“GRAPHICAL ANALYSIS 3.1” by Vernier – Users Guide for Advanced Physics

see this as a WORD Printable document

 GENERAL COMMENTS

The purpose of this User’s Guide is to focus only on those features of the program that you need to analyze experimental data. You need to know how to enter the data, plot it, transform it to a linear relationship (if necessary), and then to fit the final data to a linear function. Once you have done this you can use y=mx + b to write an equation for the data.  Only when data cannot be linearized will you use the program’s “Automatic curve fit” function.  As a scientific tool linearization is a better option than automatic curve fitting for two reasons (a) automatic curve fitting gives very precise answers, this is great for mathematics but troublesome in science because it obscures the relationship between variables by blindly factoring in experimental error; (b) linearization allows you to clearly see the units of the numbers in the equation.

 GENERAL OPERATIONS

¿ The opening screen of Graphical Analysis 3.1, called a page, includes three areas called objects: a Table Object, a Text Object (Notes:-- this is where you will write found equations and relationships), and a Graph Object. Data entered into the data table (Table Object) is automatically plotted on the graph (Graph Object). At the top of the screen are a Menu Bar and a toolbar. You can make an object active by clicking it with the mouse. An active object has a set of boxes around its perimeter, which can be used to resize the object.

¿ The Menu Bar at the top of the screen has the following menu items:

[File Edit Data Analyze Insert Options Page Help].

Clicking on any menu item in the Menu Bar brings down a list of options. To select an option, move the mouse pointer to the option you want and click on it. Clicking a 2nd time on a menu item removes the list of options.

¿ Very often there is a shortcut to a menu option when you right click on a heading in the Table Object or on a label or number on the Graph Object.

 SETTING UP COLUMNS

To label the columns of your table double click on the “x” at the top of the table.  A window will open into which to you will put the long name of the variable, the short name of the variable, and the units of the variable.  YOU MUST INPUT UNITS.  Traditionally the independent variable goes on the “x” axis, however there are exceptions to this rule.  “Time” is often placed on the x-axis even when it is not the independent variable.  When you are done inputting information for the “x” variable click “OK” and then input information for the “y” variable.

ENTERING AND PLOTTING NEW DATA

Graphical Analysis automatically plots each data point as it is entered. You can enter data two ways.

1. Click on cell 1 under the x column, type in the first x-data and press Enter or Right Arrow to enter it. Type in the first y-data and press Enter or Right Arrow to enter it. Continue in this manner until all data are entered. After each data pair is entered, the corresponding data point is automatically plotted.

OR

2. Type in the first x-data, press Down Arrow, type in the second x-data, press Down Arrow, and continue down the column until all x-data is entered. Use the Arrow Keys to move the cursor to the top of the y column and type in the y-data in the same manner using Down Arrow. As each data pair is completed, the corresponding data point is automatically plotted.

 TO EDIT DATA POINTS

1. To change a data entry. Activate the data table. Move the cursor to the cell to be modified by either clicking on the cell with the mouse or using the Arrow Keys, type in the new value and press Enter.

2. To delete a data pair. Move the cursor to the row number to the left of the data pair you wish to delete and click to highlight the row. Press Delete. The data pair is removed and the data below this row are moved up.

MAKING THE GRAPH LOOK GOOD

Even though the graph is automatically plotted, there are several things you need to do to make the graph more attractive. You can add a title to the graph, remove the connecting lines between data points and adjust the scale of each axis.

¿ To make changes on a graph, there are at least three ways to access Graph Options. The easiest is to double-click anywhere in the graph area. You can also right click on the graph and select Graph Options... or select Graph Options... from Options on the Menu Bar. The Graph Options tab allows you to title the graph and to remove the line connecting points. The Options tab allows you to scale each axis.

1. Give the graph a title. Bring up Graph Options as described above and enter a title in the title box.

2. Remove the connecting line between points. The connecting line between adjacent points is a useful tool to see the general trend of a plotted graph, but you will want to get rid of it before doing a linear regression analysis on your data. Graphical Analysis 3.1 automatically draws these lines as data points are plotted. To remove the lines, bring up Graph Options as described above and you will see a toggle box labeled Connect Lines under Appearance. A check mark in front of the label indicates that it is ON. Selecting this option toggles it ON or OFF. To remove the connecting lines, toggle this option OFF.

3. Adjust the Scale. Graphical Analysis automatically scales the graph; however sometimes this can give you a distorted view of the data and obscure the relationship between the variables. To adjust the scale of each axis bring up Graph Options as described above and click on the Axis Options tab. Ignore the Y-axis Label, click on the menu button under Scaling: and select Manual. Then enter the minimum and maximum values for the Y-axis (called Bottom and Top). A similar procedure will change the scale on the X-axis (called Left and Right).

4. To Remove or Add Cursor Position. You may have noticed that when the graph is activated, the current position of the cursor is shown at the bottom left of the graph. To turn this feature ON or Off bring up Graph Options and check or un-check the box called Mouse Position and Delta in Examine: list.

5. To change the symbol for plotted points. The symbols (circles, small squares, triangles, etc.), which surround each plotted point, are called “point protectors”. To change the shape of the symbol, you must bring up Column Options. At this point, the easiest way to get Column Options is to right click anywhere on the graph area. Place the cursor on Column Options and select the y-axis label (the plotting symbol is associated with the y-axis variable). Select the Options tab and you will find a large menu of plotting symbols under Point Protector Styles. Another way to bring up the Y-axis Column Options box is to double click on the y-axis heading in the Table Object or to select the Y-axis from Column Options under Data on the Menu Bar.

 DATA TRANSFORMATIONS AND PLOTTING TRANSFORMED DATA.

