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The Effects of Misconceptions on the Properties of Friedman's Test
Authors:Roy St. Laurent  Philip Turk
Affiliation:1. Department of Mathematics &2. Statistics , Northern Arizona University , Flagstaff , Arizona , USA;3. Department of Statistics , West Virginia University , Morgantown , West Virginia , USA
Abstract:Friedman's test is a widely used rank-based alternative to the analysis of variance (ANOVA) F-test for identifying treatment differences in a randomized complete block design. Many texts provide incomplete or misleading information about when Friedman's test may be appropriately applied. We discuss the assumptions needed for the test and common misconceptions. We show via simulation that when the variance or skew of the treatment distributions differ, application of Friedman's test to detect differences in treatment location can result in Type I error probabilities larger than the nominal α, and even when α is unaffected, the power of the test can be less than expected.
Keywords:Analysis of variance  Heteroskedasticity  Nonparametric test  Power  Size of test  Skew
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