Through a narrow window: working memory capacity and the detection of covariation

The samples of data that people use in their attempts to detect relationships in the environment are limited in size by working memory capacity. The implications of that constraint are explored by analyzing the sampling distribution of the most common measure of relationship - the product moment correlation (Pearson's r_xy). This distribution is skewed when the population correlation differs from zero (i.e., when a correlation exists), and the more so, the smaller the sample. As both the median and the mode of the sampling distribution are more extreme than the population value, it follows that samples likely to be encountered indicate a correlation stronger than that in the population. Thus, the limited capacity of working memory may serve as an amplifier that helps people to avoid missing strong relationships. As the distribution is more skewed the smaller the sample size, the effect suggests an explanation for the fact that young children detect meaningful covariation fairly rapidly.