Capacity limitations and the detection of correlations: comment on Kareev (2000)

Y. Kareev (2000) argued that the limited capacity of working memory may be an adaptive advantage for the early detection of useful correlations. His analysis indeed suggests that the optimal sample size is close to G. A. Miller's (1956) "magical number 7 +/- 2." The authors point out logical and statistical limitations of Y. Kareev's (2000) analysis, including that it neglects that the adaptive value is not determined by the hit rate but by the posterior probability of hit and that only signal trials are considered. The authors' analysis demonstrates that when these limitations are corrected for, the alleged benefit for small samples does not occur, and larger samples imply considerable improvement in the detection of correlations.