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I'm currently a third year Biology student and I've annoyingly screwed myself over by not following the golden rule of stats, always know how to analyze your data prior to conducting the experiment. I'm conducting an investigation into whether or not there is any correlation between personality and music scores using a survey of fellow students. I've collected around 96 responses and have a 'liking' score for each respondent in 4 broad music categories and 5 broad personality categories (based on the 'Big-5' personality test).

I'm really struggling to find a good way to correlate these two data matrices to determine whether certain music preferences are correlated to particular personality types.

Ideally I would be looking for results in a table similar to how they are presented in this report (page 1250, the first 5 lines under the heading Big-5).

http://gosling.psy.utexas.edu/wp-content/uploads/2014/09/JPSP03musicdimensions.pdf[1]

I've also found something called Mantels Test which calculates correlation between two matrices however this just gives me a single p-value telling you whether or not they are related at all, not particularly useful in this situation.

http://www.ats.ucla.edu/stat/r/faq/mantel_test.htm

If anyone had any ideas on how to analyze this that would be absolutely amazing as I'm getting quite desperate, as its a major project and I've already talked to three lecturers and several students and no-one has really been able to help me.

tl;dr Need help finding correlations between two matrices of personality type scores (categorical) and music preference scores (categorical).

Michael
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First, your data are not categorical - you have ratings for musical genres and ratings on personality factors, both of which can be treated as continuous or perhaps ordinal, depending on how many levels each rating can have.

The easy thing to do is to run a separate regression for each musical preference score with the personality scores as independent variables. If the music scores are something like 0 to 100, then you can use regular regression at least as a start; if they are 1 to 5, you should probably use ordinal logistic regression.

A more difficult method (but one that may get you more of what you want) would be multivariate regression with all the music scores as DVs and all the personality scores as IVs. But you may not have enough data to get good estimates of all the parameters.

Peter Flom
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    `continuous or perhaps ordinal, depending on how many levels each rating can have` I feel it's a bit of apples and oranges. Continuous vs blunt (discrete) and (equi)interval vs ordinal are two different distinctions. – ttnphns Oct 26 '14 at 11:45
  • @ttnphns In this case, I think it comes to the same thing: Should ordinal regression or OLS regression be used. – Peter Flom Oct 26 '14 at 14:06