General linear model and residuals

Question

I am using SPSS for analysis of my data using general linear model for univariate ANOVA with 3 independent factors (2 levels each), one random ordinal factor (4 levels), and 1 covariate. I saved the residuals and tested for normality with Shapiro-Wilk and Anderson-Darling tests, but the residuals are non-normal. I read in some blogs and some people say that normality of the residuals is not that important and can be ignored, but some people say that is really important! I am confused about what I should do. I looked at some plots and residuals seems to match with logistic distribution, but I don't know whether this means anything. I have included them here. The graphs are in portuguese, but the names are really similar to english.

Shapiro-Wilk normality test

data:  data$residuals
W = 0.98624, p-value = 0.01239

Anderson-Darling normality test

data:  data$residuals

A = 1.109, p-value = 0.006521

The normality assumption is important (if it is important) for significance tests and confidence intervals but not otherwise. For non-Portuguese speakers you might just want to add a sentence saying what the de-trended plots are. — mdewey, Dec 28 '16 at 13:37
detrended plots = Gráfico sem tendência standardized residuals = resíduos padronizados thanks for the help guys! — Igor Simões, Jan 02 '17 at 11:11

score 1 · Accepted Answer · answered Dec 27 '16 at 22:05

It depends on the structure of your data. If you have only a few observation you are reliant on the finite sample properties, i.e. if you want to perform tests the assumption of normality is crucial. If you have a lot of observation that satisfy some assumptions (in the literature these assumptions are often refered as "grenander assumptions") then your estimator is asymptotically normal and thus your tests are asymptotically valid.

By the way, if you use a test to test for normality you already make an alpha error, i.e. the alpha error probability in all later performed tests is higher (since they are based on the normality assumption) than the actual given significance level.

General linear model and residuals

1 Answers1