I have two variables I want to test with correlation, one is continuous and the other dichotomous. My data are non-normally distributed, plus the variance is heterogeneous, so I have to apply a non-parametric test of correlation. The problem is, I don't know of any test that fits my requirements.

Spearman's correlation coefficient requires ordinal data for both variables.

Point-biserial correlation coefficient fits my data type, but it's a parametric test.

I'm unaware if there's some test else out there. What should I do?


closed as unclear what you're asking by gung Jun 4 '18 at 20:38

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    $\begingroup$ Why do you need a correlation? Why not just run a Mann-Whitney U-test? (Btw, Spearman's correlation is fine if 1 variable is dichotomous.) $\endgroup$ – gung Feb 14 '14 at 21:36
  • $\begingroup$ I need a correlation because the groups are not independent, Mann-Whitney U-test requires independent groups if I'm right. If you tell me that Spearman is fine with a categorical dichotomy, I should kill myself for spending so much time looking for alternatives xD $\endgroup$ – Mike Feb 15 '14 at 9:39
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    $\begingroup$ In what sense are your data not independent? If eg these were pre & post measurements of the same study units, you could use a Wilcoxon signed rank test. There is no meaningful ordinal - nominal difference if there are just 2 categories; if you had 3+ nominal categories, you could not use the Spearman correlation. $\endgroup$ – gung Feb 15 '14 at 16:11
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    $\begingroup$ A brief explanation of how location tests for one binary variable relate to correlation is here: Correlations between continuous and categorical (nominal) variables. [If you properly account for the effect of the heavy ties on the distribution a correlation might be okay.] $\endgroup$ – Glen_b Feb 5 '17 at 21:45

Consider Rank Biserial Correlation.

"A formula is developed for the correlation between a ranking (possibly including ties) and a dichotomy, with limits which are always ±1. This formula is shown to be equivalent both to Kendall'sτ and Spearman's ρ"

Reference: E. E. Cureton (1956) "Rank Biserial Correlation", Psychometrika, 21, pp. 287-290.

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    $\begingroup$ As this method amounts to at most a reformulation of previously existing methods, it has few followers so far as I can tell. $\endgroup$ – Nick Cox Oct 21 '14 at 17:23

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