Graphical Analysis User Manual - Vernier Software & Technology
Contents
1. Data Browser features Time 8 Distance m E e Drag and drop from the Data Browser to objects such as tables and graphs Drag a Velocity m s A Acceleration m s kinetic energy J e When the Data Browser is Active it s been clicked on its appearance changes to potential energy 1 reflect its active state Edit menu items like Cut Copy Paste Duplicate and Select All will apply to the selected items within the Data Browser column to a y or x axis to plot it there drag a data set to a table to make it visible there i total energy J e Options and commands associated with a particular column or data set will be accessible in the Data Browser via right click control click on Mac for options and commands 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 either double click the label at the top of the column or choose Column Options from the Data Menu and enter the new label and unit in the dialog that appears Click the OK button to accept the changes To change the title of the graph either double click on the graph or choose Graph Options from the Options menu and enter a new title in the dialog that appears Changing Display Features of a Graph To change a graph choose Graph Options from the Options Menu The Graph Op2. v Xx2 xi intercept B Die 2 x LY ya DY m Zxi n x Xy2 n yl correlation coefficient correlation coefficient std dev of slope std dev of y intercept where n number of data pairs Xm mean of x values Ym mean of y values of X v B M x When Graphical Analysis performs automatic or manual curve fits it calculates and reports the mean square error which is A2 X x y mean square error where the y value of each data point yj the y value of the curve fit n number of data points 25 Graphical Analysis for Windows TEACHER S MANUAL These are fairly standard formulas he 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 Smooth Ave 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 DerivativeSG Y X returns the Savitsky Golay derivative of Y with respect to X A polynomial is fitted to N points around each point and the derivative of that polynomial is used N may be set in File Settings This is very accurate but can be slower than other methods For more information about Savitsky Golay methods see Numerical Recipes in C http lib www lanl go
3. 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 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 can change the label units and definition of the column depending on whether the column to be changed is manual or calculated The precision of the 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 and graphs Column Options Column Definition Options m Labels and Units T Generate Column Name Generate Yalues Short Name Units Start End fioo Increment Number of cells 100 Time Insert Symbol Y Lock column prevent cell editing Treat Column Cells as Text 13 Graphical Analysis for Windows USER S MANUAL If you want to automatically populate a column with generated numeric values or special labels such as months or data set names check the Generate Column box in the Column Definition tab You can then scroll the list for the values or labels you want Click the Options tab to change the point protector symbol the column color and the size of the error bars For each point you can choose an error constant or you ca
4. a column of data Text objects display notes about the data or graphs Oval and rectangle objects are especially useful for annotation and documentation where an area of a graph or data may be highlighted or framed When the program starts the screen will have a Data Table object on the left and a Graph object on the right A small Text object will be displayed in the lower left You can make an object active by simply clicking it with the mouse More than one object can be selected and active at a time This can be done by holding down the Shift key and clicking the objects with the mouse Entering and Editing Data The first step in using Graphical Analysis is usually entering a table of data Most data Data Set tables will have two manually entered columns The blank data table to the right has been set up so that Time X axis and Pressure Y axis can be manually entered into the first two columns To enter the time and pressure data simply click a cell and start typing When you have completed an entry press the lt enter return gt key to move to the next available blank data cell in the next column You can set the Enter Return key to move to the cell below in File Preferences 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 The figure to t
5. a fan was used to blow air across the leaf as the pressure was measured 22 Graphical Analysis for Windows TEACHER S MANUAL Chemistry Titration A titration is a process used to determine the volume of a solution needed to react with a given amount of another substance The data in this sample file are from a titration of an solution with an NaOH solution Beer s Law This 18 absorbance vs concentration data for a set of solutions A linear fit to the data Beer s law and the use of the Interpolate option in the Analyze menu help to determine the concentration of the unknown Conductivity This sample file contains Conductivity vs Volume in drops data Conductivity was measured as the concentration of the solution was gradually increased with the addition of drops of NaCl The experiment was repeated with drops of CaCL and AICI Evaporation These data illustrate the effects of evaporative cooling of two alcohols Methanol with a smaller molecular weight than ethanol cools the Temperature Probe to a lower temperature than ethanol Freezing Point Depression This sample file contains Temperature vs Time data for the cooling of pure phenyl salicylate and a benzoic acid phenyl salicylate mixture Physics Ball Toss The data shown here 15 a record of the position of a ball as it was tossed straight up into the air The file also includes velocity and acceleration data Fit a straight line to the free fall porti
