Statistical validity of using Chi2 p-value with Cramer V correlation coefficient

[Robert Shaw]

Background:
I have several binary variables. I am working out the correlation coefficients between a number of them. As the data is binary I am using Kramer's V as my correlation coefficient, which, handily, in this case, gives the same numeric value as if I were to use Pearson's correlation coefficient, thus allowing me to use pwcorr to produce a correlation matrix. which I can turn into a heatmap using the command heatplot (ssc install heatplot), overlaying the correlation coefficient and p-value.

Question: Since the Kramer's V statistic is calculated from the Chi2 statistic, I believe that the p-value associated with the Chi2 statistic would be valid to use as an indicator for statistical significance of Kramers V statistic - am I correct in my thinking? The correlation is being assessed by Chi2 and a p-value produced, but I am choosing to use a transformation of the Chi2 statistic to Kramers to give a more valid measure of the strength of correlation.

Kind regards
Robert Shaw

[George Ford]

Kramer's V (or Phi in the dichotomous case) seems legit. Will tetrachoric allow for all heatplot?

[Robert Shaw]

My understanding of tetrachoic is to estimate the underlying normal distribution from a binary variable. In this case, the underlying distribution that creates the binary variable is indeed normally distributed, but the aim of the correlation is to analyse purely the binary variable, so, to my level of understanding, the tetrachoic would be inappropriate (it gives a different result to pearsons/phi/creamer’s V)