Learning To Detect Patterns In 2x2 Graphs

Introduction: Factorial research designs play an important role in many academic fields. Accordingly, diverse academic disciplines commonly require students to develop skills in comprehending factorial graphs, often starting with simple 2x2 graphs. Prior studies on 2x2 graph comprehension had participants either "think aloud" (Ali & Peebles, 2013; Peebles & Ali, 2015) or provide written descriptions (Shah & Freedman, 2011) about 2x2 main effects and interaction effects. Those methods privilege declarative knowledge (what can be stated), and potentially miss perceptual patterns that participants might learn non-declaratively. To fill this gap, we measured perceptual learning in 2x2 graph-pattern-detection using a trial-and-error task that does not require declarative knowledge. Method: Participants viewed black and white 2x2 bar graphs or line graphs and classified each graph into either of two initially unknown categories. The categories corresponded to significant versus non-significant effects in one of three randomly assigned 2x2-target-factors. These included Factor A Main Effects (left vs right height differences), Factor B Main Effects (black vs white height differences) or Interactions (slope differences). Across trials, 2x2 graphs with significant effects had effect sizes that varied randomly among Cohen’s d values of 0.2 (“small”), 0.5 (“medium”), 0.8 (“large”). Results: Significantly more perceptual learning occurred for detecting significant effects in line graphs than for detecting significant effects in bar graphs (p<0.001). For line graphs and bar graphs alike, significantly more perceptual learning occurred for detecting significant interactions than for detecting significant Factor A Main Effects (p<0.001). Perceptual learning for detecting significant Factor B Main Effects fell between those two extremes. Surprisingly, perceptual learning did not depend on the effect sizes in the 2x2 graph stimuli. Discussion: Significant biases exist in how viewers perceptually organize 2x2 graphs. These biases have implications for effective data visualization (e.g., visualizing public health information), and statistics education (e.g., exploiting perceptually salient patterns).