Learning to Detect Patterns in 2x2 Graphs

Effective data visualization and statistics education both involve helping viewers detect significant patterns in 2×2 graphs. These graphs plot a continuous y-axis variable against two predictors: one on the x-axis (Factor A) and one in the legend (Factor B). Using a preregistered, trial-and-error task, we asked 416 adult participants to classify 2×2 line or bar graphs as statistically significant or non-significant. We randomly assigned each participant a Target Factor—Factor A, Factor B, or the AxB Interaction—and tasked them with learning the corresponding classification rule. Line and bar graphs displayed identical numeric information.Four primary findings emerged. First, on each graph type, participants exceeded chance-level accuracy significantly more often when detecting Interactions than when detecting Factor A main effects. Detection rates for Factor B fell between those extremes. Second, among participants who performed above chance, line graphs yielded significantly higher accuracy than bar graphs for the Interaction and Factor B groups. No such line-graph superiority emerged for the Factor A group. Third, participants tasked with detecting main effects in bar graphs often applied a flawed cognitive strategy: they judged main effects as present only when an interaction appeared. This incorrect rule produced more systematic errors on bar graphs than on line graphs when detecting Factor A or Factor B main effects. Fourth, line graphs supported more orderly perceptual learning than bar graphs. For line graphs, the Interaction group consistently outperformed the Factor B group, who in turn outperformed the Factor A group. For bar graphs, the three learning curves overlapped with no clear hierarchy.These results can inform effective data visualization and statistics education by clarifying what patterns viewers readily see—and often miss—in 2×2 graphs.