Icon Arrays: A Key to Pictures That Effectively Aid Statistical Reasoning

ABSTRACT Statistical reasoning is often aided by a picture illustrating the data, but why pictures help is a matter of both empirical and theoretical debate. To help resolve both types of debates, this research compared identical reasoning tasks with pictures of the same overall shape but different internal features. Experiment 1 found that the best performances occurred when people were given clearly distinct icons (either organized or scattered), followed by overlapping icons, and the worst performance was with a picture of solid fields (no icons). Experiment 2, with a different and more complex reasoning task, found the best performances again with distinct icons (organized or scattered) and the poorest performance with the solid field picture (slightly below a control condition of no picture). Experiment 3 further replicated and extended these findings across different texts, icons, and colors. Participants also completed measures of numerical literacy, visuospatial ability, set reasoning ability, graph literacy, and nonmathematical cognitive reflection. All were correlated with Bayesian reasoning performance, as well as each other, but only numeracy showed consistent predictive ability. In addition to practical implications for effective communication of quantitative information, these results support a view that the mind is designed to more effectively use discrete individuated items in statistical reasoning.