# How do you correlate binary & ordinal variables?

Which test to use to calculate correlations between them?

• Cramer's V,
• Kruskal-Wallis,
• or something else?
• Are you wondering how such correlations are calculated (ie, how to arrive at the number), how they are tested (ie, if they could have come from a population w/o any correlation), or what they mean? – gung - Reinstate Monica May 28 '14 at 23:33
• italic Yes! @gung – user46343 May 28 '14 at 23:46

## 1 Answer

Cramér's V and the Kruskal–Wallis test are for nominal data; the latter is a null hypothesis test, not a correlation. If you want to calculate the correlation between a dichotomous variable and an ordinal variable, you could use Kendall's $\tau$, the Goodman–Kruskal $\gamma$, or Spearman's $\rho$ (listed in the order in which I'd recommend them, I suppose). If you're estimating population parameters, you can also generate confidence intervals around these statistics or perform null hypothesis tests if you wish.
For some comparisons and a conversion method, see:

• @user46343: was there anything else you wanted to know, or is my answer acceptable? – Nick Stauner May 30 '14 at 20:55