Google

To illustrate a test of the correlation coefficient, consider a health psychologist investigating the correlation between people's calorie estimates and their weight. Having no directional expectation, she conducts a two-tailed test. For a sample of $$22$$ students, she computes Pearson's $$r$$ as $$-.21$$. Statistical software provides a $$p$$-value of $$.348$$. Because this $$p$$-value is greater than $$.05$$, she retains the null hypothesis, concluding there is no relationship between the variables. Alternatively, computing the test by hand, the degrees of freedom are $$20$$ ($$22 - 2 = 20$$), and a statistical table indicates the critical value is $$.444$$. Because the calculated correlation coefficient ($$-.21$$) is less extreme than this critical value, the $$p$$-value is confirmed to be greater than $$.05$$, leading to the same conclusion to retain the null hypothesis.

Learn Before

Related