# Normality test for anova mixed model in SPSS: I did it in two ways but the results are contrasting

I'm conducting an ANOVA mixed model 2 X 3 (group X condition). Right now, I'm checking for the assumptions of ANOVA, such as normality. I should check indipendently for group and condition, right? I did it in two ways: 1) By, at first, splitting the sample (selecting "Data/Split file..." and entering the group variable) and then running the "1 sample Kolmogorov-Smirnov Test" and choosing "Normal distribution". 2) Without splitting the sample, but selecting "Analyze/Descriptive Statistics/Explore..." and entering the group variable as a factor and clicking "Plots..." and checking "Normality plots with test".

The 1) returns all variables absolutely not significant (0.80 < p < 0.90). The 2) ran both the Kolmogorov-Smirnov and Shapiro-Wilk tests, with the former resulting not significant for all variables (but all p values lower than or equal to 0.20), instead the latter in some cases considerably significant (e.g. 0.012).

I don't know which one should I trust, can you help me? Thanks!

## 1 Answer

The K-S test under Nonparametrics menu (your point 1) assumes that you know the population parameters (mean and variance) of the distribution; by default they are set equal to your sample statistics but they are treated as true parameters. You shouldn't rely on such K-S test unless your sample is very large.

The K-S test under Explore menu (your point 2) applies Lilliefors correction to account for the uncertainty fact that your mean and variance are just sample statistics, not true parameters. You should generally prefer this test. It "stands for" non-normality: p-value is lower.

There are known a number of good alternatives to K-S normality test. Shapiro-Wilk is one of them; others include Anderson–Darling, D'Agostino–Pearson, Jarque–Bera - they all test different aspects of a distribution.

• Thank you for your answer! I have some more doubts: using K-S test under Explore menu I have such contrasting results with Shapiro-Wilk, which one should I trust? (my sample size is 20 people, 10 in each group) Moreover, I don't understand what it means that most of the p-values of the K-S are 0.200* with the * meaning "inferior limit of the effective significance" – Federico Nov 18 '12 at 21:36
• Lilliefors correction is only accurate with low p-values, that's where that footnote comes from. Shapiro-Wilk is good test for continuous data, it is not recommended with descrete data – ttnphns Nov 18 '12 at 21:48
• Thank you. The dependent variable is continous so I assume both are ok, aren't they? Nevertheless they give different results in most cases, e.g. p = 0.187 vs. p = 0.026. However I found that at least in one case, group1-measure1 (=the first of the 3 repeated measures of one of the two groups), both resulted a significant. Shouldn't I use ANOVA 2x3 then? – Federico Nov 18 '12 at 22:02
• Here is a picture of the result of the normality tests: s11.postimage.org/5udsqz2ub/image.jpg (you can't see the p = 0.187 vs. p = 0.026 in the image because those are from another test, actually to simplify I wrote about a 2x3 anova but I need to conduct two anovas, one 2x2 and one 2x3, but the problematic is the 2x2) – Federico Nov 18 '12 at 22:15