How to word the results if a chi-square test of independence is significant, but no single post-hoc test is?

Question

I ran a chi-square test of independence on a 2-dimensional cross table, which resulted in a significant p-value.

I then ran post-hoc tests for all pairs of populations and adjusting by a bonferroni correction (I used the function chisq.post.hoc from the fifer package in R, if that matters).

There, no single pair was significant.

I understand that this can happen and is not out of the ordinary, but it's hard to put a justification for this result in writing. How would you word this situation correctly? I am thinking of something to the likes of:

The significant p-value of the chi-squared test on the whole cross table suggests a dependency between the variables A and B. However, no specific group was found in the subsequent post-hoc tests, meaning that the overall dependency could not be linked to a specific pair of populations.

To me, this sounds correct but not helpful. Is there a better way to describe what the significant overall-test means if no single pair of population is found in the post-hoc tests?

Answer 1

Taking a stab:

A chi-squared test works by assuming that variables A and B are independent and then looking for evidence that contradicts that assumption. The stronger the overall evidence against independence, the lower the p-value will be. In this case, the low p-value from the test on the whole table suggests significant evidence for a dependency between variables A and B. A follow-up post hoc analysis found that the overall conclusion results from the accumulation of small amounts of evidence from many cells in the table rather than from large contributions of evidence from any particular cells.