Learning to detect patterns in 2 × 2 graphs

Effective data visualization and statistics education both depend on helping viewers detect meaningful patterns in graphs. Here we investigated pattern detection in 2 × 2 graphs, a widely used form of data visualization. The 2 × 2 graphs display a continuous dependent variable across two predictors, each with two levels. Factor A appears on the x-axis. Factor B appears as distinct visual series, such as black versus white lines or bars. Prior research on 2 × 2 graphs examined viewers' verbal descriptions of Factor A, Factor B, and A × B interaction patterns. Those studies revealed what people can describe but not what they can perceive. The present experiment addressed that gap by testing how viewers learn to perceptually organize Factor A, Factor B, and interaction patterns in 2 × 2 graphs. In a preregistered trial-and-error task, 416 adults learned to classify 2 × 2 line or bar graphs according to Factor A, Factor B, or A × B interaction patterns. The line and bar graphs contained identical numeric information. Two primary findings emerged. First, line graphs produced higher accuracy than bar graphs for interaction and Factor B patterns. No such advantage appeared for Factor A patterns, where accuracy remained low across graph types. Second, participants who trained on bar graphs often adopted a flawed rule. They reported Factor A and Factor B patterns only when an interaction appeared. This classification error did not occur for line graphs. Both primary findings matched preregistered predictions. These results show that data visualization choices, including graph type and predictor placement, influence the perceptual availability of patterns in 2 × 2 graphs. Clarifying those perceptual limits advances both data visualization design and statistics education.