Sample-Size Planning for More Accurate Statistical Power: A Method Adjusting Sample Effect Sizes for Publication Bias and Uncertainty

Numerous rules-of-thumb have been suggested for determining the minimum number of subjects required to conduct multiple regression analyses. These rules-of-thumb are evaluated by comparing their results against those based on power analyses for tests of hypotheses of multiple and partial correlations. The results did not support the use of rules-of-thumb that simply specify some constant (e.g., 100 subjects) as the minimum number of subjects or a minimum ratio of number of subjects (N) to number of predictors (m). Some support was obtained for a rule-of-thumb that N ≥ 50 + 8 m for the multiple correlation and N ≥104 + m for the partial correlation. However, the rule-of-thumb for the multiple correlation yields values too large for N when m ≥ 7, and both rules-of-thumb assume all studies have a medium-size relationship between criterion and predictors. Accordingly, a slightly more complex rule-of thumb is introduced that estimates minimum sample size as function of effect size as well as the number of predictors. It is argued that researchers should use methods to determine sample size that incorporate effect size.

The call for researchers to report and interpret effect sizes and their corresponding confidence intervals has never been stronger. However, there is confusion in the literature on the definition of effect size, and consequently the term is used inconsistently. We propose a definition for effect size, discuss 3 facets of effect size (dimension, measure/index, and value), outline 10 corollaries that follow from our definition, and review ideal qualities of effect sizes. Our definition of effect size is general and subsumes many existing definitions of effect size. We define effect size as a quantitative reflection of the magnitude of some phenomenon that is used for the purpose of addressing a question of interest. Our definition of effect size is purposely more inclusive than the way many have defined and conceptualized effect size, and it is unique with regard to linking effect size to a question of interest. Additionally, we review some important developments in the effect size literature and discuss the importance of accompanying an effect size with an interval estimate that acknowledges the uncertainty with which the population value of the effect size has been estimated. We hope that this article will facilitate discussion and improve the practice of reporting and interpreting effect sizes.