A note on testing the nullity of the between group variance in the one-way random effects model under variance heterogeneity

In an unbalanced and heteroscedastic one-way random effects model, we compare, by way of simulation, several test statistics for testing the null hypothesis that the variance of the random effects, also named the between group variance, is zero. These tests are the classical F-test, the test proposed by Jeyaratnam & Othman, the Welch test, and a modified version of Welch's test.