Seven (indeed, plus or minus two) and the detection of correlations

Capacity limitations of working memory force people to rely on samples consisting of 7 ± 2 items. The implications of these limitations for the early detection of correlations between binary variables were explored in a theoretical analysis of the sampling distribution of φ, the contingency coefficient. The analysis indicated that, for strong correlations (φ > .50), sample sizes of 7 ± 2 are most likely to produce a sample correlation that is more extreme than that of the population. Another analysis then revealed that there is a similar cutoff point at which useful correlations (i.e., for which each variable is a valid predictor of the other) first outnumber correlations for which this is not the case. Capacity limitations are thus shown to maximize the chances for the early detection of strong and useful relations.