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A robust approach for analyzing unbalanced factorial designs with fixed levels
Guillermo Vallejo1, Manuel Ato, M Paula Fernández
1University of Oviedo, Oviedo, Spain. gvallejo@uniovi.es
Behavior Research Methods
|May 19, 2010
Summary
Hall
Area of Science:
- Statistics
- Statistical Methods
Background:
- Factorial designs often assume normality and homogeneity of variance.
- Violations of these assumptions can impact the reliability of statistical tests.
Purpose of the Study:
- To evaluate Hall's transformation and Box-Cox transformation for Brunner-Dette-Munk (BDM) and Welch-James (WJ) tests.
- To assess performance under separate and joint violations of normality and variance homogeneity in factorial designs.
Main Methods:
- A simulation study using Monte Carlo methods was conducted.
- Data were sampled from various distributions, including skewed ones, with small sample sizes.
- Unweighted marginal means were used to explore operating characteristics.
Main Results:
- Original BDM and WJ tests showed robust error rates with symmetric distributions.
- Skewed distributions led to poorly controlled error rates for original BDM and WJ tests.
- Hall's transformation improved Type I error control compared to Box-Cox transformation, especially with skewed data.
Conclusions:
- Hall's transformation of the BDM test offered the best Type I error control.
- While powerful, WJ tests with Hall's transformation were sometimes less powerful than original WJ tests when error rates were controlled.
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