How Effective Are Normality Tests at Detecting Violations of the Least Squares Regression Assumptions?

• Activity Number: 247
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Education
• Author(s): John H. Walker*+ and Jimmy A. Doi and Hongyan Wang
• Companies: Cal Poly and Cal Poly and Cal Poly
• Keywords: regression ; diagnostics ; residuals ; robustness ; normality ; teaching

Abstract

The ordinary least squares regression model assumes the independence, normality, and constant variance of the regression errors. Typically, these assumptions are verified using diagnostic plots of the regression residuals. However, there are hypothesis tests to check these assumptions. These tests could be very useful-especially for students, who often dislike the subjective nature of the plots. But, how effective are hypothesis tests at diagnosing regression problems? Since the t-tests for regression coefficients are robust to non-normal errors at large sample sizes, normality tests can detect non-normality when it has no effect on the regression results. For small sample sizes when we need them most, normality tests may have low power. We present a simulation study to investigate these issues and discuss how this affects the teaching of regression.