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I have two nominal variables and some numeric variables.

  1. The first nominal variable is a binary one. I want to measure the correlation between this binary variable and the other numeric variables.
  2. The second nominal variable has 37 categories. Again, I should measure the correlation between this nominal variable and the other numeric variables.

Based on this, I am not allowed to use one-way Anova because my data is not normally distributed. According to the answer to this post, Eta is associated with one-way Anova, so due to the non-normality of my data, it is not possible to use Eta. Therefore, I decided to use Kruskal-Wallis for my second nominal variable with 37 categories based on this post.Should I use Mann–Whitney U-test for my first binary nominal variable? Is it true to do so?

It should be noted that my data set includes 2200 observations. Besides, I want to do it as a Exploratory Data Analysis step.

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  • $\begingroup$ You use the words "non-normal" but I think you mean "nominal". i.e., non-normal is a term usually reserved for variables that are numeric but that do not follow a normal distribution. $\endgroup$ – Jeromy Anglim Aug 24 '18 at 7:25
  • $\begingroup$ @JeromyAnglim Thanks. My data is not normally distributed, so I used the term non-normal. Besides, I need to measure the association between nominal and continuous variables, which are non-normal. $\endgroup$ – ebrahimi Aug 24 '18 at 7:29
  • $\begingroup$ @JeromyAnglim Thanks a lot. Sorry, I need to measure the association between a nominal and some continuous variables. I already used Cramer's V to measure the association between two nominal variables. $\endgroup$ – ebrahimi Aug 24 '18 at 7:33
  • $\begingroup$ @JeromyAnglim As a matter of fact, I already used one-way Anova but as I understood that my data is not normally distributed, I doubt it would be right to use one-way Anova. However, I am not sure about using kruskal-Wallis and Mann-Whitney U-test. $\endgroup$ – ebrahimi Aug 24 '18 at 7:38
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    $\begingroup$ Your title contradicts to your two points. You actually are asking about binary - nominal and nominal - nominal associations. I don't see any "numeric"/continuous variable in the points asked. $\endgroup$ – ttnphns Aug 24 '18 at 8:47
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Nominal with nominal: There are a few measures of association designed for two or more nominal variables (i.e., 3 or more unordered categories for one variable; and two or more unordered categories for the other variable).

Here are two that come to mind.

Nominal with numeric: I agree that eta-squared or ICC are two common approaches to quantifying the association between a nominal and numeric variable.

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    $\begingroup$ (+1) Aside on notation: As I recall, Cramér originally used the symbol $\nu$ (lower case Greek letter nu). The widespread but not universal present convention to use roman letters for sample statistics would lead to transliterating this as $n$, not a good idea. I suppose $V$ may be customary for the good reason of using a roman letter and/or as a misreading of $\nu$. There lies a very small historical question which may be of interest to some. $\endgroup$ – Nick Cox Aug 24 '18 at 7:52
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    $\begingroup$ Just an addition: Cramer's V is exactly related to the averaged canonical correlations squared (stats.stackexchange.com/a/140057/3277) which puts Cramer V into the context of linear model (performed on the dummy sets). $\endgroup$ – ttnphns Aug 24 '18 at 10:04
  • $\begingroup$ @JeromyAnglim Thanks a lot. I upvote your answer but still I am not sure about the p-value of Eta. $\endgroup$ – ebrahimi Aug 24 '18 at 15:16

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