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Graphical Analysis of Data

 

Graphical analysis is a useful method for determining the mathematical relationship between the dependent and independent variables of an experiment. The usefulness of the method lies in the fact that the variables represented on the axes of a straight-line graph are represented by the expression

y = m*x + b
where m = the slope of the line

b = the y-intercept of the line

The above equation holds true only if the data fit a straight-line graph. Thus, once the data set has been collected, modified, and plotted to achieve a straight-line graph, the mathematical equation can be derived. The discussion below describes the procedure.

 

Computing the Slope of the Line (if not using the computer):

1. Choose two points which lie on the straight line. The two points do not need to be actual data points. The two points should be spaced reasonably far apart.

2. Clearly write on the graph the x- and y- coordinates of the two points which you chose. Write the coordinates in the form of (x1,y1) and (x2,y2).

3. For the two chosen points, calculate the difference in the x-coordinate: x1 - x2.

4. For the two chosen points, calculate the difference in the y-coordinate: y1 - y2.

5. Calculate the slope by dividing the difference in the y-coordinate by the difference in the x-coordinate.

slope = (y1 - y2) / (x1 - x2)

 

Reading the y-intercept (if not using the computer):

6. From the graph,read the y-intercept. That is read the y-coordinate value of the line when the x-coordinate is zero.

Deriving the Equation:

7. Substitute the values of m (slope) and b (y-intercept) into the equation y = m*x + b.

8. Substitute the symbols of the dependent and independent variables into the y = m*x + b equation. The variable which is plotted along the vertical (y) axis is substituted into the equation for y. The variable which is plotted along the horizontal (x) axis is substituted into the equation for x.

 

Using the Graphical Analysis Software Program

Graphical Analysis is a software program which will graph experimental data, assist in finding a linear relationship between the variables studied in an experiment, and compute the slope of a line on the graph. Glenbrook South High School is liscenced to allow its students to use the program on any computer in the school. To use the program, follow these directions.

1. Insert the Graphical Analysis disk (or use the program on the hard drive).

2. Double-click on the disk icon to open the disk.

3. Open the Graphical Analysis 1.3.1 (or later) folder by double-clicking on it.

4. Open the application by double-clicking on the Graphical Analysis 1.3.1 icon. The main screen appears. This main screen is composed of two windows - a Data window (on the left) and a Graph window (on the right).

5. Note that there are two columns in the Data window - one is labeled X and the other is labeled Y. Move the hand tool to the X and click.

6. Type the symbol that represents the variable which you want to plot on the x-axis and press the Return key. For example, type d for distance if you wish to plot distance along the x-axis. Type R for radius if you wish to plot radius along the x-axis.

7. Type the units for this variable and press the Return key.

8. Move the hand to the Y and repeat steps 6 & 7 for the variable which you wish to plot along the y-axis.

9. Move the hand into the first cell (i.e., row) in the first column of the data table. The hand becomes a cross. Click once. Observe that the cell is enclosed by a box.

10. Using the keyboard, enter your data values into the cells of the data table. Pressing the Return key will advance the cursor down a column. Pressing the Enter or Tab key will advance the cursor across the column.

11. After entering the data, move mouse so that the cursor appears inside the Graph window and click. Horizontal lines will appear across the title bar at the top of the Graph window.

12. From the Graph menu, select the following graph features: Point Protectors, Regression Line, and Statistics. A check beside a Graph menu option indicates that the item is selected. Be sure that the other options in the Graph menu are not checked.

13. If the data points fit the straight line constructed by the computer (see box below), then select Print Graph from the File menu.

or

If the data points do not fit the straight line, change the power of the x-axis until the points do fit a straight line. Steps 14 - 17 will direct you through the task of changing the power in order to find a straight-line relationship between the two variables which you have measured.

 

Determining if the Data Points Fit a Straight Line

The software program is set up to draw the best straight line fit through the data points. This does not mean however that the data points fit the straight line. Thus, even though a straight line appears on the graph, there is not necessarily a straight line relationship between the two variables as graphed.

To decide whether or not the data points fit the straight line, observe the statistical indicators at the bottom of the graph. The slope and y-intercept should represent meaningful information. The C.O.R. represents the correlation coefficient of the regression line. This coefficient is a measure of how well the data points fit the straight line. A C.O.R. of 1.00 indicates that the data fit the straight line perfectly. Roughly speaking, a C.O.R. above 0.996 indicates that the data points fit the straight line reasonably well.

