st: [Non Stata] within and between "dispersion" in a plane

[Antoine Terracol <Antoine.Terracol@univ-paris1.fr>]

Hello _all,

I have the following data setup:

N individuals have been asked to report subjective beliefs 
(probabilities) 48 times. These 48 answers can be grouped into 12*4 
answers, as in fact there are only 12 question, each of them being asked 
4 times in a slightly different form.

Each answer is a vector of three probabilities, summing to one; so I 
really have 2 coordinates in a 2-dimensional simplex.

Graphing the data at the individual level, it looks like the answers for 
the groups of 4 similar questions tend to be clustered, while the 
overall dispersion of answers is much larger; but I'm not sure how to 
properly test for it.

In other words, I would like to know whether the overall dispersion of 
points in the simplex for each individual (48 points) is larger than the 
within questions dispersions (4 points per question, 12 questions).

Would you think that a manova of the two coordinates of the answers 
using a nested design would be appropriate? Something like

manova coordinate1 coordinate2 = id / question|id /


or would that be completely wrong/inapropriate?

I'm not used to analysing such data, and I'd appreciate any hint as to 
the correct way (if any) to analyse them.

Best,
Antoine

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