n    one tail alpha 0.0025 0.005 0.01 0.025 0.05 two tail alpha 0.005 0.01 0.02 0.05 0.10 50 0.391 0.361 0.328 0.279 0.235 60 0.358 0.33 0.3 0.254 0.214 70 0.332 0.306 0.278 0.235 0.198 80 0.311 0.286 0.26 0.22 0.185

Some tables listing critical values for correlation coefficients provide more information than others. The table shown to the left (small portion show to save space) gives a little more information than Table A-6 presented in the appendix (Triola). In particular, it allows the calculation of critical values for more alpha levels and for one- or two-tailed tests. However, almost all tables have “gaps” in that they do not present all possible sample sizes for larger n. If you have a sample size that does not appear in a table, then take the conservative estimate provided in the table. This is done by rounding your sample size DOWN to the nearest n value in the table, and finding the appropriate critical value in that row.

You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that $\displaystyle {H}_{{a}}:\rho\ne{0}$. You have a data set with 54 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of $\displaystyle \alpha={0.005}$.

Find the critical value for this test (using the table provided above).
r_c.v. = $\displaystyle \pm$

Report answers accurate to three decimal places.