The parametric groups by trials analysis of varianceFratio is a widely used statistical test. When the variancc‐covariance assumption of the test is not met, researchers are commonly advised to use an epsilon‐correctedFratio. A non‐parametric alternative has also been recommended when this assumption is not tenable. The present study compares the Type I error rate and power of the conventionalFratio, the epsilon‐correctedFratio, and a non‐parametric statistic under various degrees of violation of the variance‐covariance assumption. The results indicate that only under gross violation of the assumption does the non‐parametric test show superior power to the parametric test. Additionally the results indicate that the power of the non‐parametric test is also affected by violation of the variance‐covariance assumption. In general the epsilon‐correctedFratio is recommended under the cond