# How do I find correlation measure between two nominal variables?

A survey was made where people chose what they use a certain smiley to represent and entered their country of origin. I have recoded the text responses to numeric.

What form of analysis should be used (preferably in SPSS) to check the level of correlation between where the people come from and the representations they chose?

There are a bunch of measures of nominal-nominal association.

There's the phi coefficient, the contingency coefficient (which I think applies to square tables, so perhaps not suitable for you), Cramer's V coefficient, the lambda coefficient, and the uncertainty coefficient. There are no doubt still more.

Many of them turn out to be a function of the chi-square statistic.

(If you have one or more ordinal variables, there are many other coefficients that are suitable for that situation.)

This wikipedia page lists the ones I mention.

I believe SPSS can compute the ones that I think match your rectangular nominal-vs-nominal situation - at least I am certain in the case of phi and Cramer's V and the lambda coefficient:

(Tables from here and here)

• I was thinking of using Cramer's V, but I read in Statistical Methods for Psychology (Howell) that "The problem with V is that it is hard to give a simple intuitive interpretation to it when there are more than two categories and they do not fall on an ordered dimension." I am not really sure what he means by that. Mar 11, 2013 at 1:10
• I think that criticism applies to most such measures. It's rectangular ($m\times n$) nominal-nominal association. How much intuition is there going to be? Mar 11, 2013 at 1:13
• Quite a lot. The survey is just a small part of the research, so conclusions will be drawn from other sources as well. Also knowing that there is correlation or not is good enough. Mar 11, 2013 at 1:23
• That sounds great (that you have in-subject knowledge that will convey intuition), though my point was more that almost any measure of nominal nominal association in a rectangular table is not in itself going to convey much intuition; I don't think it's a particular criticism of Cramer's V. For example, V is monotonic in phi; it the criticism applies to one surely it applies to the other. Mar 11, 2013 at 1:27

If you want more insight into the associations, you can fit a loglinear model to these data. (Analyze > Loglinear > General) or GENLOG, for starters.