Cut Copy Data Paste Data Delete Data Select All Window Arrange Windows Close Window Window Options Copy Window Cut Copy Data Paste Data Delete select all The Undo command can usually cancel the most recent action performed on either the graph or the data Not all actions can be undone and you will be warned when some commands or operations cannot be undone The currently selected window is copied into the Windows clipboard as a bitmap Th
79. taken of the golf ball The value of the slope M is a measure of the acceleration due to gravity GALILEO DAT d c t This data represents the distance traveled from rest for a ball rolling down an inclined plane The timing was done using a waterclock in an attempt to duplicate the work of Galileo The table was taken from Project Physics p 62 1970 The data was converted to metric units GRAINS DAT G 2 X 1 The data in this file is based on the old story of the man who was paid 1 grain of wheat on the first day 2 on the second day 4 on the third day 8 on the fourth day etc The data is the number of grains vs day The file is intended for demonstrations of the exponential function A semi log graph In y vs x gives a straight line with a slope of log base e of 2 The intercept is the negative of the same number a L Graphical Analysis for Windows TEACHER S MANUAL 2500000 Period vs Radius KEPLER DAT 2 _C R3 2000000 T C R 1so000 i This file consists of data comparing the mean periods and radii of the nine planets The data is from PSSC Physics Fifth Edition page 97 The radius units were converted to earth radii Graphing R3 vs T verifies Kepler s third law Period Ho 1000000 1 an m m 1 20 30 lt gt Radius Earth Radii gt Histogram Window PENNY DAT Mass Distribution Penny Masses This file contains data collected with the Mass Plotter program for MS
80. ted Wate using the method of least squares If more than one set is to be plotted you will be asked to select a data set _ 3 E 2 5 D 2 a A 015 020 O25 O30 035 lt 2 Time s This option uses the trapezoid rule to approximate the area under the curve for the selected data The integral is estimated by adding the area of the trapezoids under the curve as shown here data points vert axis TRAPEZOIDS USED IN AREA CALCULATION horz axis Before integrating you must click and drag a rectangle on the graph to mark the region over which you want to integrate The program will then calculate the area and display the result The calculation of the integral is affected by the direction in which you drag the mouse If you drag the mouse left to right the integral is positive while dragging the mouse right to left yields a negative integral If integration is performed on a graph with more than one data set you will be asked to select a data set The manual curve fitting option is used to apply a mathematical model to experimental data A list of mathematical functions will be displayed including linear exponential polynomial etc You will have to enter coefficients constants and exponents for the model When the model is finalized the program displays a curve representing your equation on the graph along with a floating box that summarizes the curve fitting results This option is similar to the Manu
81. the numeric results To fit a regression line to only a portion of the data click and drag the mouse across the area of interest then click the Regression Line button To remove this line and the curve fit information click the small box in the upper left corner of the floating box You can use the Curve Fit button to fit various mathematical equations to the data This process is explained in detail in the Automatic Curve Fitting section of the User s Manual Displaying a Range of the Graph If you need to determine the difference between two points on a graph you could examine the data at the two points record the point coordinates and make a calculation Alternatively click the Examine button so that it is active Hold the left mouse button down and drag it over the region of interest in the graph A box will appear in the upper left corner of the graph from which you can read the changes in the X and Y values This feature can be helpful in analysis situations such as determining the amplitude and period of a periodic wave or determining the change in temperature during an experiment 11 Graphical Analysis for Windows USER S MANUAL Creating a New Column of Data One of the most useful features of Graphical Analysis is the ability to plot graphs of modified data This is extremely helpful in looking for the relationship between variables The section entitled Graphing Modified Data later in this User s Manual has severa
82. tions ULI Timing Module and Graphical Analysis for Macintosh when the file was exported as text This option can be used to import lists stored on your TI 73 TI 82 TI 83 TI 83 Plus TI 85 TI 86 TI 89 TI 92 or TI 92 Plus calculator This is useful if you have collected data using the LabPro CBL 2 or CBL system and you would like to analyze the data further or to produce higher quality graphs You will need the TI GRAPH LINK cable to use this option Contact Vernier Software or your Texas Instruments dealer for information about this product The procedure for importing data is the following e Connect the TI GRAPH LINK cable between a serial port of your computer and the TI Graphing Calculator or LabPro CBL 2 CBL e With Graphical Analysis running and a blank data table displayed select the column where you want the first column of imported data to appear If more than one list is transmitted each list will be placed in the subsequent columns e Choose the Import from TI Calculator option from the File menu e On the calculator follow the same procedure you would if you were sending Linking lists from your calculator to another calculator e When transferred to Graphical Analysis the lists will appear in columns of the data table They will be labeled with the simple list names from the calculator If you want to rename them or add units double click the column heading and enter the new name on the pop up menu that
