Testing for Correlations MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts

We have seen scatter plots that depict positive correlations, negative correlations, and no correlations. It was fairly easy to choose which type of correlation existed by looking at the scatter plots. But what do you do if you look at the scatter plot and have no idea what type of correlation may exist (without using your graphing calculator)?

There is an unique strategy that can be used to help determine the type of correlation.

1. Create your scatter plot for the data points.

 Divide the scatter plot grid according to the following rules:

2.  Draw a vertical line so that half of the points are to the left, and half of the points are to the right of this line.  Count the points to be sure of your placement of the line.  If you have an odd number of points, the "extra point" can go on either side of the line.

3.  Draw a horizontal line so that half of the points are above, and half of the points are below this line.  Count the points to be sure of your placement of the line.  Again, if you have an odd number of points, the "extra point" can go on either side of the line.

4.  Number these newly formed sections as you would number quadrants I, II, III, IV - starting in the upper right section and moving counterclockwise.

 To determine a possible correlation:

5. Count the number of points in each quadrant.  Record these numbers.

6. Add together the number of points in quadrants I and III.

7. Add together the number of points in quadrants II and IV.

8. Determine the type of correlation, based upon the following conditions:

 If the sum of I and III is more than twice the sum of II and IV, there is a positive correlation. If the sum of II and IV is more than twice the sum of I and III, there is a negative correlation. If neither condition is true, no evidence of correlation exists. This process was described in the CORD Math program.

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