Making sense of Chi-square and Cramer's V

I read a lot about chi-square tests that do not ever talk about Cramer's V (or comparable stat), but if I'm understanding correctly, it seems like a chi-square test is not complete without something like the Cramer's V as a check.

So would the following be an accurate summary of how to interpret Cramer's V?

When doing a chi-square test, you can state that an association exists between the two categorical variables only if BOTH the p-value < .05 (or whatever your threshold is) AND the Cramer's V is "high".

If p-value > .05 then the probability of this result happening again is low. Or if the Cramer's V is "low", then any apparent association is nullified since it's due only to a large sample size.


Super Moderator
Cramers V is a kind of post hoc test that tests the strength of the association. So, you can have an existing association with a low p-value and a low Cramers V, but you can say that the association is stronger as the v-value increases - in a similar way that you can have a significantly different from zero slope in a regression with a low pearsons correlation coefficient.

It is a bit more tricky to interpret because Cramers V will depend also on the number of levels of the categorical variables.