On Small Sample Properties of Permutation Tests: a Significance Test for Regression Models*

In this paper, we consider a nonparametric permutation test on the correlation coefficient, which is applied to a significance test on regression coefficients. Because the permutation test is very computerintensive, there are few studies on small-sample properties, although we have numerous studies on asymptotic properties with regard to various aspects. In this paper, we aim to compare the permutation test with the t test through Monte Carlo experiments, where an independence test between two samples and a significance test for regression models are taken. For both the independence and significance tests, we obtain the results through Monte Carlo experiments that the nonparametric test performs better than the t test when the underlying sample is not Gaussian and that the nonparametric test is as good as the t test even under a Gaussian population.