Some Large-Sample Tests for Nonnormality in the Linear Regression Model

Abstract

This study provides conditions under which several well-known and easily computable statistics for testing nonnormality (√b ₁, b ₂, D, W′, W) can be modified for large-sample use in the classical linear regression framework by replacing the true stochastic error with the least squares residual. Monte Carlo simulations indicate that the modified statistics perform acceptably well even for n = 35. None of the tests clearly dominates the others, although the modified version of W′ performs well for moderate sample sizes, while the modified D and omnibus R test, based on joint use of √b ₁ and b ₂, perform well for larger samples (n = 50, 100). We illustrate the use of normality tests using a recent empirical study by Lillard and Willis.

Key Words:

• Comparison of power
• Computer simulation
• Directional test
• Departures from normality
• Least squares residuals
• Omnibus test