The robustness of the t test of the correlation coefficient and the need for simulation studies

Abstract

The t test of the Pearson product moment correlation coefficient for the null hypothesis that the population correlation, ρ, is zero, is very robust to violations of normality as long as the variables are independent. This conclusion is based on the results of simulation studies. But to reach this general conclusion, no simulation studies arc needed. It is a consequence of the virtual coincidence of the permutation distribution of r with the normal‐theory distribution. This implies that the test is also robust in most of the cases not examined by simulation studies, as long as the variables are independent. Only some predictable and extreme situations can give problems. Simulation studies should be directed to these situations to gain further insight in the robustness of the t test. This has not been done and much effort is misdirected on the simulation studies. When the variables are non‐independent it might be expected that the test is non‐robust. Also in this case simulation studies are useful to gain insight in the robustness of the test.