Hello everyone,
As I touched upon in a previous mail - I know that, when conducting a repeated measures analysis, there are various tests to see if specific assumptions are met e.g. when dealing with within subjects factors- Mauchly's Sphericity Test to test the null hypothesis that the variance-covariance matrix of the transformed variables (to test the effect) has covariances of 0 and equal variances and, in addition, Box's M (when incorporating a between subjects factor) to test the null hypothesis that the variance-covariance matrix of the transformed variables (for a particular effect) is equal for all levels of the between-subjects factor(s)......
Additionally, I would like to ask about the testing of the normality assumption in a repeated measures analysis (and MANOVA).
Repeated Measures:
1) In the simple case if we have N subjects and 1 within subjects factor. The within subjects factor has k levels. There is a single dependent variable (measure) recorded k times for each subject....
One reference I have found says that - for each level of the within subjects factor, the dependent variable must have a normal distribution. So I assume that I would have to conduct k separate tests to test the normality assumption - one for every level of the within subjects factor?
2) For the more complicated case (mixed design) where we have a between subjects factor (say with 3 levels) and a within subjects factor (say with 5 levels). There are a different set of (say) 20 subjects in each of the three levels of the between subjects factor - there is a single dependent variable (measure) recorded 5 times for each subject....thus the design has 15 'cells' (3 x 5) and there are 300 values recorded in the table (3 x 5 x 20).
How would I test the normality assumption in this case?
MANOVA:
3) On another topic (MANOVA) : one of the assumptions is that 'the vector of dependent variables follow a multivariate normal distribution'.
Say, for argument's sake, we had one factor with three levels and we had 2 dependent variables - our aim being to establish if there is a difference between the levels of the factor (as regards the combinatory effect of the 2 dependent variables). Am I correct in thinking that we would determine if 'the vector of dependent variables follow a multivariate normal distribution' by testing for multivariate normality in each of the 3 levels of the factor *separately*?......so, for level 1 of factor, we would establish if there was evidence of MVN - similarly, we would do the same for level 2 and level 3 of the factor. I could use the %MULTNORM macro in SAS to test for MVN in each level of the factor.
I have read that repeated measures ANOVA is robust to departures from normality (when we have a moderate/large sample size) - but often we do not have a lot of subjects to work with.....also, for MANOVA, sample sizes are often small.
Any advice would be appreciated or a reference to a good, clear text with an example (especially for application in SPSS). Information is very thin on the ground.
All the very best,
Kim
Dr Kim Pearce PhD, CStat
Senior Statistician
Haematological Sciences
Institute of Cellular Medicine
William Leech Building
Medical School
Newcastle University
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Newcastle upon Tyne
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