Seven (indeed, plus or minus two) and the detection of correlations.
Psychol Rev, 107 (2):
397--402 (April 2000)Abstract
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 phi, the contingency coefficient. The analysis indicated that,
for strong correlations (phi > .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.
