Computing the Pearson Correlation

 

After entering the data, the next step is to order the program to actually compute the correlation coefficient for you. Use the mouse to go to the top of the screen and click on the following sequence: Statistics > Correlate > Bivariate. This will open another input window. You will see two boxes with the one on the left containing the complete list of variables for the study. [Note: The variables will appear in alphabetical order which is the default variable display. However, it can often be more convenient to display the variables in the same order as they appear on the spreadsheet or input window. The display order can be changed by clicking Edit > Preferences. Then change "Alphabetical" to "File" by clicking the empty circle next to "File" under "Display Order for Variable Lists." Unfortunately, SPSS will need to be exited and then reloaded before this option will take effect.] The box on the right will be empty. In between the boxes is a right-pointing arrow. The sequence for computing a correlation is to highlight variables from the list on the left and then use the mouse to click the right-pointing arrow. This will cause each highlighted variable to jump to the box on the right. Each variable in the box on the right will be included in the correlation matrix computed by SPSS. Thus, in order to compute the correlation between COLGPA and STUDYHRS, move both variables over to the box on the right. A variable can be removed from the box on the right by highlighting it and clicking the arrow in the middle which will now face in the opposite direction. Once the variables you want to correlate are in the right-hand box, the OK button could be clicked which would cause the correlations to be computed and appear in an Output window. However, there are a couple of additional points worth considering.

First, it can be extremely helpful to click the Options button which appears at the bottom of the input window. This will cause another input window to appear. Generally, all options can be left on their default settings. However, one option allows you to print means and standard deviations for each variable in the analysis by just clicking the box. This is worth doing. The other options should be left alone unless you have a specific reason for changing one. At this point you must click the Continue button in order to close this box and move on with your task. The next step is simply to click the OK button. After a short delay, an Output window will appear with the results of your analysis. The information in the output file can be viewed or saved to a disk using standard Windows conventions. Additional analyses can be performed and their results will be appended to the end of the current output window so the results of a complex series of analyses can be contained in one output window. Be sure to give this file a name that will remind you of its contents. The results for the example are shown below:

 

  Mean Std. Deviation    N  
COLGPA 2.9455 .7285 11
STUDYHRS 23.8182 13.4001 11


                                Correlations

  COLGPA STUDYHRS
COLGPA Pearson Correlation 1.0000 .868**
  Sig. (2-tailed) . .001
  N 11 11
STUDYHRS Pearson Correlation .868** 1.0000
  Sig. (2-tailed) . .001
  N 11 11

**. Correlation is significant at the 0.01 level (2-tailed).

To interpret the output, look at the table labeled Correlations. This is a correlation matrix with three numbers for each correlation. The top number is the actual Pearson correlation coefficient which will range from -1.00 to +1.00. The further away the correlation is from zero, the stronger the relationship. The correlation between study hours and college GPA in this fictional study was .868 which represents an extremely strong relationship. The next number is the probability. Remember, you are looking for probabilities less than .05 in order to reject the null hypothesis and conclude that the correlation differs significantly from a correlation of zero.  The third number is the sample size, in this case 11. Correlation coefficients that can not be computed will be represented as a dot.

Another nice thing to do when computing a correlation is to look at the scatter diagram. To produce a scatter-plot, click Graphs > Scatter > Define >. Use the same technique as before to transfer variables to the x-axis and y-axis boxes. Then click OK and the graph will appear in the Chart Carousel window. To insert the plot in another document, click on File > Copy Chart, open your word processing document, and Paste it into the document.

 

Saving Output and Data Files

If you attempt to close either the data input or data output windows of SPSS, the program will respond with another window prompting you to save the file with either a user-supplied name or a generic name. Output files are given the extension, .spo, and data files are given the extension, .sav. The usual Windows conventions with respect to saving and reopening files apply using commands under the File menu.

 

 

 


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