6. by Vernier Software amp Technology The program was designed by Garth Upshaw Christopher Corbell David L Vernier and Rick Sorensen The Help system and manual were written by Erik Schmidt The manual is copyrighted 2002 by Vernier Software amp Technology Vernier LabPro is trademarked by Vernier Software amp Technology Microsoft and Windows are registered trademarks of Microsoft Corporation Calculator Based Laboratory CBL 2 CBL and TI GRAPH LINK are trademarks of Texas Instruments Inc Macintosh and Apple are registered trademarks of the Apple Computer 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 3 0 USER S MANUAL General Description of the Program and online Help Graphical Analysis is a user friendly program that 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 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 Calculator Based Laboratory 2 CBL 27 or CBL interfaces using a TI GRAPH LINK cable Graphical Analysis is also a document creator with the ability to include several pages in one document Data can be displayed in spreadsheet form and as a graph You h
7. discussed in the Curve Fitting section of the User s Guide Online Help This manual will give you an introduction to Graphical Analysis 3 0 Much more information about this program is included in the online help You can access the online help in several ways e To geta brief description of the toolbar buttons move the mouse over them and read the short message e To obtain help choose Graphical Analysis Help from the Help menu You can also right click Windows ctrl click Mac on an object to call up a contextual menu that contains Help In addition you can double click on an object and select Help from the dialog box Choosing Graphical Analysis Help from the Help menu launches the online Help You will be provided with a list of five general help topics These topics include Getting Started How to perform certain operations Menus Objects and Screen Hotspots You also have access to the Search feature of the Help system Click on the Search tab in the Help program If you opt to use the Index tab a box will appear from which you can type in a keyword As you type in a word the search list will automatically scroll through an alphabetical list of topics Windows requirements Windows 95 Windows 98 Windows 2000 Windows NT 4 x Windows ME and Windows XP 133 MHz Pentium processor or better 16MB physical RAM plus free hard disk space for virtual memory Color monitor gt 256 colors Macintosh requirements
8. e MacOS 8 x MacOS 9 x MacOS X e 66 MHz PowerPC processor or better e 16MB machine RAM 8MB for the application partition 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 Close button in the Tip of the Day box to continue Enter data into the data table Double click on the graph to change its features Click on the numbers at the ends of the axes to change the scaling Experiment with the toolbar buttons Choose Graph Additional Graphs Table etc from the Insert menu to add new objects Move the objects around or choose Auto Arrange from the Page menu to rearrange the page layout Try the various menus Have fun experimenting If you have questions check the extensive online help guide To import data from a TI Graphing Calculator connect the TI GRAPH LINK cable to the computer and calculator Choose Import from TI Calculator from the File menu Using the Graphical Analysis Program Typical Screen Start up the program by double clicking on the Graphical Analysis 1con Click the OK button in the Tips 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 Transpiration ga3 file include
9. Graphical Analysis 3 0 COPYRIGHT 2002 Vernier Software amp Technology ISBN 1 929075 16 2 S Transpiration ga3 Graphical Analysis File Edit Data Analyze Insert Options Page Help gt HRR a Latest Time Pressure Transpiration with Fan in 1 0 00 101 85 a 0 25 101 73 1 0 50 101 68 Am 0 75 101 73 E 1 00 101 73 db Linear Fit For Latest Pressure 5 1 25 101 68 y mx b E 1 50 101 73 m Slope 0 0831 1 8 1 75 101 62 ff 101 5 M J 9 200 101 56 orrelation u 2 25 101 56 11 2 50 101 62 mm 2 75 101 62 E 1 3 00 101 51 i A 3 25 101 51 F This transpiration experiment was done with fan blowing on a leaf 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 03 01 02 Graphical Analysis 3 0 TABLE OF CONTENTS Graphical Analysis 3 0 How to Use this Manual This manual is divided into two main sections the User s Manual and the Teacher s Guide The User s Manual includes a quick introduction to the most important features of the program The Teacher s Guide contains computer requirements how to install the software details on importing data suggested uses and descriptions of the sample data Some familiarity with the use of Windows and or Macintosh computers and a mouse is assumed in this manual If this is th
10. ave 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 Y ou can easily copy your data and graph to a word processing or spreadsheet program via the clipboard Many sample files are included for your experimentation The Graphical Analysis program has been designed with overlapping objects Cartesian graphs text boxes tables etc We chose this approach for added user modification As you create new objects you can easily move them about the screen or opt to have them automatically arranged to maximize screen space You can adjust the size of objects by dragging the handles that frame them Graphical Analysis is also a document creator with the ability to include several pages in one document In previous versions of Graphical Analysis the emphasis has been on teaching students to modify their data with mathematical operations They would then create and analyze graphs looking for linear relationships This approach is still supported in this program and explained in the Graphing Modified Data section of the User s Guide In addition curve fitting functions have been improved Students can easily fit a curve to data and quickly test various mathematical models Curve fitting is
