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.