Small is Beautiful. The Use and Interpretation of R^2 in Social Research

Abstract

Few statistical measures are as highly respected by social researchers as is the coefficient of determination. In fact, its sheer magnitude is very often seen as the most important indicator of the quality of a study. In this paper, I challenge this view and argue that in research aimed at the test of a theory, R² whether big or small, is, in general, completely irrelevant. I maintain, moreover, that the common interpretation of R: as a measure of “explanatory power” is misleading, as is the belief that a high value of R² testifies that the “true” or “best” or “complete” model has been found. I also discuss the implications for research practice of the effect that the spread of the independent variable exerts on thecoefficient of determination.