Managing heteroscedasticity in general linear models.

Heteroscedasticity refers to a phenomenon where data violate a statistical assumption. This assumption is known as homoscedasticity. When the homoscedasticity assumption is violated, this can lead to increased Type I error rates or decreased statistical power. Because this can adversely affect substantive conclusions, the failure to detect and manage heteroscedasticity could have serious implications for theory, research, and practice. In addition, heteroscedasticity is not uncommon in the behavioral and social sciences. Thus, in the current article, we synthesize extant literature in applied psychology, econometrics, quantitative psychology, and statistics, and we offer recommendations for researchers and practitioners regarding available procedures for detecting heteroscedasticity and mitigating its effects. In addition to discussing the strengths and weaknesses of various procedures and comparing them in terms of existing simulation results, we describe a 3-step data-analytic process for detecting and managing heteroscedasticity: (a) fitting a model based on theory and saving residuals, (b) the analysis of residuals, and (c) statistical inferences (e.g., hypothesis tests and confidence intervals) involving parameter estimates. We also demonstrate this data-analytic process using an illustrative example. Overall, detecting violations of the homoscedasticity assumption and mitigating its biasing effects can strengthen the validity of inferences from behavioral and social science data.