11. bled the installation will launch automatically otherwise choose Choose Settings Control Panel from the Start menu Double click on Add Remove Programs Click on the Install button in the resulting dialog box 3 The Graphical Analysis installer will launch and a series of dialog boxes will step you through the installation You will be given the opportunity to either accept the default directory or enter a different directory To install Graphical Analysis on a computer running MacOS 8 x MacOS 9 x MacOS X follow these steps 1 Place the Graphical Analysis CD in the CD ROM drive of your computer 2 Double click on the Install Graphical Analysis icon and follow the directions Using Graphical Analysis in Science Classes Students should 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 You can use various mathematical models to fit a curve to the data The tutorial titled Curve Fitting takes you through the basics of automatic curve fitting with standard equat
12. d units LabPro CBL 2 and CBL You can attach LabPro CBL 2 and CBL interfaces to the computer via a TI GRAPH LINK cable and you can transfer data lists directly from them Those data lists will be from the most recent data collection run The data will be added to a data column graphed on the screen and ready for further analysis Saved or archived experiments in LabPro can also be imported Note This function is useful for interfaces that have been used for remote data collection Graphical Analysis cannot be used to initiate data collection The procedure for importing is Import From TI Calculator 1 Connect the TI GRAPH LINK cable to a free serial or USB port of the computer Pot 2 and to the LabPro CBL 2 or original CBL Gray SeisiCeble Black Link Cable Status 2 Make certain that the LabPro CBL 2 or original CBL has power Modet CBL2 Ready bo impart 3 With Graphical Analysis running pull down the File menu and choose Import iN From TI Calculator or LabPro CBL This dialog box should appear Catal If you want to import saved experiments check the box next to Scan for Saved Scan for Saved Exparimerts Experiments to get a listing of archived experiments in LabPro p Choose Data to Import Tau may choose mare than onc item 4 Graphical Analysis will identify your interface and display the data within 5 Highlight the lists and or saved experimen
13. d with this program This screen includes three different objects with a menu and a toolbar at the top Important features of the program have been identified on this figure S Transpiration ga3 Graphical Analysis Menu Bar Edit Data Analyze Insert Options Page Help Toolbar Data set Tite Et g Transpiration with Fan Graph Title Table Object Column Title Graph Object Linear Fit For Latest Pressure 4 y mx b m Slope 0 0831 b Y Intercept 102 Helper Object Correlation 0 993 Pressure kPa o e I This transpiration experiment was done with d _ afan blowing on a leaf m 100 5 Text Object Axis Label Graphical Analysis for Windows USER S MANUAL Objects Graphical Analysis provides different objects that can be displayed on the screen in an overlapping format Numerous combinations allow you to customize the presentation The Page Object is the foundation upon which you can add modify and delete objects As you work with the Graphical Analysis program you can choose from six types of objects Data Table objects use a table to display data in the same way a spreadsheet does Graph objects plot data on a scatter graph or bar graph Histogram objects plot the number of occurrences of the various data values Fast Fourier Transform FFT Graph objects plot the frequency components of
14. e across the graph As you do a tangent line will be drawn at each data point A helper object will also display the numeric value of the slope at that point To turn off the tangent line click the Tangent button or deselect the Tangent option in the Analyze menu The number of points used to calculate the slope is controlled in the Settings For option in the File menu The Statistics feature calculates the minimum maximum mean standard deviation and number of points of the selected region or the whole graph if no selection is made A floating box helper object which contains the statistics 1s added to the graph To determine the Integral click and drag the mouse across the region of interest then click the Integral button Clicking the Integral button without selecting a region will perform an integral for the entire graph The area under the curve will be shaded and a box will display the numeric results The integral 1s calculated using the trapezoid method The Linear Fit button is used to calculate the best fit line for a selected curve or region of a curve A best fit line will be drawn on the graph and a helper object will display 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 Linear Fit button You can use the Curve Fit button to fit various mathematical equations to the data This process 1s explained in detail in the Automatic Cu
15. e first time you are using the Graphical Analysis program look over the User s Manual Refer to the online 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 software If you have a particular question about program operation Graphical Analysis has extensive online help describing every menu item every dialog box and every type of object To obtain help choose Graphical Analysis Help from the Help menu You can also double click on an object and select Help from the dialog box Tutorials covering popular commands are provided After you have installed and started Graphical Analysis choose Open from the File Menu to access them Graphical Analysis 3 0 is a copyrighted program by Vernier Software amp Technology The program does not have copy protection and back up copies may be made using standard procedures Purchasers of Graphical Analysis 3 0 are permitted to make as many copies of the program as they wish for use within their own high school or college department This includes a student site license for home use Making copies for any other purpose is prohibited Graphical Analysis 3 0 was programmed by Garth Upshaw Christopher Corbell Jessica Fink Stephen Beardslee and Mary Dygert and is copyrighted 2002
