Pearson's r is a correlation coefficient used to measure the strength of association between two variables that fall into the interval ratio category. Interval ratio variables are those which have a numerical value and can be placed in rank order. This coefficient is used in statistics. There are other correlation coefficient equations, such as correlation determination, but the Pearson's r formula is most commonly used.
View the following given information as an example:
Covariance = 22.40
Standard deviation x = 9.636
Standard deviation y = 3.606
Plug the given information into the following equation:
Pearson's Correlation Coefficient r = covariance/(standard deviation x)(standard deviation y) or use r = Sxy/(S2x)(S2y).
The result with the example is:
r = 22.40/(9.636)(3.606)
Calculate r = 22.40/(9.636)(3.606)
r = 22.40/34.747
r = .6446
r = .65 (round to two digits)
The answer can be positive or negative. The positive or negative shows the direction of the relationship. The closer the answer is to -1 or +1 the stronger the relationship is between the variables.
If you are given the variances instead, you will need to use the following formula: r2 = covariance squared/(variance x)(variance y). Square root the answer. You will need to add a negative sign if the original covariance in the equation was negative.