# Strength of the correlation between a qualitative and a quantitative variable

Hello
Does anybody know, how I can identify the correlation strength between a qualitative variable and a quantitative variable?
With ANOVA I could identify through the p-value, that there is a significant association, but I don't know how to identify the strength of the correlation in R-studio.

For instance I did it with two qualitative variable with a chi-square test to identify if there is a relationship and then in a next step with the Cramers V to find the strength of the association.

Is there also something like a Cramers V for the ANOVA model?

Best regards

Hi, MAY90,

(it looks like we're compatriots), it doesn't make sense to talk about correlation between a qualitative, also known as categorical or nominal variable, and a quantitative (i.e., an integer or continuous variable), because correlation, intuitively, answer the following question: "if A increases, does B increase, decrease or stay the same, on average?" with a number which goes from -1 to 1. Now, of course it doesn't make sense to ask if a categorical variable increases or decreases: is "brown" or less than "green"? Is "drama" more or less than "comedy", "sci-fi", etc.? Also, it doesn't make sense to talk about the average of a nominal variable. Thus, you can see that there's no hope of recovering a symmetric measure of association between a nominal and a continuous variable, unlike the case of two continuous variables, where the coefficient of correlation of A and B is obviously the same as the coefficient of correlation of B and A. Because of this, from now on I'll use a notation which is not symmetric on purpose, indicating with A the nominal variable and Y the continuous variable

What makes sense, though, is to ask if the average of Y, conditional on the level of A, changes significantly, and by how much. Both questions are answered by a simple linear regression (or equivalently one-way ANOVA). To measure only the strength of correlation you could use intraclass correlation. I have to run now, but feel free to ask for more details.

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Amazing! Thank you very much for your explanation dear Andrea 1 Like

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