16. e 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 11 Graphical Analysis for Windows USER S MANUAL Analysis Tools Six very useful analysis tools can be found on the toolbar Those tools are available by clicking any of the following buttons Examine L 2J Tangent Line H2 Statistics L398T Integrate Regression Line _ or Curve Fit A floating box helper object will appear showing the results of this analysis To delete the object and the graph item to which it points to an integral regression line curve fit etc click the small close box in the upper corner of the Helper Object Note that these tools can also be found in the Analyze menu Distance vs Time 1 0 80 Time 1 067 0 40 Distance m 0 20 p Ca C Using Examine Points The Examine feature of the program will display the values of individual data points 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 The Examine option works on any graph object When you are finished examining click the Examine button or deselect the Examine option from the Analyze menu To see the Tangent line click the Tangent button and move the mous
17. eparate curve fit lines Graphing the various data sets on the same graph provides a convenient way to compare results You can however by checking New Data Sets have X Y box in Preferences assign new data sets to have columns labeled X and Y 14 Graphical Analysis for Windows USER S MANUAL To create a new data set select New Data Set from the Data menu or click the al button from the Data Browser The new data set 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 You can have as many rows or columns as your computer s memory will allow 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 or select Data Set options from the Data menu and enter a new name or modify the existing name that appears in the dialog box Printing Graphs or Data You have three printing options Print Print Data Table and Print Graph Select the Print option in the File menu or click the print button from the toolbar This option only print
18. essary you can store the data temporarily in a clipboard file To copy a whole data table make sure the data table 15 active choose Select from the Edit menu then choose Copy 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 open the new file and paste in the data Graphical Analysis can also export data as text files that can be opened by other applications Transferring Data from Other Applications You can import data created on other applications as well as older versions of Graphical Analysis Here s how e import from Logger Pro Run Logger Pro and use Export from the File menu to create a file that Graphical Analysis 3 0 can read e import from older versions of Graphical Analysis The easiest method is to simply copy the data from the old version and paste it into Graphical Analysis 3 0 However you can also import the saved data Mac 1 In the older version save the data you want by choosing Export as Text from the File menu This will be a text file type 2 In Graphical Analysis 3 import the data by choosing Import from Text file from the File menu Windows 1 In the older version save the data as you normally would This will be a dat file type 15 Graphical Analysis for Windows USER S MANUAL 2 In Graphical Analy
19. etric pressure data recorded in Portland OR during the biggest storm in the last 20 years of the last century Bungee Jump A 3 Axis Accelerometer was used to record acceleration in three directions during a bungee jump Driving Through Mountains Here are temperature air pressure and relative humidity data collected as a car drove from Portland Oregon over the Cascade Mountain Range to Madras Oregon Drop Zone Ride This data was collected with a Low g Accelerometer data on the Drop Zone ride at Great America Santa Clara CA Heart Rate While Running This is heart rate date collected by a 50 year old male running on hilly terrain Hot Air Balloon Ride Here are temperature and pressure data during a hot air balloon flight Lake Data This Dissolved Oxygen pH and Total Dissolved Solids data was collected at Hagg Lake Oregon Riding up the Space Needle Acceleration and air pressure data taken during a ride up the Seattle Space Needle 24 Graphical Analysis for Windows TEACHER S MANUAL General Notes Statistics The standard deviation used in statistical calculations is x n x2 std dev 4 n i where Xm mean 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 nx yi Exi e n Xx Zxj Zx Xv Exi
20. formation on disk before quitting 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 online Help system built into the program Create a new data set Select the New Data Set option from the Data menu or click the 18 button from the Data Browser Resize an object It is possible to resize objects and they can even overlap 1 Select an object by single clicking on it When an object is selected its border becomes visible along with eight resizing handles 2 Clicking and dragging a resize handle will resize the object in the appropriate direction Remove an object 1 Select the object by clicking on it 2 Scroll under the Edit menu and select Delete Delete a column or data set Choose Delete Data Set or Delete Column from the Data menu Choose a column or data set from the list and click OK If the column chosen is a calculated or manual column the remaining columns will be unchanged Sort the data You can re order your data based on any column Select Sort Data dialog from the Data menu where you can choose the column and whether the data are sorted in ascending or descending order 16 Graphical Analysis for Windows USER S MANUAL Generate data If you want to automatically populate a colu
