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


From   Antoine Terracol <Antoine.Terracol@univ-paris1.fr>
To   statalist@hsphsun2.harvard.edu
Subject   st: [Non Stata] within and between "dispersion" in a plane
Date   Fri, 23 Sep 2011 12:01:53 +0200

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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