# Can you compare Cramer's V and Spearman's $\rho$ values?

I did correlation tests between a number of variables consisting of both interval and categorical scales ($n = 1274$, one sample). I used $\chi ^2$ test for categorical vs ordinal and Spearman's $\rho$ for interval vs ordinal data.

The correlation between climate zone (zone $1, 2, 3, 4$) and daily exposure to air-conditioning (low, medium, high) is $0.35$ (Cramer's V).

The correlation between exposure to AC and pro-environmental attitude score ($1-5$, interval) is $0.21$ (Spearman's $\rho$).

Can I compare the strength of the relationship if I used different correlation tests, say the relationship between climate and exposure to AC is stronger than that between the pro-environmental attiudes and exposure to AC?

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Two small points:

1) As mentioned before - the two correlation measures are measuring different things, so a strict comparison of the two is risky.

2) If you also want to make a formal inference of the difference between the two, you will probably need to go with a permutation test, since (to my knowledge) there is no formal test that will make this comparison.

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Many thanks Tal Galili. Could you please explain more about the permutation test? I really have no idea what it is. –  tida Sep 23 '12 at 8:47