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Is it possible to compare the standardized pearson residuals for two given cells from two different chi-squared tests? The respective variables have different numbers of factor levels.

I am not looking for an inferential test. I just want to say that cell a_xy in table A contributed more to the overall significance test for table A than cell b_xy did for the overall significance test for table B.

Is that something that can be interpreted from the standardized pearson residuals? Are they always on the same "scale" - are they actually standardized?

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    $\begingroup$ Will this help to an extent? stats.stackexchange.com/a/178068/3277 $\endgroup$
    – ttnphns
    Oct 21, 2022 at 17:52
  • $\begingroup$ It is somewhat helpful, thank you. However, I cannot find how to calculate the "adjusted residuals" that are described in this answer. I have found at least three different formulas by now... $\endgroup$
    – Max J.
    Oct 21, 2022 at 19:41
  • $\begingroup$ For anyone finding this: R's chisq.test outputs a statistic called stdres which is similar to the adjusted residuals described in the linked answer. $\endgroup$
    – Max J.
    Oct 21, 2022 at 20:15

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As has been described here (thanks to ttnphns for linking it), standardized residuals alone are not sufficient to compare across multiple tables. Rather, adjusted standardized residuals should be used as they are described by Agresti (2007). These can be outputted in SPSS. In R, these can be found as stdres in the output from chisq.test.

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