Testing Normality in Designs With Many Parameters

• Published in: Technometrics 2006-08, Vol.48 (3), p.436-444
• Main Authors: Lockhart, Richard A, Perera, Chandanie W
• Format: Article
• Language: English
• Subjects: Anderson-Darling test; Applied sciences; Approximation; Computer science; control theory; systems; Covariance; Cramér-von mises test; Critical points; Data processing. List processing. Character string processing; Datasets; Design of experiments; Distribution functions; Empirical distribution function; Empirical process; Exact sciences and technology; Goodness of fit; Hypotheses; Integral transforms; Mathematics; Memory organisation. Data processing; Normal distribution; P values; Photons; Probability; Probability and statistics; Radiation; Radiation dosage; Random errors; Regression analysis; Sciences and techniques of general use; Software; Statistics; Thermoluminescence
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/004017006000000147

Goodness-of-fit tests are proposed for the assumption of normality of random errors in experimental designs where the variance of the response may vary with the levels of the covariates. The exact distribution of standardized residuals is used to make the probability integral transform for use in tests based on the empirical distribution function. A different mean and variance is estimated for each level of the covariate; corresponding large sample theory is provided. The proposed tests are robust to a possible misspecification of the model and permit data collected from several similar experiments to be pooled to improve the power of the test.