SAMPLE SIZE IN MULTIPLE REGRESSION: 20 + 5K

摘要

There are many instances when a statistical power analysis is not reliable due to lack of information or because it doesn't suit the research goals. In these cases, other performance characteristics of the regression should be considered when trying to determine an appropriate sample size. Many informal rules of thumb have been provided as recommendations for the minimum sample size to be used in a multiple regression. The goal of these simple sample size formulas is to avoid overparameterization and insure generalizability rather than to accommodate a given statistical power. They are useful when conducting pilot studies, or working with new variables and/or new populations, or when reliability and predictive discrimination is of primary interest. However, these recommendations are largely unsubstantiated, somewhat arbitrary, and vary quite widely from one another. In this paper, reliability is used as the criterion for developing a formula for minimum sample size in the multiple regression model with continuous predictors. The ultimate formula, n = 20 + 5k, where k = number of predictors, is simple and optimal with respect to a principle based on the rate of change of the reliability criterion relative to n.