Can you calculate confidence intervals when performing a chi square test of independence. Someone asked me to provide CI but I'm not sure how this is possible since the test only tests for indepedence.

Im comparing countries and whether or not they are single offenders or repeatable offenders. I found that a 5% level of siginficance to reject the null hypothesis. What is there to say more than there is an association between both variables.

I mean I could also measure that association with phi or cramers v but that's all I can really provide?

Am I wrong ?

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    $\begingroup$ Confidence interval for what? // What if you did a correlation test? How would you accompany that with a confidence interval? $\endgroup$
    – Dave
    Commented Apr 21, 2022 at 16:04

1 Answer 1


The correct response would be, "Confidence intervals for what statistic [estimate of what parameter] ?"

Probably the most useful would be providing the confidence interval for phi (or Cramer's V), or for a meaningful odds ratio for the table.

Beyond that, you can provide whatever information is useful for the readers. Maybe, the proportions within each row or column ? Or the ratios of these ?

  • $\begingroup$ That makes a lot of sense. I've provided the ratios of each variable. Not sure how to get the probabilities? Any idea how to calculate the CI for Cramer's V? $\endgroup$ Commented Apr 21, 2022 at 16:08
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    $\begingroup$ I meant "proportions" rather than "probabilities" (corrected now). That is, just the proportions of counts for each cell in say a column or row, if that's helpful. $\endgroup$ Commented Apr 22, 2022 at 13:56
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    $\begingroup$ There is a hint at a reference for calculating the CI for phi here: rdrr.io/cran/statpsych/man/ci.phi.html. Also, I've written algorithms to compute the confidence intervals for Cramer's V by bootstrap. (Caveat that I wrote it.) rdrr.io/cran/rcompanion/man/cramerV.html. ... These functions are easy to run in R, even without installing software. $\endgroup$ Commented Apr 22, 2022 at 13:57
  • $\begingroup$ Gotcha, so CI for Cramers V. Yea I need to find a way to calcualte it on python. I don't use R. $\endgroup$ Commented Apr 23, 2022 at 20:33

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