A Lens model analysis of covariation research

Abstract

Abstract Researchers have obtained conflicting results regarding which of the four cells of a two‐by‐two information matrix affect covariation judgments. Here published covariation studies are used as data in a lens model study. Regression models were estimated for actual correlation and subjects' judged correlation, with the four cells used as independent variables in the models. It was concluded that all four cells affected covariation judgments in this meta‐analysis and that the complex Pearson's phi was well approximated by a linear model. Additionally, aggregated judgments of covariation matched phi better than they matched the linear model of phi. Additional analyses were conducted to test whether cell usage results differed when data sets with negative correlation were deleted (they did not), whether experimenter emphasis on cells affected subjects' use of cell data (it appears likely), and to test whether the match with Pearson's phi was an artifact of using aggregated data (it appears likely).

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