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Nonparametric Competitors to the Two-Way ANOVA

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  • Larry E. Toothaker
  • De Newman

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.

Suggested Citation

  • Larry E. Toothaker & De Newman, 1994. "Nonparametric Competitors to the Two-Way ANOVA," Journal of Educational and Behavioral Statistics, , vol. 19(3), pages 237-273, September.
    • Handle: RePEc:sae:jedbes:v:19:y:1994:i:3:p:237-273
    DOI: 10.3102/10769986019003237
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