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Test Statistics for Hypothesis Tests Concerning Correlation Coefficient
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\(t_{n-2} = \frac{r\times\sqrt{n-2}}{\sqrt{1-r^2}}\)

  • \(t_{n-2}\) - t-statistic with "n-2" degrees of freedom
  • \(r\) - sample correlation
  • \(n\) - number of observations

For normally distributed variables, we can use the sample correlation coefficient and t-test with n-2 degrees of freedom to test whether the two variables are linearly correlated.

We use a two-tailed test with: the null hypothesis stating that the correlation coefficient in the population is equal to 0 and the alternative hypothesis stating that the correlation coefficient is different than 0.

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