I would be very grateful if you would tell me how I can find the degree of correlation between a nominal dependent variable and an independent ordinal variable. The nominal variable has only two levels: YES and NO.
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$\begingroup$ Does this Q&A help stats.stackexchange.com/questions/102778/… $\endgroup$– mdeweyCommented Sep 2, 2017 at 13:22
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$\begingroup$ stats.stackexchange.com/q/73065/3277 is about such correlations. Jonckheere-Terpstra test is for ordinal independent variable. $\endgroup$– ttnphnsCommented Sep 2, 2017 at 14:19
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4$\begingroup$ I'm not trying to be picky, but to me, "correlation" implies that you aren't designating one variable dependent and one variable independent. In some cases, this can make a difference as to which effect size is appropriate. $\endgroup$– Sal MangiaficoCommented Sep 2, 2017 at 15:08
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1 Answer
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EDIT: New answer as of 10 Dec 2018.
Because the nominal variable has only two levels, you could use either Kendall or Spearman correlation. Readers would most likely be more familiar with these measures (tau or rho, respectively) than with alternatives.
Again, because there are only levels in the nominal variable, you could also use effect size statistics that might be used alongside a Wilcoxon-Mann-Whitney test. I find Vargha and Delaney's A easy to interpret, and some prefer the related Cliff's delta. There is also an r which is defined as the Z value from a WMW test divided by the total sample size. There is some information on these statistics on this webpage, of which I am the author.
In general, the degree of association between a nominal variable and an ordinal variable can be assessed with Freeman's theta or a statistic sometimes called epsilon-squared. Epsilon-squared is described here, and is pretty commonly spotted around the internet. Freeman's theta is mentioned around the internet, but I think for the calculations, you have to get the Freeman 1965 book or see the R function freemanTheta, of which I am the author. There is some information on these statistics on this webpage, of which I am the author.
answered Sep 2, 2017 at 15:16