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Using Johnson's transformation and robust estimators with heteroscedastic test statistics: An examination of the effects of non‐normality and heterogeneity in the non‐orthogonal two‐way ANOVA design
Author(s) -
Luh WeiMing,
Guo JiinHuarng
Publication year - 2001
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711001159438
Subject(s) - type i and type ii errors , mathematics , heteroscedasticity , normality , statistics , estimator , transformation (genetics) , statistical hypothesis testing , monte carlo method , truncated mean , variance (accounting) , normality test , econometrics , biochemistry , chemistry , accounting , business , gene
The present study proposes a procedure that combines Johnson's transformation and the trimmed means method to deal with the problem of non‐normality. An approximate test such as the Alexander‐Govern test or Welch‐James type test is then employed to deal with the heterogeneity of cell variance in the non‐orthogonal two‐way fixed effects completely randomized design. Both unweighted and weighted means analyses are considered. The empirical Type I error rates and the statistical power for comparing population means are investigated by Monte Carlo simulation. The simulated results show that Johnson's transformation with trimmed mean and the approximate test is valid in terms of Type I error rate control, and that the magnitude of the statistical power for non‐normal distributions is better than that of conventional methods.