Weighted normal plots are proposed as graphical checks on the normality of random effects in Gaussian linear models. The technique is illustrated using the one-way comparisons model Yi= μi+ ϵi, where the (μi, ϵi), are independent pairs with μiand ϵi, independent N(0, σ2) and N(0, σ2i), respectively, for i = 1, …, n. When the variance components σ2and σ2iare known, an unweighted normal plot of the standardized Zi= Yi(σ2+ σ2i)−1/2provides a check of the overall adequacy of the model. Weighted normal plots involve a modification that gives the ith observation a sample weight of Wi= (σ2+ σ2i)−1. Under the null hypothesis, the sample size must be larger by a factor of (1 + v/m2), where m and v are the mean and variance of the weights, to produce a weighted plot with approximately the same sampling variance as an unweighted normal plot. Despite this higher variability, we show that weighted plots are more sensitive than unweighted plots to several departures from the assumed distribution on the random effects, μi. Several numerical examples are included and the effects of substituting maximum likelihood estimates for the parameters σ2and σ2iare considered briefly. © 1985 Taylor & Francis Group, LLC.
Lagakos, S & Ryan, LM 1985, 'Statistical-analysis Of Disease Onset And Lifetime Data From Tumorigenicity Experiments', Environmental Health Perspectives, vol. 63, no. NA, pp. 211-216.
Lagakos, SW & Ryan, LM 1985, 'On the representativeness assumption in prevalence tests of carcinogenicity', Journal of the Royal Statistical Society Series C: Applied Statistics, vol. 34, no. 1, pp. 54-62.
View/Download from: Publisher's site
Conditions for the validityo f the Hoel-Walburga nd Peto tests, which compare dose groups with respect to tumour prevalence,a re replaced by a more generalc ondition, representativenesAs. large carcinogenicityex perimentp rovideda unique opportunityt o assess empiricallyif t his conditionh olds. Though representativenesws as generallyv iolated, neithert he Hoel-Walburgn or the Peto tests were seriouslyd istorted.A nalyticc onsiderationss uggestt hat such robustnessc an occur in manys ituations
RYAN, LM 1985, 'THE ANALYSIS OF TUMORIGENICITY EXPERIMENTS, USING INFORMATION ON TUMOR STAGE', BIOMETRICS, vol. 41, no. 2, pp. 567-567.
RYAN, LM & LAGAKOS, SW 1985, 'REPRESENTATIVENESS IN TUMOR PREVALENCE TESTS AND ITS IMPLICATIONS FOR ASSIGNING CAUSE OF DEATH', BIOMETRICS, vol. 41, no. 1, pp. 319-319.