Correlation for 2 sets of continuous values: Pearson Product-moment Coefficient (r)

Use the Pearson coefficientwhen both variables are at the interval level of measurement and normally-distributed in the population. It can be calculated in Excel if you have the data analysis module installed.

Example: A researcher wants to know whether scores on a linguistic ability test predict scores on the final exam in an Arabic language class. Here are the data from a dozen participants:

 Subject Linguistic aptitude (X) Final exam score (Y) 1 5 5 2 10 20 3 6 4 4 8 15 5 4 11 6 4 9 7 3 12 8 10 18 9 2 7 10 6 2 11 7 14 12 9 17

Take a look at the formula - just to get the idea (and in case you ever need it). You don't need to memorize it.

Here is the statistical result for the above language data:

 For correlation, the null hypothesis is that r = 0 -- that there is no relationship between the variables. The correlation coefficient is .667 (+ is assumed). The positive (+) coefficient indicates that the relationship is a positive one. The p value is less than .05, we can reject the null hypothesis. Conclusion: Linguistic aptitude predicts success on the final exam.

Hand calculation example.

Next section: Correlation for ranks, Spearman rs