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This study examined the type I error and power properties of usual ANOVA, rank transform and aligned rank transform methods in the context of a balanced 2 x 4 fixed-effect layout. Different versions of F-test and Kruskal-Wallis test are used with four transformations (ranks, Blom normal scores, Van der Waerden normal scores, Savage scores) and three techniques of alignment (least-square, Lehmann, medians). In order to compare the robustness and the power of tests, simulations were employed for a variety of situations (absence or presence of nuisance parameters, small or large sample size, normality or non normality, equal or unequal variances). This study also examined these properties after a normal pre-test (moment test on standardized residuals) and a variance pre-test (Bartlett test or Brown-Forsythe test). The results showed that ANOVA is the more robust test among studies methods for all situations. Even if ANOVA has a moderate inflation in the type I error rate for some situations of unequal variances, non parametric alternatives of that study are not recommended for two-way fixed effects layouts.

Statistical methods --- Statistical methods