{'fraction_non_alphanumeric': 0.029488291413703384, 'fraction_numerical': 0.0008673026886383347, 'mean_word_length': 5.073684210526316, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Accuracy of p-values of approximate tests in testing for equality of means under unequal variances

Seemingly, testing for fixed effects in linear models with variance-covariance components has been solved for decades. However, even in simple situations such as in fixed one-way model with heteroscedastic variances (a multiple means case of the Behrens-Fisher problem) the questions of statistical properties of various approximations of test statistics are still alive. Here we present a brief overview of several approaches suggested in the literature as well as those available in statistical software, accompanied by a simulation study in which the accuracy of p-values is studied. Our interest is limited here to the Welch’s test, the Satterthwaite-Fai-Cornelius test, the Kenward-Roger test, the simple ANOVA F-test, and the parametric bootstrap test. We conclude that for small sample sizes, regardless the number of compared means and the heterogeneity of variance, the ANOVA F-test p-value performs the best. For higher sample sizes (at least 5 per group), the parametric bootstrap performs well, and the Kenward-Roger test also performs well.