One of the useful features of Graphical Analysis 3.1 is the ability to plot graphs of transformed data.

1. Create a New Column. To create a new data column of transformed data, click on Data on the Menu Bar and select New Calculated Column. The New Calculated Column dialog box appears.

Select the Column Definition tab enter the name and units for the new column and then move to the Equation box. Enter the formula for the data transformation in the Equation box. As you enter the formula, you can choose various functions (i.e. sin, tan, ln, etc.) from the Functions box. To use data from another column in the transformation formula, click on the button next to the Variables (Columns) box and select the required data column. The name of the column will appear in quotes in the formula. For example, to create a data column for the square of time where time data is an original column, you would select time from the Variables (Columns) box and then enter ^2 (which means raise to the power 2). The result in the Equation box would look like “time”^2. The multiplication symbol is *. The Options dialog tab in the New Calculated Column dialog box allows you to change the precision of the calculated numbers in the new column. When the formula is correct, select OK and the transformed data are computed and placed in the new column. Note that the new column appears in the Table Object and a slider appears below the table to allow you to view the various columns. The new data points are not automatically plotted. You must instruct the program what data to plot as described below.

2. To Delete a Column. If you make an error or no longer need a data column, delete it by selecting Delete Column from Data on the Menu Bar.

3. Plot the New Data - X-axis. To choose which data are plotted on the x-axis of the graph, move the cursor to point at the x-axis label and click. This brings up the X-Axis Options box. Click on the button next to the X-Axis window and select what column to plot on the x-axis. Using the mouse, click on the column you want to plot on the x-axis. Only one column at a time can be plotted on the x-axis. Before leaving the X-Axis Options box, change Scaling to Automatic so that the new data will plot on your graph.

4. Plot the New Data - Y-axis. To choose which data is plotted on the y-axis of the graph, point at the y-axis label on the graph and click to bring up the Y-Axis Options box. Select the column you wish to plot on the y-axis. You can also change the scale of the y-axis on this menu. Note that several y columns can be checked thus displaying several graphs on the same y-axis. When this occurs, the y-axis label shows the name of all the selected columns.

LINEAR REGRESSION – If you think your graph is linear you need to do a linear regression.  If you select no data points the program will use all of your data to find the regression equation. If you wish to use only a portion of your data click and drag a shaded box over the selected portion of your data.  You can do this either on the graph or the data table.

1. Find the Regression Function. To bring up the Linear Regression box either click on the icon (second from the right, it says R= at the bottom of the icon) on the Tool Bar or click on Analyze on the Menu Bar and select Linear Fit... A Linear Fit box appears.

2. To Change the Position and Format of the Regression Function Box. The Linear Fit box shows the function (y=mx +b), its slope, y- intercept, and some statistics. The COR statistic tells how closely the data correlates to a line, a COR of ׀1׀ gives a good indication of a linear graph, however you must also consider if the y-intercept is logical.  You must not blindly follow the statistics, you must think!

¿ You can click on the regression function box and drag it (hold the mouse key down) to any convenient position.

3. To Delete the Regression Function Box. To delete the regression function box click on the tiny box in the upper-right corner of the floating box or, alternatively, right click on the box and select Delete from the menu that appears.

AUTOMATIC CURVE FIT – Use Wisely

One way to determine the relationship between two variables is to modify the variables until you get a linear relationship. Another way is to try to fit various functions to your data and see which curve fits best. This option should be used 1) if you are having trouble determining which test plot to try in order to linearize your data; 2) if you have exhausted all other possibilities and have good reason to believe your data can not be linearized.

Automatic Curve Fit under the Analyze menu offers a list of standard functions to try as well as the ability to enter other functions. Find the Regression Function. To bring up the Curve Fitting box either click on the icon (it is on the far right and says f(x)=) on the Tool Bar or click on Analyze on the Menu Bar and select Curve Fit... A Curve Fitting box appears which shows a small graph of your data and a menu of possible functions that can be used to fit the data using regression analysis. Select (Linear) from the menu and click Try Fit. The test function is plotted on the small graph and its coefficients appear in a table on the right side of the box. Note that without leaving the Curve Fitting box, you can try any of the possible regression functions and immediately see the results on the small graph. When you are happy with the function, select OK. The trial fit will appear on the graph and the function, constants, exponents, and mean square error.  A low value for the mean square error indicates a good fit. Click on OK-Keep Fit if the fit is fine. The curve will appear on the graph and the function, constants, exponents, and mean square error will appear on the graph. If the fit is not good, click on the button Try New Fit to try other functions. Remember “Automatic Curve Fit” can only be your final answer if your data cannot be linearized. WARNING- if the “Automatic Curve Fit” gives you any power function (this includes: inverse power, inverse square, nth inverse) the data can be linearized and if the data can be linearlized you must linearize the data.

FINISHING

1. Write the found equation in the text box.  Make sure you use the names of the variables or correct abbreviations for the names of the variables in the equation, NOT “x” and “y”.  If needed use the ^ (shift 6) sign to indicated a power function.  Also remember to put in the correct numbers AND UNITS for the slope and y-intercept. 

2. Put the name of each group member and your lab group number into the text box.

3. Turn on PAGE- PAGE LAYOUT VIEW Arrange the windows so that the graph, text box, and as much of the data table as possible can be seen.  PAGE- AUTO ARRANGE may be helpful, but it will not arrange things perfectly.  You can click and drag each window just like you can in any WINDOWS program. You can also right click on boxes and change the size of the font.

4. Specific directions for saving or printing will be given for each assignment. For your own personal insurance it is suggested that you save your work to either a Floppy disk, USB key, or your school network drive.

The school’s site license for “Graphical Analysis” does allow us to make student copies of the program.  If you would like to have your own copy of the program please bring in $1.00.