83. w Windows U 5 Graph Point Protectors Point Protectors Every Error Bars This item will replace the currently selected window with one of the following windows e Graph e Data Table e Histogram Graph e FFT Graph e Text Window These windows are discussed in the next section of this manual Use this option to split the currently selected window horizontally as the graphic suggests and make the right hand window one of the five available windows types Use this option to split the currently selected window vertically and make the lower window one of the five available windows types Window amp eniim Data Analyze gt Point Protectors J Point Protectors Every Error Bars Connecting Lines Bar Graph Background Grid Legend Help oom In oom Out Auto Scale Axis Options Y Axis Options Column Appearance More Graph Options If this option is activated each data point will be surrounded by a small geometrical shape to make it more visible These point protectors vary in shape depending on the data set being plotted Point protectors generally make the data points easier to see and are especially useful if more than one data set is used If you are plotting a large number of data points you may want to turn off the point protectors to avoid cluttering the graph or at least to limit their number Use this option to control how often the point protector is used on the
84. wn arrow The changes will also be accepted if you click another cell with the mouse Data Table Window 2 5 Incline Data cm 2 700 3 300 l 40 000 4 200 50 000 4 500 60 000 4 500 70 000 C O If you are entering numbers in scientific notation use the E or e key as in the examples below D an cn Lo ha To enter this number Type this 3 5 x 104 3 5E4 2 4 x 108 2 4e3 5 5 x 10712 5 5 E 12 Editing the Axis Labels Units and Graph Title When the program starts the labels for the horizontal and vertical axes are simply X and Y and no units are displayed To change this double click the top cell of either column and enter the new label and unit in the pop up menu that appears Click the OK button to accept the changes To change the title of the graph click the title of the graph window and enter a new title in the pop up box that appears lThe range of numbers allowed to be entered is 1 7 x 103 to 1 7 x 10308 9 Graphical Analysis for Windows USER S MANUAL Changing Display Features of a Graph To change a graph move the mouse to the graph and click it once to make the graph the active window Now try selecting different options from the Graph menu Selecting a menu item toggles it on or off If an item is preceded by a check mark the item is on Here 1s a list of the available options Point Protectors small squares triangles etc that make the data points more visible Error Ba
85. xis If the line goes through the point 0 0 on the graph then the relationship is even simpler whatever you whatever you ihe sloje graphed on the graphed on the x ofthe i vertical axis horizontal axis In other words the variables graphed are proportional Graphical Analysis provides a way to experiment with different graphs and to try to find one that produces a straight line If you are successful you have probably found the relationship between the variables The examples and graphs below illustrate this idea Graphical Analysis Example 1 Consider the relationship between the variables X and Y in the upper graph shown to the right naa Clearly Y is not proportional to X or else the graph of 1 Era vs X would be a straight line Is Y proportional to X Maybe Y is proportional to X Perhaps the relationship is more complicated You can do some quick checking by creating a modified data column and plotting a graph of the modified data To test whether Y is proportional to X plot a graph of Y vs X If this graph turns out to be a straight line then Y is proportional to X If this graph is not a straight line you can try plotting Y vs X If this graph is a straight line then the relationship is that Y is proportional to X Whenever the straight line graph is found you have determined the relationship between X and Y By trying several different graphs with X axis data raised to different powers you c
86. y a whole data table make sure the data window is active choose Select All from the Edit menu then choose Copy Data Set from the Edit menu If you want to copy only part of a data table drag the cursor across the data table until all the data you want is highlighted then choose Copy from the Edit menu Once the data has been copied to the clipboard from another application switch back to the Graphical Analysis program Click on the first column of the Graphical Analysis Data Table and then select Paste Data from the Edit Menu or press CTRL V Saving Information After you have entered edited and graphed information you may want to save it on the disk Two save commands appear in the Graphical Analysis File menu Save and Save As To save your work back to the original data file choose Save from the File menu This saves the data and the graphs exactly as you have them set up If the data have not been previously saved you will be asked to enter a file name When you use the Save As command it makes a new file containing the current data and graph Save As always allows you to enter a file name and choose a location for the new file Two file formats can be used when saving the data These are data DAT and text TXT When you save a file as a DAT file everything about that file including data text and graph setups is saved This format is the default file format Data and graphs are saved quickly in this format using the Save and S

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