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I would like to find the correlation between a continuous (dependent variable) and a categorical (multinomial) variable. I found that the appropriate test is Eta ($\eta$) coefficient, however, I haven't found enough resources support this test.

Is this the right test ?

kjetil b halvorsen
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nora
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  • See https://stats.stackexchange.com/questions/102778/correlations-between-continuous-and-categorical-nominal-variables – kjetil b halvorsen Nov 12 '19 at 17:33
  • I assume your approach with Eta would be to run a one-way analysis of variance, calculate eta-squared from that analysis, and then take the square root of eta-squared... (?) – Sal Mangiafico Nov 13 '19 at 01:35
  • Jacob Cohen, 1988, Statistical Power Analysis for the Behavioral Sciences, 2nd, discusses the use of Eta and Eta-squared as effect size statistics in the case of analysis of variance. – Sal Mangiafico Nov 13 '19 at 01:47

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I suggest that you do a one-way analysis of variance.

The aim will be to compare the means of each group determined by the categorical variable. I.e., the null hypothesis will be: $$ H_0: \mu_a = \mu_b = \mu_c = \ldots $$

Ertxiem - reinstate Monica
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