Nonparametric Competitors to the Two-Way ANOVA

Abstract

The ANOVA F and several nonparametric competitors for two-way designs were compared for empirical α and power. Simulation of 2 × 2, 2 × 4, and 4 × 4 designs was done with cell sizes of 5 and 10 when sampling from normal, exponential, and mixed normal distributions. Conservatism of both α and power in the presence of other nonnull effects was seen in the tests due to Puri and Sen (1985) and, to a lesser degree, in the rank transform tests ( Conover & Iman, 1981 ). Tests by McSweeney (1967) and Hettmansperger (1984) had liberal α for some designs and distributions, especially for small n. The ANOVA F suffers from conservative α and power for the mixed normal distribution, but it is generally recommended.

Results of a survey of attitudes of dairy veterinarians in New Zealand regarding painful procedures and conditions in cattle

“…This is clearly the case; however, the current analysis suggested that both effects were important as there was no signifi cant interaction between age and gender in estimated pain score. The analysis used, the Scheirer-Ray-Hare test, is conservative (Toothaker and Newman 1994). However, the p-values for all fi ve analyses were >0.8, which suggests that the lack of interaction was a robust fi nding.…”

Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?

“…Consequently, interaction and main effect relationships are not maintained after rank transformations are performed (Blair et al 1987). Parametric tests for interaction applied to ranks lack an invariance property, which produces distorted Type 1 and Type 2 error rates and have performed poorly compared with their normal theory counterparts (e.g., Salter and Fawcett 1993; Mansouri and Chang 1995; Toothaker and Newman 1994). Interaction tests for the rank transform (Conover and Iman 1981) have also performed poorly for a variety of other designs (Akritas 1990; Thompson 1993) including polynomial and response surface regression (Headrick and Rotou 2001), analysis of covariance (Headrick and Sawilowsky 2000; Headrick and Vineyard 2001) and repeated measures designs (Beasley 2002).…”

Influence of Media Type and Moisture on Adult Development and Pupal Mortality inRhagoletis indifferens(Diptera: Tephritidae)

“…A few data sets were not normal. No fully developed nonparametric equivalents to two-way ANOVA are available (Toothaker and Newman 1994), and according to McDonald (2009), ANOVA is not very sensitive to moderate deviations from normality; thus, two-way ANOVA was also performed for non-normal data. For experiment 2, a KruskalÐWallis test was performed.…”