21. he 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 lt Enter Return gt tab or arrow keys To move vertically within the data table use lt enter return gt if it is set as such in File Preferences or up or down L ES arrow keys Once the cell is selected edit the cell by either typing in a new value or in using the left and right arrow keys and the delete keys to change a limited number of 4 075 101 73 digits in entry To accept the changes and automatically adjust the graph press 5 ii I1 73 lt enter gt tab or either the up or down arrow The changes will also be accepted if B 125 101 68 you click another cell with the mouse 7 1 50 101 73 If you are entering numbers in scientific notation use the E or key as in the examples below To enter this number Type this 3 5 x 104 3 5E4 2 4x 102 2 4e3 5 5 x 10712 5 5 E 12 l The range of numbers allowed to be entered is 25 x 10 to 25 x 10 absolute value 9 Graphical Analysis for Windows USER S MANUAL The Data Browser The Data Browser represents all the data available to the current document not simply the i Data Browser data from the current graph table or page data will always be accessible in the browser e a regardless of whether it s visible in the current page the current table or graph
22. ion Data are imported only into the latest data columns You can also use this feature to import data prepared or collected in another program into Graphical Analysis Several different formats are supported and are automatically detected Supported formats are Data exported as text from Logger Pro or from Graphical Analysis 3 0 Graphical Analysis for Windows 2 1 files saved as dat not exported as text Data exported as text from Graphical Analysis 2 for Macintosh Generic tab or comma separated data Data can be strings or numbers Note Ifa word processing program is used to prepare data in any of these formats the file must be saved as text Each text file created in Graphical Analysis file has a specific structure that includes a time stamp data column names short names units and data If you make changes to the exported file be sure to preserve the structure After choosing this option select the appropriate file name in the Open File dialog Sample Data Files A variety of sample data is included with the Graphical Analysis 3 software This data can be found in the Sample Data folder of Graphical Analysis The Sample Data folder contains five folders Biology Chemistry Physics Imported Data and from older versions of Graphical Analysis Here are the contents of each folder Biology Cell Respiration Cell respiration is the process of converting the chemical energy of organic molecules into a form immediately
23. ions It also teaches you how to enter or define your own functions 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 Two tutorials Linearization Part 1 and Linearization Part 2 teach you how to linearize data in order to find data pair relationships 19 Graphical Analysis for Windows TEACHER S MANUAL Graphing Data Collected with Texas Instruments Graphing Calculators LabPro CBL 27 and CBL TI Graphing Calculators You can use the Graphical Analysis program to transfer the data on the calculator to your computer for analysis or printing To do this you need a TI GRAPH LINK cable which is part of the TI GRAPH LINK package and 15 sold by Vernier Software amp Technology and other Texas Instruments dealers This cable connects the TI graphing calculator to the serial or USB port of your computer Importing procedures for TI 73 TI 83 TI 83 Plus TI 83 Plus Silver Edition TI 86 TI 89 TI 92 TI 92 Plus 1 Connect the T GRAPH LINK cable to a free serial or USB port ofthe computer mE and to the TI calculator COM 2 Turn on the calculator Gray SedalCable Black Link Cable 3 With Graphical Analysis running pull down the File menu and choose Import Modet THB3 Pius From TI Calculator or LabPro CBL or click the butt
24. mn with generated numeric values or special labels such as months or data set names select New Manual Column from the Data Menu Check the Generate Column box in the Column Definition tab You can then scroll the list for the values or labels you want Click OK and the new column will be added to your current Data Set Interpolate or extrapolate from the Perform a curve fit then choose Interpolate from the Analyze menu regression line or fitted curve of the data Load Data from a TI 73 TI 82 TI 83 Connect the TI GRAPH LINK cable Choose Import from TI 83 Plus TI 85 TI 86 TI 89 TI 92 TI Calculator on the File menu or click the import button or TI 92 Plus graphing calculator 17 Graphical Analysis 3 0 TEACHER S MANUAL Getting Started Computer Requirements Windows requirements e Windows 95 Windows 98 Windows 2000 Windows NT 4 x Windows ME and Windows XP e 133 MHz Pentium processor or better e 16MB physical RAM plus free hard disk space for virtual memory e Color monitor gt 256 colors Macintosh requirements e MacOS 8 x MacOS 9 x MacOS X e 66 MHz PowerPC processor or better e 16MB machine RAM 8MB for the application partition Loading Graphical Analysis onto Your Hard Drive To install Graphical Analysis on a computer running Windows 95 98 2000 M E NT XP follow these steps Place the Graphical Analysis CD in the CD ROM drive of your computer 2 If you have Autorun ena
25. n get the error values from another column This error number can then either be interpreted as a percentage of the base value or as a fixed value Column Options E4 Column Definition Options Paint Protectors 606 Style Empty Square E EH ej custom Display Every fi Paints m Displayed Precision Error Bar Calculations C Percentage Cc Pived value genteeecennsnerscncassnnenegroncanoes A nr Tr nstz At Decimal Places Constant ee Significant Figures Cancel 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 Creating a New Graph To create a new graph select Graph from the Insert Menu There are a number of ways to choose which columns are graphed 1 Click on each axis and check a column 2 Drag a column from the Data Table or 3 Data Browser to the graph 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 Grouping Objects Objects may be grouped togethe
