Sample size and multiple regression analysis.
Despite the development of procedures for calculating sample size as a function of relevant effect size parameters, rules of thumb tend to persist in designs of multiple regression studies. One explanation for their persistence may be the difficulty in formulating a reasonable a priori value of an effect size to be detected. This article presents methods for calculating effect sizes in multiple regression from a variety of perspectives and also introduces a new method based on an exchangeability structure among predictor variables. No single method is deemed superior, but rather examples show that a combination of methods is likely to be most valuable in many situations. A simulation provides a 2nd explanation for why rules of thumb for choosing sample size have persisted but also shows that the outcome of such underpowered studies will be a literature consisting of seemingly contradictory results.
Maxwell
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Department of Psychology, University of Notre Dame, 118 Haggar Hall, Notre Dame, Indiana 46556, USA. smaxwell@nd.edu
D002648:Child; D006801:Humans; D015233:Models, Statistical; D011581:Psychological Tests / Q000706:statistics & numerical data*; D011594:Psychometrics; D012044:Regression Analysis