Statistical (non-parametric) test for different sized groups, changes over time

#1
I want to compare two groups at two time points with measurements for the same quantitative variables two years apart. The participants within the groups are the same at both time points.

One group is larger than the other (n=40, n=10), the data is not normally distributed. The grouping criterion is based on physical aspects and is not randomized.

I want to look at difference over time within the groups, and also between the groups. Suggestions on how to do?
 

Karabiner

TS Contributor
#2
Repeated measures analysis of variance with an additional grouping factor (a.k.a. mixed ANOVA, split-plot ANOVA).

And, no, "the data is not normally distributed" is a meaningless consideration within ANOVA (unless you mean
data within groups; but even this is not important if total sample size is large enough, as is the case here).

With kind regards

Karabiner
 
#3
Thanks for your reply.
I meant that the data within the groups are not normally distributed. I thought that normal distribution was an assumption for the repeated measures ANOVA, though I might be mistaken? I get significant results when testing for normality with both the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Is this not a problem?
 

Karabiner

TS Contributor
#4
In general, normality (within groups, or of the residuals) is considered a less important assumption, and even
irrelevant if the sample is large enough. Maybe you would like to perform a search for ANOVA normality
assumption robustness
and/or for ANOVA normality assumption central limit theorem .

With kind regards

Karabiner