26. ng this and other Vernier Software amp Technology 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 27
27. on from the toolbar aatia The dialog box to the right should appear 4 From the Port menu choose USB port or serial port COM 1 4 on a PC modem E or printer on a Mac to which the TI GRAPH LINK cable is connected m Choose Data fo rper Tau may choose mare than one tem 5 If you are using a PC serial cable identify whether it is a gray or black cable 6 Click on the Scan for Calculator button The calculator model you are using should now be identified and you should see a message Ready to Import 7 Click on the data lists that vou want to import To select more than one list on a Macintosh hold down the amp amp key while you click 8 Click OK to send the data lists to the computer The data will appear in columns in the data table They will be labeled with the simple list names from the calculator If you want to re name them or add units double click on the column heading in the data table and enter new labels and units Importing procedures for the TI 82 and TI 85 1 Repeat steps 1 5 above 2 Click on the Scan for Calculator button The calculator model you are using should now be identified and you should see a message Waiting for you to transmit data from your calculator 3 You can then choose which lists to transmit to the computer Here s how TI 82 Calculators On the TI calculator press LINK then select 2 Select All from the SEND menu Use
28. on of the velocity graph or a quadratic function to that portion of the distance graph to determine the acceleration due to gravity Bouncing Ball The data shown here is a record of the position of a bouncing ball In addition to the raw distance and time data numerous calculated columns appear including velocity acceleration kinetic energy potential energy and total energy Capacitors This data is the voltage or potential difference across a capacitor as it was discharged and charged through resistor Use the data to investigate exponential and inverse exponential functions Trumpet and FFT This file contains the waveform for a trumpet sound produced by an electronic keyboard The also contains a Fast Fourier Transform or FFT analysis of the data The FFT shows the frequency and amplitude of the fundamental frequency and overtones for this sound Tuning Fork Here is the waveform pattern from a 256 Hz tuning fork recorded by a microphone You can analyze the data to determine the amplitude period and frequency of this waveform Y ou can also fit a sine function to the data either automatically or manually 23 Graphical Analysis for Windows TEACHER S MANUAL Imported Data Accelerating a Car This is acceleration data collected with a Low g Accelerometer The data was collected as a Toyota Celica with a four speed manual transmission accelerated from 0 to 95 km hr 26 4 m s Barometer During a Storm This is barom
29. pear Enter the name short name and units for the new column and move to the Equation box Define the new column in this box by either typing in a formula or by scrolling and selecting a Function derivative integral smoothing and absolute value etc Variable and or Constant provided If you choose to type in the formula you must include the name of any column in double quotes You can then select which axis to assign the column to X or Y New Calculated Column x Column Definition Options Data Sets m Labels and Units Name Calc Column 1 Short Name Units Insert Symbol Equation Functions Variables Columns Constants H When Adding This Column to a Graph Add itto the Y Axis C X Asis To demonstrate this process consider the example where you have pressure and volume data from an experiment and it is stored in columns labeled pressure and volume 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 Calculated Column dialog box After entering reciprocal volume for the new column name Vol 1 for the short name and reciprocal mL for the new column unit click the the Equation box Next type in the 1 followed by the divide key Pull down the list of variables to see all the columns Choose the volume
30. plays a legend using Data Column labels in the graph object 10 Graphical Analysis for Windows USER S MANUAL New Data Whenever a data set or column is created it will automatically be added to the graph or table Appearance X and Y Error Bars The ranges or error bars are defined by the raw values in the selected variables This error number can be interpreted as a percentage of the base value or as a fixed value Point Protectors Mark every nth point with a point protector Set the styles and the spacing between point protectors in the Column Options Dialog Connecting Line Connect data points with lines to create a continuous plotted line Bar Graph Draw line from horizontal axis to points Grid Major and Minor Tick Style Select line style for grid lines Major and Minor Tick Color Select grid line color Click OK to make your selections take effect Changing the Scale of a Graph In most circumstances the program automatically adjusts the axis scales of the graph but you may want to change them To change the scale of a graph move the Ss mouse to the graph and click either axis label A dialog box like the one to the Fm H right will appear You have three different choices for the scaling of each axis If you select Manual pues Scaling you can enter the minimum and maximum values to be used on the axis E Enter the appropriate value in each box If you choose Autoscale the program
