I have two ordinal variables. I would like to know if there is a dependency between these two variables and also how strong this dependency is. So, I performed a chi-square test (34.53, df=8) where the p-value < 0.05. No problem here.

Then because these two variables are ordinal I choose gamma and Somers' d to show how strong the dependency is. The problem is that both Somers' d (-0.036) and gamma (-0.056) show no statistical significance p-value for both 0.345.

I don't know how to interpret these results: there is statistical significance in dependency (chi-square) and also no statistical significance in the strength of this dependency ?


  • $\begingroup$ Can you provide a graph. A scatterplot. Real units do not matter. $\endgroup$
    – AlainD
    Commented Aug 22, 2018 at 8:36
  • $\begingroup$ A 5 x 3 table of frequencies would be even better. (It allows drawing suitable graphs too.) $\endgroup$
    – Nick Cox
    Commented Aug 22, 2018 at 8:47
  • 1
    $\begingroup$ Please explain how a variable with categories 100-1000, 1001-2000, 0 is ordinal. If it is, why is that the right order? $\endgroup$
    – Nick Cox
    Commented Aug 22, 2018 at 9:00
  • 2
    $\begingroup$ Yes; the ordering of rows and/or columns is crucial for measures of ordinal association. I confirm your chi-square result using Stata. If you order 0-99 [NB], 100-1000, 1001-2000 then Somers' d I get as 0.13682421 with P-value .00004898, also using Stata. . $\endgroup$
    – Nick Cox
    Commented Aug 22, 2018 at 9:43
  • 2
    $\begingroup$ @NickCox has probably solved one issue: that the ordinal categories weren't in the correct order. But you should also understand that a chi-square test of association and testing (?) with either gamma or Somers' d treat the data as very different things. Or, you could say that they test very different hypotheses. You should decide ahead of time if you are treating a variable as ordered categorical or nominal (unordered) categorical. It doesn't make much sense to use gamma or Somers' d as an effect size statistic after a chi-square test of association. $\endgroup$ Commented Aug 22, 2018 at 11:01


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