14. Click on the Data window to make it active. Horizontal lines should appear across the title bar for this window. Click on top of the x-axis data column (i.e., the first column). All data values in the column should be highlighted (darkened).

15. From the Data menu, select Raise to A Power (or any other modification option). A new column is added to the Data window and the software program waits for you to decide on the power to which you raise this variable (see Appendix A). Type in a power and press the Return or Enter key. Data values for the new column of data are written into the proper cells of the new column.

16. Click on the Graph window to make it active. Horizontal lines should appear across the title bar of the Graph window.

17. Move the arrow to the label of the horizontal axis and depress the mouse button. A pop-up menu appears. With the mouse button depressed, select the new variable to be plotted along the x-axis.

18. If the points do not fit a straight line, then repeat steps 14 - 17 using a different value for the power. If the points fit a straight line, then select Print Graph from the File menu. Note that this option is not available unless the Graph window is active (i.e., has horizontal lines across the title bar).

Before Quitting:

If you have been instructed to include the graph and/or data in a word processing document, then consult the directions below.

19. From the File menu, select Quit.

 

Copying Graphs into Word Processing Documents

The following instructions explain the procedure for copying a graph from the Graphical Analysis program and pasting it into a word processing document such as a lab report or writing assignment done with Microsoft Works, Microsoft Word, or any word processing program. The procedure assumes that the Graphical Analysis application is open and that the graph to be copied is already constructed. The procedure also assumes that you know how to use a word processing application and have already started the document (i.e., lab report or writing assignment) and have titled and saved it on a personal floppy disk.

1. Click inside the graph window to make it "active". An active window will have horizontal lines across the top of the window bar.

2. From the Edit menu, choose Copy Graph. The graph will then be copied into the clipboard. The clipboard is the Macintosh's invisible storage place for saving copied material which can later be pasted into a document.

3. Quit the Graphical Analysis application by choosing Quit from the File menu. If a dialogue box appears, asking if you wish to save your document, respond by clicking the appropriate box.

4. Open the document (i.e., the lab report or writing assignment) in which you wish to paste the graph by double-clicking on the document icon.

5. Scroll through the document to the position at which the graph is desired. Position the I-beam at the precise line where the graph is to be pasted and click the mouse. A blinking cursor should appear in the document at the desired location of the graph.

6. From the Edit menu, choose Paste. The graph should appear in your document at the designated location.

7. Once the graph is pasted into the document, it can be positioned in the usual manner using the ruler and the Format menu. The graph can also be resized in the usual manner. Placing the cursor immediately above (or below) the graph, clicking, and then pressing the Return key will add space between your graph and lines of text.

 

Copying Data into Word Processing Documents

The following instructions explain the procedure for copying columns of data from the Graphical Analysis program and pasting them into a word processing document such as a lab report or writing assignment done with Microsoft Works or Microsoft Word. The procedure assumes that the Graphical Analysis application is open and that the columns of data have already been entered. The procedure also assumes that you know how to use a word processing application and have already started the document (i.e., lab report or writing assignment) and have titled and saved it on a personal floppy disk.

 

1. Clickinside the Data window of Graphical Analysis to make it active. An active window will have horizontal lines across the title bar at the top of the window.

2.From the Edit menu, select Copy Data Set. The data will then be copied into the clipboard. The clipboard is the Macintosh's invisible storage place for saving copied material which can later be pasted into a document.

3. Quit the Graphical Analysis application by choosing Quit from the File menu. If a dialogue box appears, asking if you wish to save your document, respond by clicking the appropriate box.

4. Open the document (i.e., the lab report or writing assignment) in which you wish to paste the data set by double-clicking on the document icon.

5. Scroll through the document to the position at which the data set is desired. Position the I-beam at the precise line where the data set is to be pasted and click the mouse. A blinking cursor should appear in the document at the desired location of the data set.

6. From the Edit menu, choose Paste. The data set should appear in your document at the designated location.

7. Once the data set is pasted into the document, it can be positioned and reformatted in the usual manner using the ruler and the Format menu.

 

Survival Packet Contents:

[ Cover Page | Course Description | Grading Policy | Policy on Late Work and Makeup Work | The Be Attitudes | Problem Solving Tips | Graphical Analysis of Data | Henderson's Incomplete List of Frequently Used Abbreviations ]

 

 

E-mail: Tom Henderson || Last update: 8/24/2001