Access Type

Open Access Dissertation

Date of Award

January 2013

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Education Evaluation and Research

First Advisor

Shlomo Sawilowsky

Abstract

The t test has been suggested to be robust to departures from normality as long as group sizes are equal and samples approach 30 or more. The F statistic has also been proposed to have the same robust qualities as the t, though researchers have suggested that because a test is robust to departures from normality, that does not necessarily make it the best test for every situation. With the increase in computing capabilities, the permutation ANOVA has been explored as an alternative to the ANOVA under non-normal conditions to rehabilitate the loss of statistical power. Since the permutation ANOVA does not operate under the assumption of normality and uses actual scores, many researchers suggest that the permutation ANOVA is superior to rank tests such as the Kruskal-Wallis because ranking data disposes of valuable information. To compare the power of the ANOVA, randomization ANOVA, and the Kruskal-Wallis test, the researcher performed a Monte Carlo analysis on group sizes of n=10 to n=30 and groups of k=3 and k=5 using Fortran program language and the IMSL subroutine library. In 12 different treatment conditions, the researcher implemented equal treatment effect sizes of small (0.1 sd) to huge (1.0 sd) on each treatment group in graduated increments, until all but one group had received a treatment. Data were drawn from three theoretical distributions: the normal (Gaussian) distribution, the uniform distribution, and the chi-square (df=2) distribution. Results indicated that regardless of the number of treatment groups, the ANOVA and randomization ANOVA exhibited almost equal power under every distribution and effect size. The power of the Kruskal-Wallis was slightly less than the ANOVA and randomization ANOVA under the normal and uniform condition, and was significantly more powerful under the chi-square (df=2) distribution. The sample size and treatment effect had little to do with the relationship between the performances of the three tests but did affect the rate of power increase and maximum power achieved. Implications of the findings as well the contribution to existing literature is discussed.

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