Using Yates's correction in situations where the chi-square test is applied to contingency tables larger than 2x2 is not common practice. Yates's correction is primarily used to address the issue of continuity in 2x2 contingency tables when the expected frequencies are low.

In your case, where the age groups are discrete and the youngest two groups have significantly smaller sample sizes compared to the older groups, using Yates's correction may not be appropriate. The correction is intended to be used when the expected cell frequencies are below 5, and it is not designed to address issues related to small sample sizes or skewed distributions.

Your initial suggestion of using a t-test with age as a continuous variable or considering dropping the youngest two groups may be more appropriate approaches. A t-test would be suitable if the assumption of normality and equal variances is met, and it would allow you to compare the means of different age groups directly. Alternatively, if the sample sizes in the youngest two groups are indeed too small, it might be reasonable to consider excluding them from the analysis to avoid biased results.

In your response, you can kindly explain that Yates's correction is typically used in 2x2 contingency tables when the expected frequencies are low, and it may not be the most suitable approach for the specific scenario in question. You can suggest considering alternative methods such as a t-test or carefully evaluating the inclusion of the youngest two groups based on their small sample sizes. Additionally, it would be helpful to provide references or supporting evidence to further support your suggestions.

Hello Karen H Schmeelk-Cone. I have a few comments/questions.

1) Many reputable authors do not recommend Yates' correction these days, even for 2x2 tables, because it is too conservative. See Ian Campbell's nice simulation study and related materials, for example.

https://www.iancampbell.co.uk/twobytwo/twobytwo.htm

2) Even if one was going to use Yates' correction, it would be to address low expected counts, not a discrepancy in the sizes of groups. (You described group sizes of 120 vs 10K, but said nothing about the magnitude of the expected counts.)

3) You mentioned age, but I did not see anything about the other variable in the cross-tabulation. What is the other variable? And how many levels does it have?

4) Is Age clearly a DV and the other variable explanatory?

Thanks for clarifying.

Thanks Bruce Weaver

for 3 - they're looking at suicidal ideation (yes/no) and cyberbullying (yes/no). I would say the expected count for yes for both for the youngest ages might be expected to be quite low, but not likely below 5.

for 4 - age is IV here.

Thanks Ajit Singh! I really don't want to be evil Reviewer 2, so your suggestion at the end was very helpful. I hadn't even heard of the Yates correction, so I wanted to be sure I wasn't missing something.

Hello Karen H Schmeelk-Cone. I understand that you probably cannot share the table with us here, as it is from a ms under review. But presumably, you have the table, so you can work out the expected counts (E = row total * column total / grand total).

You mentioned 5 as a minimum expected count. That is indeed the usual minimum E for a 2x2 table. But here is another rule of thumb for tables larger than 2x2:

"No more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater" (Yates, Moore & McCabe, 1999, p. 734).

For your 8x2 table, 20% of 16 cells = 3.2 cells.

Finally, as your table has one dichotomous variable and one ordinal variable, one could--and maybe should--use the so-called ordinal Chi2. As the following note by (the late) David Howell shows, it goes by various names, including the test of linear-by-linear association in SPSS:

• https://www.uvm.edu/~statdhtx/StatPages/More_Stuff/OrdinalChisq/OrdinalChiSq.html

One thing that people may not always appreciate about the ordinal Chi2 is that its value depends on the actual numbers that are used to code the ordered categories. But in your case, as the categories are ages ranging from 11-18, I would just use those values as they are.

HTH.