Computing Correlations Using Pearson Correlation Coefficients

Enter the data for the X variable into the webulator and click through the panels. Be sure to record the values as the numbers are not stored. Then, enter the data for the Y variable into the webulator and click through the panels. Be sure to record the values as the numbers are not stored.

In this example, consider the treadmill VO2 max scores to be the X variable and consider the 12 minute run VO2 scores to be the data for the Y variable.

12 Minute Run Scores: 33,19,25,41,27,39,36,31,28,44

 Position of number in the dataset Input Column 01 02 03 04 05 06 07 08 09 10 N = 10 Sum = (sum of scores) / N = mean =

Next click the button labelled "Difference scores", located at the bottom of the next form to compute the exact difference between each observed age that you entered, and the average age that was computed.

 (raw score - mean score) mean = difference score 1 difference score 2 difference score 3 difference score 4 difference score 5 difference score 6 difference score 7 difference score 8 difference score 9 difference score 10

Click Square Difference Scores
This will advance the calculation through to the computation

 (difference scores)2 squared score 1 squared score 2 squared score 3 squared score 4 squared score 5 squared score 6 squared score 7 squared score 8 squared score 9 squared score 10

Print the following table (or copy it to your word processor) to record the output from the computations in the webulator above so that you can compute the correlation coefficient.

The mean for X is: _______________________

The mean for Y is: _______________________

 Participant Number treadmill VO2 maxml/kg/minX 12 minute run VO2 maxml/kg/minY (xi- mean)ΔX (yi- mean) ΔY Cross Productof ΔX * ΔY (xi- mean)2 (yi- mean)2 01 47 33 02 36 19 03 55 25 04 39 41 05 57 27 06 46 39 07 43 36 08 29 31 09 54 28 10 37 44 Σ(ΔX * ΔY) Σ(Xi - mean)2 Σ(Yi - mean)2

The numerator is: Σ(ΔX * ΔY)
: _______________________

The denominator is:  the square root of the product of Σ(Xi - mean)2 * Σ(Yi - mean)2 _______________________