Sample size and correlational inference

Abstract

In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty, N. D. Berg, and J. C. Friedrich (2005). The results of a simulation study in the present article confirmed and extended previous theoretical claims (R. B. Anderson et al., 2005) that in a yes/no correlation detection task, small-sample advantages should occur but should be restricted to particular decision conditions. In 3 behavioral studies, participants viewed larger or smaller samples of data pairs and judged whether each sample had been drawn from a population characterized by a zero correlation or from one characterized by a greater-than-zero correlation. Consistent with traditional statistical theory, accuracy tended to be greater for larger than for smaller samples, though there was a small-sample advantage in 1 experimental condition. The results are discussed in relation to alternative theoretical and behavioral paradigms such as those of Y. Kareev (e.g., 2005) and K. Fiedler and Y. Kareev (2006).