when one size does not fit all a simple statistical method to deal with across-individual variations of effects当一个大小并不适合所有人一个简单的统计方法来处理各个变化的影响.pdfVIP

When One Size Does Not Fit All: A Simple Statistical Method to Deal with Across-Individual Variations of Effects Philippe Vindras*, Michel Desmurget, Pierre Baraduc Cognitive Neuroscience Center, CNRS UMR 5229, Bron, France Abstract In science, it is a common experience to discover that although the investigated effect is very clear in some individuals, statistical tests are not significant because the effect is null or even opposite in other individuals. Indeed, t-tests, Anovas and linear regressions compare the average effect with respect to its inter-individual variability, so that they can fail to evidence a factor that has a high effect in many individuals (with respect to the intra-individual variability). In such paradoxical situations, statistical tools are at odds with the researcher’s aim to uncover any factor that affects individual behavior, and not only those with stereotypical effects. In order to go beyond the reductive and sometimes illusory description of the average behavior, we propose a simple statistical method: applying a Kolmogorov-Smirnov test to assess whether the distribution of p-values provided by individual tests is significantly biased towards zero. Using Monte-Carlo studies, we assess the power of this two-step procedure with respect to RM Anova and multilevel mixed-effect analyses, and probe its robustness when individual data violate the assumption of normality and homoscedasticity. We find that the method is powerful and robust even with small sample sizes for which multilevel methods reach their limits. In contrast to existing methods for combining p-values, the Kolmogorov-Smirnov test has unique resistance to outlier individuals: it cannot yield significance based on a high effect in one or two exceptional individuals, which allows drawing valid population inferences. The simplicity and ease