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Abstract:
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In repeated measures factorial designs involving clustered units, parametric methods such as linear mixed effects models are used to handle within subject correlations. However, assumptions of these parametric models such as continuity and normality are usually hard to come by in many cases, not even to mention homoscedasticity. Furthermore, these assumptions may not even be realistic when data are measured in a non-metric scale. In this article, nonparametric effect-size measures for clustered data in factorial designs with pre-post measurements will be introduced. The effect-size measures provide intuitively-interpretable and informative probabilistic comparisons of treatment and time effects. The dependence among observations within a cluster can be arbitrary across treatment groups. The effect-size estimators along with their asymptotic properties for computing confidence intervals and performing hypothesis tests will be discussed. ANOVA-type statistics with \chi^2 approximation that retain optimal asymptotic behaviors in small samples are investigated. Missing data problem is also addressed. Our methods are shown to be effective in the presence of multiple forms of clustering.
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