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See detailAnalyse de la variance ou méthodes de transformation en rangs alignés : quelle méthode utiliser quand des conditions d'application ne sont pas rencontrées ?
Carletti, Isabelle; Claustriaux, Jean-Jacques ULg

in Bulletin USAMV-CN (2005), 62

Normality and homocedsticity of populations are the main assumptions to use analysis of variance. Il these assumptions are not fulfilled, alternatives are rank transform and aligned rank transform methods ... [more ▼]

Normality and homocedsticity of populations are the main assumptions to use analysis of variance. Il these assumptions are not fulfilled, alternatives are rank transform and aligned rank transform methods. To compare these methods, simulations have been conducted for study robustness properties of analysis of variance and aligned rank methods applied to two-fixed effects layouts in condition of non-normality or unequal variance. The results showed that aligned rank transform methods are more affected by unequal variances than analysis of variance especially when sample sizes are large. When variances are equal, these methods are theoretically robust to non normality but in practice when a normality pre-test rejects normality assumption, these methods are also not advised. [less ▲]

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