Belief Clustering in Inferences about Correlation


One important characteristic of human society is that individuals have intuitive beliefs about how various aspects of their environment (physical, social, etc.) correlate to other aspects. This paper tests the hypothesis that the mathematical environment can give rise to multiple clusters of beliefs when those beliefs concern the degree of co-relatedness between variables. Simulations were conducted demonstrating that when the sample size is extremely small (i.e., 3), the sampling distribution of correlations is either U-shaped (for distributions of the Pearson r) or W-shaped (for distributions of signed r squared). Behavioral data indicated distributions that tended to approximate a W shape. There was also evidence that when people guessed, because they felt they could not extract any useful information from the sample, they were biased to guess that the population correlation was zero. The findings support the hypothesis that a natural, multi-clustering of sample correlations leads to a multi-clustering of beliefs about the population correlation.

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