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