2 groups, 1 way, repeated measure anova in MaLlab

Question

I have 2 groups of persons with repeated measures (the order of the measures does not matter [1,2] is the same as [2,1]). The data could look like that (3 persons per group, 6 measures each):

groupA = [1 3 6 5 2 9; 2 5 3 4 5 8; 8 7 3 6 2 4];
groupB = [3 4 5 4 4 1; 2 8 4 2 1 2; 3 2 5 5 1 2];

A straightforward way would be to compare the 2 groups via a ranksum test of the mean values of each person:

meansA = mean(groupA, 2); % => [4.3 4.5 5.0]
meansB = mean(groupB, 2); % => [3.5 3.2 3.0]
[p, h] = ranksum(meansA, meansB)

However, this type of analysis neglects that each of the mean values consists of several measures (and therefore underestimates the significance).

A statistician told me to use a "repeated measure ANOVA" instead but none of the ANOVA functions of MatLab seems to do exactly what I want. The closest thing that I could find was:

>> [p, atab] = anovan([1 3 6 5 2 9 2 5 3 4 5 8 8 7 3 6 2 4 3 4 5 4 4 1 2 8 4 2 1 2 3 2 5 5 1 2], {[zeros(1,18) ones(1,18)],[1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6]}, 'varnames', {'individual', 'groupAorB'}, 'display', 'off')
p =
       NaN
    0.9774

But this seems not to work in the way I want it (NaN value and unrealistic p-value). I would be happy for any suggestions on how to perform an appropriate statistical test on these data in MatLab.

Answer 1

You should have a look at this FileExchange entry that deals with the one-way repeated measure ANOVA:

http://www.mathworks.com/matlabcentral/fileexchange/5576-rmaov1

The author (Antonio Trujillo-Ortiz) made some other nice entries for different designs (2 and 3 way anovas with repeated measures).

Unfortunately, the regular statistical functions in Matlab do not allow for repeated measure designs.

Answer 2

The nan signifies that a model which accounts for INDIVIDUAL, accounts for all of the variance of GROUP. In otherwords, if you fit an intercept for each INDIVIDUAL, then try to find the variability due to GROUP, you have no variance left. The model is "overspecified".

This is because you actually need a mixed effects model - you are looking for a between-subjects effect. In order to achieve this, you need to tell MATLAB that INDIVIDUAL is nested inside GROUP. So you use the following parameters for anovan:

'random', INDIVIDUAL
'nested', INDIVIDUAL_within_GROUP

Having said that, I don't know what error covariance assumptions this makes - i.e. does it assume a diagonal covariance matrix?

If you want more control over the assumptions being made, I suggest you investigate NLMEFIT from the statistics toolbox. This allows mixed effects models specifying the covariance.