# Thread: determening normality in repeated measures ANOVA

1. ## determening normality in repeated measures ANOVA

Hi guys,

I'm not entirely clear on how to determine if the normality assumptions of a test are satisfied. I'll put my question in a step by step fashion:

I'm testing for normality by means of a Shapiro Wilk test.

1) randomized controlled trail with 2 groups
In you want to compare two groups for say blood glucose, with an indepdent sample t-test, do you test whether blood glucose is normally distributed in the first group and then test it again for the second group? Or do you just test the variable for your entire sample?

2) non-randomized controlled trail with 2 groups
Same question as with the randomized controlled trail, I'm just wondering if the non-randomized part changes something, because your sample could potentially come from 2 different populations in this case

3) repeated measurements
Imagine blood glucose is measured at 10 time moments. Do you have to test for normality for each of those time moments? What happens if 1 is not normally distribued? (RM is quite robust, so you could probably ignore it, but what if 4-6 of the 10 are not normally distributed?) If you don't have to determine it at each time point seperately, then what is the proper way (also when you have RM for multiple treatments?)

2. ## Re: determening normality in repeated measures ANOVA

Regarding question 1) You would need to test it in both groups separately. If you test it on the combined data, then you will be picking up treatment effects. If there is a big difference between control and treatment groups, then the distribution of the combined data will most certainly not be Gaussian (it will be bimodal).

A better method than looking at the raw data is to examine the residuals of the model (Google "residual analysis"). If you have two groups, then you will have to do two tests of significance. Then do you correct for multiple testing, and if so, which test? P-values and adjusted p-values can change depending on your decisions. This gets much worse when you have more groups.

It is also helpful to plot your residuals (histogram and Q-Q plot: http://en.wikipedia.org/wiki/Q-Q_plot) rather than relying only on a p-value. Remember: very small deviations from normality will be statistically significant with a large sample size, but are not relevant for inferences from the analysis, since many common tests are robust to small deviations from normality.

3. ## Re: determening normality in repeated measures ANOVA

Your answer is very clear. The only thing I'm not sure of, if you have to investigate normality at each time point in a repeated measure ANOVA (which has time as whithin subject factor). I think so?

4. ## Re: determening normality in repeated measures ANOVA

To be honest, I haven't used a repeated measures (RM) ANOVA in about 6 years. I don't know why it's even being taught still, mixed effects models are preferred (see http://www.ncbi.nlm.nih.gov/pubmed/14993119). But if I remember correctly, one of the assumptions of a RM ANOVA is multivariate normality, and looking at the normality at each time point separately won't provide you with this information. Don't worry about the normality of the raw data, it is the normality of the residuals that is important.

5. ## Re: determening normality in repeated measures ANOVA

SE_Lazic is right. multivariate normality is what you are after if you want to look at it from the raw data because multivaraite noramlity there would imply normality on the residuals, since a multivariate normal distribution guarantees than any linear combination of random variables sampled from it will also be normally distributed. nonetheless, normality on the residulas is what you should be concerned about.

6. ## Re: determening normality in repeated measures ANOVA

Thanks guys. I've been reading up/trying out the linear mixed model based on your suggestion, but I'm having trouble with it:

7. ## Re: determening normality in repeated measures ANOVA

Hi guys, I follow exactly what you are saying, and I am actually also trying to test the normality of the residuals. But I am not sure how to do so. My design is a crossover and involves 6 different treatments (with 5 different drugs added and 1 control) for each of which we measure the Dependent Variable at 9 time points. So I am using a SAS proc MIXED with 2 levels of repetition. But to test the residuals of my model, can I simply use a proc UNIVARIATE on the model residuals with a normality test and plots or do I need to test the residuals by treatment, by time?? do something else? Because so far the proc univariate shows graphs that do not have a very bad fit but the normality tests reject the normality hypothesis, and as my sample size is 30, I was lead to believe that you need to pay a lot of attention to those tests. Therefore I log transformed my DV, checked again the residuals of the model, nothing changed...

I hope you can help me

Thanks a lot!!

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