Managing heteroscedasticity in general linear models.

Abstract

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.

The Reliability of aVISION COACHTask as a Measure of Psychomotor Skills

“…The sample-based mean difference is an unbiased estimate of the population mean difference, regardless of the difference in sample sizes (Kirk, 1995). Although differences in sample sizes can have a deleterious effect on Type I error rates and power when the homogeneity of variance assumption is violated (Rosopa et al, 2013), because this assumption was not violated, inflated Type I error rates and low statistical power are not likely to be threats to statistical conclusion validity (Shadish et al, 2002). Future studies should investigate the effect of age with a sample that includes participants within the missing age range.…”

Core self‐evaluations and subjective well‐being in the U.S. and the Philippines: The moderating role of self‐construal

“…To test Hypothesis 2 and Hypothesis 3, multiple linear regression was used with SWB as the dependent variable. Note that assumptions of normality (Fox, 2008) and homoscedasticity (Rosopa, Schaffer & Schroeder, 2013) were not violated. To test Hypothesis 2, CSE, country, and CSE 9 country were used as predictors; the three predictors significantly explained a total of 31.6% of the variance in SWB (F(3,899) = 138.229, p < 0.01).…”

Task and person-focused leadership behaviors and team performance: A meta-analysis

“…Although based on the Schmidt and Hunter (2015) method, we were able to correct effect sizes for three types of errors (i.e. systematic error, sampling error and dichotomization) alternative methods like weighted least squares regression (Rosopa, Schaffer &Schroeder, 2013 andSteel &Kammeyer-Mueller, 2002) could further help, especially in exploring plausible moderators.…”