A Criterion-Specific Advantage for Small Samples in the Detection of Correlation

Abstract

The present work examines the counterintuitive hypothesis that small samples provide better grounds for inferring the existence or non-existence of a population correlation than do larger samples. Researchers have long cited capacity limitation as an explanation for sub-optimal performance (e.g., Miller, 1956; Broadbent, 1958). Yet, recent work (e.g., Kareev, 2000) has challenged the notion that more information is always better—and this challenge takes place in the domain of correlation detection which is, without question, fundamental to learning and cognition. Kareev (e.g., Kareev, 2000) noted that the sampling distribution of the Pearson correlation coefficient is skewed, and that the amount of skew increases as n (the number of elements in each sample) decreases. The top half of Figure 1 illustrates two such distributions (n = 5 and n = 10)

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