31. r When multiple objects are selected the group command causes their relative positions to be linked and they can be moved selected and relatively resized as a single rectangular entity complete with resizing handles Grouping a locked object will make the group locked Grouping may be nested that is a group can contain other group Objects can be grouped by selecting more than one object click on an object hold down the Shift key and click on another object or Lassoing by holding down the mouse button and encircling the objects to be selected and choosing Group from the Page Menu Multiple Data Sets Graphical Analysis data can be stored in multiple data sets The use of different sets of data is a good way to compare various experimental results For example the figure to the right shows time and pressure data for sugar fermentation in two different runs The aad 26 LS data set on the left was collected using lactose while dextrose was EE 02 rm ns 3 0500 0 995 0500 1 00 used for the second data set In this example each data set in a Data l 4 0 0750 100 Table object contains the same set of columns and each can be 100 ne 1 100 graphed separately Note that data sets don t need to have the same _ 125 ee 101 set of columns When several data sets are combined on a graph 150 0 995 1 40 1 01 every set has a different shape point protector a separate point to point line and s
32. rve Fitting section of the User s Manual Note Black brackets mark the beginning and end of a selected range You can click and drag the brackets and the curve fit statistics etc will update automatically 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 Or when you hold the mouse button down and drag the mouse pointer over the graph the X and Y differences delta appear at the bottom of the graph This 1s only available if you have the Mouse Position and Delta option in Graph Options selected 12 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 several examples showing the use of this concept To create a new column select either New Calculated Column or New Manual Column from the Data Menu You can also click the Hie button for a calculated column or the d button for a manually entered column from the Data Browser If you choose a manually entered column enter the name short name and units for the new column and click OK If you choose to add a calculated column the dialog below will ap
33. s the active object on the screen If you select this option for a document that includes a large data table the entire data table may not appear You can print individual tables or graphs only by selecting Print Data Table or Print Graph from the File menu The Data Table option will print the entire data table including rows not displayed in the object This option may produce many pages of paper In printing with a network it is useful to attach identification To do so select Printing Options from the File menu An options dialog will appear If you check the Footer checkbox you can enter your name the data comments page number and page title and it will appear in the bottom 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 program For example you may want to include the graphs in a report being written with a word processing program To copy a graph click the graph object to make it active and then choose Copy from the Edit menu This places a bitmap of the graph in the clipboard You can then paste the graph into another application Y ou 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 object to the clipboard You can then paste it into the other application If nec
34. sis 3 import the data by choosing Import from Text file from the File menu Choose Files of types As you go to load the file you will get a warning message Click on OK and import the file as text e To import from Excel Run Excel and load or create your spreadsheet Go to File Save As and choose the option Text tab delimited e To import from a word processor Type in rows of data separating each data point by a tab Separate columns with Enter Return Save this as text 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 file Graphical Analysis saves data in the ga3 format When you save a file as a ga3 file everything about that file including data text and graph setups 1s saved 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 1f you want to save this in
35. tions tab allows you to control how your data are plotted The other tab Axes Options allows you to choose which data columns are plotted and how the graph is scaled You can also bring up this box by double clicking on the graph Graph Options x Graph Options Axes Options r Title butterscotch Examine Appearance E Te Em Hate Eia bar M e LOU CU calculations and Point Ie Position and Delta Enter Bars Protector styles ane set m Iuno M for each column Mew Data Connect Lines T Add Mew Date Sets and Columns 7 Ba Graph r Gre Tick Ste dak ary Mina Tick style XP gor att pugne Dotted gray Help Cancel Title You can add and change the title text and its color The title will be placed at the top of the graph Examine Interpolate To use interpolation you must first create a curve fit or linear fit on a graph When you select Interpolate the helper object connected to the linear fit line or curve fit will extend to show the coordinates at the current point By moving the mouse along the curve you can read values from the graph Mouse Position and Delta A display of the current cursor position will be given When you hold the mouse button down and drag the mouse pointer over the graph the X and Y differences delta appear at the bottom of the graph Legend Dis
