Differences in Variance, Skewness, and Kurtosis Can Account for Differences in Binary Outcomes

When researchers consider the relation between continuous predictors (e.g., perceived threat) and binary outcomes (e.g., being stopped by police), they typically adopt a means-focused approach, (a) attributing observed differences in binary outcomes to expected mean differences in continuous predictors and/or (b) predicting expected differences in binary outcomes using observed mean differences in continuous predictors. Because non-mean distribution moments of the continuous predictor (variance/skewness/kurtosis) also predict binary outcomes, this means-based approach can lead researchers to make inaccurate inferences about the relation between continuous predictors and binary outcomes and overlook viable cognitive explanations for individual or group differences in binary outcomes. We describe the extent to which differences in non-mean distribution moments for continuous predictors translate to differences in binary outcomes (Part I). We show that modeling non-mean distribution moments can change predicted binary outcomes (Part II) and inform existing psychological theory (Part III).