What Correlations Mean for Individual People: A Tutorial for Researchers, Students and the Public
Authors
René Mõttus
Department of Psychology, University of Edinburgh, Edinburgh, Scotland;
Institute of Psychology, University of Tartu, Tartu, Estonia
Abstract
Trisecting and cross-tabulating (TACT) two related variables shows what their correlation means for individual people. For example, knowing an individual's conscientiousness (lowest, medium or highest third among other people) improves the accuracy of predicting their health by 1.4, their child's conscientiousness by 4.2, and their job performance by 7.2 percentage points, compared to the random-guess accuracy of 33.3%. There’s a 35% probability that they will score differently in a few years and a 50% probability that their partner would rate their conscientiousness differently. For typical correlations in psychology, about 40% of individuals with a low or high value in one variable have a similar value in the other variable, while medium values carry almost no predictive information. Hence, correlations’ intuitive interpretations like "someone high in x is likely to be high in y" are almost always incorrect. An R package is provided for calculating and visualising TACT.
