The sampling distribution of Pearson's r is normal only if the population correlation (ρ) equals zero; it is skewed if ρ is not equal to 0 (click here for illustration). Therefore, different formulas are used to test the null hypothesis that ρ = 0 and other null hypotheses.

A hypothetical experiment is conducted on the relationship between job satisfaction and job performance. A sample of 100 employees rate their own level of job satisfaction. This measure of job satisfaction is correlated with supervisors' ratings of performance. The question is whether there is a relationship between these two measures in the population.

- The
first step is to specify the
null hypothesis and an
alternative hypothesis. The null hypothesis
is ρ
= 0; the alternative hypothesis is ρ ≠ 0.

- The second step is to choose a
significance level. Assume the 0.05 level
is chosen.

- The third step is to compute the sample value of Pearson's correlation (click here for the formula). In this experiment, r = 0.27.