Accuracy of $p$-values of approximate tests in testing for equality of means under unequal variances

Rok, strany: 2009, 679 - 692

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.

ISO 690:

Volaufová, J. 2009. Accuracy of $p$-values of approximate tests in testing for equality of means under unequal variances. In Mathematica Slovaca, vol. 59, no.6, pp. 679-692. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0156-x

APA:

Volaufová, J. (2009). Accuracy of $p$-values of approximate tests in testing for equality of means under unequal variances. Mathematica Slovaca, 59(6), 679-692. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0156-x