Data Analyses When Sample Sizes Are Small: Modern Advances for Dealing With Outliers, Skewed Distributions, and Heteroscedasticity

in Journal of Applied Biomechanics
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The paper reviews advances and insights relevant to comparing groups when the sample sizes are small. There are conditions under which conventional, routinely used techniques are satisfactory. But major insights regarding outliers, skewed distributions, and unequal variances (heteroscedasticity) make it clear that under general conditions they provide poor control over the type I error probability and can have relatively poor power. In practical terms, important differences among groups can be missed and poorly characterized. Many new and improved methods have been derived that are aimed at dealing with the shortcomings of classic methods. To provide a conceptual basis for understanding the practical importance of modern methods, the paper reviews some modern insights related to why methods based on means can perform poorly. Then some strategies for dealing with nonnormal distributions and unequal variances are described. For brevity, the focus is on comparing 2 independent groups or 2 dependent groups based on the usual difference scores. The paper concludes with comments on issues to consider when choosing from among the methods reviewed in the paper.

Wilcox is with the Department of Psychology, University of Southern California, Los Angeles, CA, USA. Peterson is with the Department of Exercise Science, California Lutheran University, Thousand Oaks, CA, USA. McNitt-Gray is with the Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA. McNitt-Gray is also with the Department of Biological Sciences, University of Southern California, Los Angeles, CA, USA.

McNitt-Gray ( is corresponding author.

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