Tests of Pearson's Correlation (1 of 6)

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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.

Null Hypothesis: ρ = 0
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.
  1. 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.

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

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

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