Sample size and correlational inference.

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).

Sample size and the detection of correlation--a signal detection account: comment on Kareev (2000) and Juslin and Olsson (2005).

Simulations examined the hypothesis that small samples can provide better grounds for inferring the existence of a population correlation, p, than can large samples. Samples of 5, 7, 10, 15, or 30 data pairs were drawn either from a population with p=0 or from one with p>0. When decision accuracy was assessed independently for each level of the decision criterion, there was a criterion-specific small-sample advantage. For liberal criteria, accuracy was greater for large than for small samples, but for conservative criteria, the opposite result occurred. There was no small-sample advantage when accuracy was measured as the area under a receiver operating characteristic curve or as the posterior probability of a hit. The results show that small-sample advantages can occur, but under limited conditions.