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I'm trying to determine which cells' values account for/contribute the most to a significant chi-square omnibus test result. Please see the below contingency table showing the numbers of diagnoses by age group by calendar year using this online chi-square calculator:

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I did read the answers to similar questions at the following web pages and they were useful:

"Partition" of Chi-Square Table

Interpret Chi-square test

It looks like the chi-square value for each cell is shown in parentheses. If so, and in order to see the extent to which a particular cell's value is consequential in influencing the overall result, should I divide the omnibus chi-square value by the degrees of freedom and compare it against χ2/df = 30.32 which is listed beneath the table? If so, can I assume that the number of diagnoses of unipolar depression among individuals 60+ years old in 2018 (χ2 = 93.58) relatively made the largest contribution to the significant overall omnibus result of χ2 = 151.189?

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    $\begingroup$ The $\chi^2$ value of $151.589$ is, by definition, the sum of the parenthesized contributions in the cells--all of which are (necessarily) positive. This is the basis for comparing them. I find it informative to examine the chi-squared residuals as defined and illustrated at stats.stackexchange.com/a/52343/919: these are the square roots of the parenthesized quantities, selecting the sign according to whether the count exceeds its expectation or not. The "60+,2018" cell has the largest positive residual, which is almost balanced by large negative residuals at "60+,2016" and "60+,2014." $\endgroup$
    – whuber ♦
    Commented Oct 23, 2019 at 19:34
  • $\begingroup$ Whuber, thank you for your guidance here with respect to considering positive and negative residuals to determine relative contributions to the overall chi-square. It's very useful! So, can we say that neither one of the large negative residuals by itself, i.e., at "60+,2016" or "60+,2014", is significant when compared to the square root of the adjusted individual-cell chi-square critical value of χ2/df = 30.32? But if we add the squared residuals together we get χ2 = 31.66 which exceeds that critical chi-square value of 30.32. Now is this combined decrement interpretable? $\endgroup$
    – LeeZee
    Commented Oct 23, 2019 at 23:14
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    $\begingroup$ The significance of the test is established solely by the $\chi^2$ p-value at the bottom of the output. The residuals are useful for assessing the departures between the observed and expected counts (under the null hypothesis, which you are now rejecting). Although one can apply post hoc tests to individual residuals, that's rarely the objective and, even when it is, those tests do not compare the residuals to the original chi-squared statistic. When you add the squared residuals in this example correctly you get the total of 151.189. Please ignore the 30.32 value: it's unhelpful. $\endgroup$
    – whuber ♦
    Commented Oct 24, 2019 at 14:47

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