ERIC Number: ED371023
Record Type: RIE
Publication Date: 1994-Apr
Reference Count: N/A
Type I Error Rates and Statistical Power for the James Second-Order Test and the Univariate F Test in Two-Way Fixed-Effects ANOVA Models under Heteroscedasticity and/or Nonnormality.
Hsiung, Tung-Hsing; Olejnik, Stephen
This study investigated the robustness of the James second-order test (James 1951; Wilcox, 1989) and the univariate F test under a two-factor fixed-effect analysis of variance (ANOVA) model in which cell variances were heterogeneous and/or distributions were nonnormal. With computer-simulated data, Type I error rates and statistical power for the two tests were estimated. With data sampled from normal distributions, the F test was not robust to variance heterogeneity for equal or unequal sample sizes, but the James second-order test was robust in these situations. With normal distributions, equal variances, and equal sample sizes, the magnitude of power difference between the two tests was generally small when testing the main effects, but the magnitude of power difference between the two tests varied when testing the interaction effects. With data sampled from nonnormal distributions, although the James second-order test generally was liberal when the population distribution was skewed, the test was robust under several nonnormal distribution situations. Additionally, the robustness of the James second-order test in factorial designs may be affected by combinations of nonnormal distributions, sample sizes, and variance patterns. (Contains 22 references and 7 tables.) (Author/SLD)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: F Test; Factorial Designs; Nonnormal Distributions; Type I Errors; Univariate Analysis; Variance (Statistical)
Note: Paper presented at the Annual Meeting of the American Educational Research Association (New Orleans, LA, April 4-8, 1994).