36. to locate the lists on the SELECT menu Position the arrow in front of a list you want to send to Graphical Analysis and press to select it More than one list may be selected in this manner A Bl will appear beside each list that will be sent To deselect press ENTER The BI will disappear Press then select 1 Transmit The lists will appear in the import window on the computer They will be labeled with simple list names from the calculator TI 85 Calculators On the TI calculator press LINK then press lt SEND gt Press MORE then press lt LIST gt Use v Jto locate a list you want to send and press lt SELCT gt to select it More than one list may be selected in this manner A Bl will appear beside each list that will be sent To deselect press ENTER J The W will disappear Press XMIT gt to transmit the list s to the computer The lists will appear in import window They will be labeled with simple list names from the calculator 5 Click on the data list s that you want to import To select more than one list on a Macintosh hold down them Apple key while you click 20 Graphical Analysis for Windows TEACHER S MANUAL 6 Click OK to send the data lists to the computer The data will appear in columns in the data table They will be labeled with the simple list names from the calculator If you want to re name them or add units double click on the column heading in the data table and enter new labels an
37. ts you want to import 6 Click OK The lists or saved experiments will be assigned to a Data Table Click the Refresh Catalog button if you have connected a new interface or calculator to the computer Port Cable It is important to correctly identify the port and type of cable being used so that Graphical Analysis can successfully communicate with the interface If the TI GRAPH LINK cable is connected to a different serial or USB port you can choose the port from the pull down menu Status The interface will be detected automatically Click the Refresh Catalog button if a new device has been connected Choose Lists to Import The LabPro CBL 2 or original CBL s catalog will be listed Highlight the list s you wish to import into the current page and click OK Troubleshooting Tips e Make certain that the cable ends are firmly attached to the computer and interface e The interface needs power batteries or AC adapter e Ifyou are using a serial port make sure that the port is working and not tied up by another application e g TI GRAPH LINK Palm Pilot Note Choosing Import will terminate any ongoing LabPro CBL 2 data collection 21 Graphical Analysis for Windows TEACHER S MANUAL Importing Text You can import data saved with the Export Text menu item or files created and saved from other software e g Excel The file must be in the tab delimited or comma separated text format a txt TEXT dat or csv extens
38. usable by organisms These data show the CO gas levels during the respiration of germinating peas Notice that a linear fit has already been done to show the rate at which CO was produced Diffusion This data compares the increased conductivity that results when various concentrations of saline solution diffuse through dialysis membranes into dissolved water A linear fit to the data in a particular run represents the rate at which the salt is diffusing EKG The EKG is a graphic tracing of the heart s electrical activity A typical tracing consists of a series of waveforms occurring in a repetitive order A little more than one waveform is displayed in this sample file Fermentation When yeast ferments sugars anaerobically CO gas 15 produced The data shown represent the change in pressure as the gas 1s produced A linear fit to the data determines the rate at which fermentation occurs Transpiration Transpiration is the loss of water from the leaves of a plant The rate of evaporation of water from the air spaces of the leaf to the outside air depends on the water potential gradient between the leaf and the outside air The data shown here represent the pressure change in an airtight tube filled with water into which a cut leaf is inserted As the leaf takes up water into the stem replacing that lost from transpiration the pressure in the tube decreases A linear fit to the data determines the rate of transpiration In this experiment
39. v numerical bookcpdf html chapter 15 i n wi yo o __ i n i n wW 2 m i j 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 call up Preferences from the File menu Uncheck the box next to Allow Automatic Curve Fit When you are finished editing the file save it From there you can have that file get called up whenever Graphical Analysis is launched or New is selected from the File menu Use the Browse button to locate your Startup File Refer to a statistics text for more information for example An Introduction to Error Analysis by John R Taylor Oxford University Press 1982 26 Graphical Analysis for Windows TEACHER S MANUAL Questions about Graphical Analysis Graphical Analysis is the fifth version of a program first written in 1982 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 usi
40. will automatically calculate a scale for the graph just fitting all the points on the graph If you choose from 0 the program will automatically choose the axis scale but it will always include zero on the axis i Cancel There are other ways to quickly adjust the axis limits from the graph itself 1 You can change each limit by clicking on that limit entering a new value in the small box that appears and pressing Enter Return I 2 When the cursor changes to the double arrow just outside the x or y axis line r click and drag to stretch or shrink the axis ss 10 Zooming In on a Graph You can zoom in on any region of a graph to examine it more carefully This command zooms in 50 or zooms to the selected area within a graph q Velocity vs Time Al 00 05 i10 15 20 1 Time s Cy To zoom in on a portion of a graph first click and drag the mouse to select a region on the graph then choose Zoom In from the Analyze menu or click on the Zoom In button Velocity m s on the toolbar The graph will rescale expanding the selected region to fill the plotting area Ai In this example the region is expanded to yield the graph to the right 4 Velocity vs Time ri f To go back to the original graph click the Zoom Graph Out button on the toolbar ps aw d rub sl 1 y pin 1 3 21 the numbers to be graphed are all positive the axis will start with zero If the numbers to b
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