Checking Normality and Homoscedasticity in the General Linear Model Using Diagnostic Plots

References

• Atkinson , A. C. ( 1981 ). Two graphical displays for outlying and influential observations in regression . Biometrika 68 : 13 – 20 .
   Web of Science ®Google Scholar
• Atkinson , A. C. ( 1985 ). Plots, Transformations and Regression . Oxford : Oxford University Press .
   Google Scholar
• Atkinson , A. C. , Riani , M. ( 2000 ). Robust Diagnostic Regression Analysis . New York : Springer .
   Google Scholar
• Beckman , R. J. , Trussell , H. J. (1974). The distribution of an arbitrary studentized residual and the effects of updating in multiple regression. Journal of the American Statistical Association 69:199–201.
   Web of Science ®Google Scholar
• Bradley , J. V. ( 1980 ). Nonrobustness in Z, t, and F tests at large sample sizes . Bulletin of the Psychonomic Society 16 : 333 – 336 .
   Google Scholar
• Bradley , J. V. ( 1984 ). The complexity of nonrobustness effects . Bulletin of the Psychonomic Society 22 : 250 – 253 .
   Google Scholar
• Bürkert , A. , Bationo , A. , Piepho , H.-P. ( 2001 ). Efficient phosphorus application strategies for increased crop production in sub-Saharan West Africa . Field Crops Research 72 : 1 – 15 .
   Web of Science ®Google Scholar
• Cook , R. D. , Weisberg , S. ( 1982 ). Residuals and Influence in Regression . London : Chapman and Hall .
   Google Scholar
• Cook , R. D. , Weisberg , S. ( 1994 ). An Introduction to Regression Graphics . New York : Wiley .
   Google Scholar
• Cox , D. R. , Hinkley , D. V. ( 1974 ). Theoretical Statistics . London : Chapman and Hall .
   Google Scholar
• Csorgo , M. , Seshadri , V. , Yalovsky , M. ( 1973 ). Some exact tests for normality in the presence of unknown parameters . Journal of the Royal Statistical Society B 35 : 507 – 522 .
   Google Scholar
• Denis , J.-B. , Piepho , H.-P. , van Eeuwijk , F. A. ( 1997 ). Modelling expectation and variance for genotype by environment data . Heredity 79 : 162 – 171 .
   Web of Science ®Google Scholar
• Draper , N. R. , Smith , H. ( 1998 ). Applied Regression Analysis . New York : Wiley .
   Google Scholar
• Dufour , J.-M. , Farhat , A. , Gardiol , L. , Khalaf , L. ( 1998 ). Simulation-based finite sample normality tests in linear regression . Econometrics Journal 1 : 154 – 173 .
   Google Scholar
• Eskridge , K. M. ( 1990 ). Selection of stable cultivars using a safety first rule . Crop Science 30 : 369 – 374 .
   Web of Science ®Google Scholar
• Levene , H. ( 1960 ). Robust tests for equality of variances . In: Olkin , I. , Ghurye , S. G. , Hoeffding , W. G. , Mann , H. B. , eds. Contributions to Probability and Statistics . Essays in honor of Harold Hotelling. Stanford , CA : Stanford University Press , pp. 278 – 292 .
   Google Scholar
• Nelson , W. ( 1982 ). Applied Life Data Analysis . New York : Wiley .
   Google Scholar
• Meeker , W. O. , Escobar , L. A. ( 1998 ). Statistical Methods for Reliability Data . New York : Wiley .
   Google Scholar
• Piepho , H.-P. ( 1995a ). A robust test for homoscedasticity in a two-way layout . Biometrical Journal 37 : 151 – 160 .
   Web of Science ®Google Scholar
• Piepho , H.-P. ( 1995b ). Detecting, interpreting and handling heteroscedasticity in yield trial data . Communications in Statistics B—Simulation and Computation 24 : 243 – 274 .
   Web of Science ®Google Scholar
• Piepho , H.-P. ( 1996a ). A Monte Carlo test for variance homogeneity in linear models . Biometrical Journal 38 : 461 – 473 .
   Web of Science ®Google Scholar
• Piepho , H.-P. ( 1996b ). Weighted estimates of interlaboratory consensus values . Computational Statistics & Data Analysis 22 : 471 – 479 .
   Web of Science ®Google Scholar
• Piepho , H.-P. ( 1998 ). Methods for comparing the yield stability of cropping systems . Journal of Agronomy & Crop Science 180 : 193 – 213 .
   Web of Science ®Google Scholar
• Press , W. H. , Flannery , B. P. , Teukolsky , S. A. , Vetterling , W. T. ( 1989 ). Numerical Recipes in PASCAL . Cambridge : Cambridge University Press .
   Google Scholar
• Römisch-Margl , L. , Spielbauer , G. , Schützenmeister A., Schwab , W. , Piepho , H.-P. , Genschel , U. , Gierl , A. ( 2010 ). Heterotic patterns of sugar and amino acid components in developing maize kernels . Theoretical and Applied Genetics 120 : 369 – 381 .
   PubMed Web of Science ®Google Scholar
• Seber , G. A. F. ( 1977 ). Linear Regression Analysis . New York : Wiley .
   Google Scholar
• Seber , G. A. F. , Lee , A. J. ( 2003 ). Linear Regression Analysis. , 2nd ed. New Jersey : Wiley .
   Google Scholar
• Thode , H. C. ( 2002 ). Testing for Normality . New York : Marcel Dekker .
   Google Scholar