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Type I error and test power of different tests for testing interaction effects in factorial experiments
Author(s) -
Mendeş Mehmet,
Yiğit Soner
Publication year - 2013
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2012.00528.x
Subject(s) - mathematics , statistics , type i and type ii errors , factorial experiment , analysis of variance , factorial , normality , homogeneity (statistics) , main effect , f test , interaction , fractional factorial design , normality test , statistical hypothesis testing , mathematical analysis
A simulation study was conducted to investigate the effect of non normality and unequal variances on Type I error rates and test power of the classical factorial anova F ‐test and different alternatives, namely rank transformation procedure (FR), winsorized mean (FW), modified mean (FM) and permutation test (FP) for testing interaction effects. Simulation results showed that as long as no significant deviation from normality and homogeneity of the variances exists, generally all of the tests displayed similar results. However, if there is significant deviation from the assumptions, the other tests are observed to be affected at considerably high levels except FR and FP tests. As a result, when the assumptions of factorial anova F ‐test are not met or, in the case those assumptions are not tested whether met, it can be concluded that using FR and FP tests is more suitable than the classical factorial anova F ‐test.