Decisions Under Violation of Regression Normality

Two water resources engineering questions are considered to study the statistical effect and associated loss of incorrectly assuming normality in linear regression analysis. Monte Carlo simulation is used to investigate the small sample behavior of the estimated regression coefficients, estimated variances, and predicted values of the dependent variable when the errors are not normally distributed. The distributions simulated are lognormal, Pearson and LogPearson with varying degress of skew. The estimated values of the regression coefficients are not appreciably affected by skew of the error distribution. Decisions based on both the mean and variance are less robust to nonnormality than decisions based only on the mean. Many hydrologic decisions are based on confidence intervals or percentiles, which involve estimated standard deviations and, thus, may be quite sensitive to violation of the normality assumption.