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I was wondering if someone could provide me some insights on sample size calculation for Chi Square tests.

$$\begin{array}{|c|c|c|} \hline & \text{Group 1} & \text{Group 2}& \text{χ2} \\\hline \ \text{var 1} & a & b& p= \\ \hline \text{var 2} & c & d& p= \\ \hline \text{var 3} & e & f& p= \\ \hline \end{array}$$

I have a table like this where I am doing simple chi square test for each variable. So there are 3 tests. When calculating sample size using G power is my $\text{Df}=1$? Since $ \text{Df}=(c-1)(r-1)$ for each individual test.

Moreover, the sample size I get is for one variable I assume. How do I adjust for multiple variables?

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  • $\begingroup$ The df will be 1 since it amounts to a test of two proportions. If you are willing to assume that tests for var1–var3 are independant, a very simple yet conservative procedure would be to use Bonferroni correction. Now, you need to tell us what your design really is, and why you are interested in determining the sample size required to reach a given statistical power for three variables. $\endgroup$
    – chl
    Commented Nov 27, 2020 at 19:35
  • $\begingroup$ Hello, thank you for answer!. The study is a retrospective study. I am measuring symptoms and certain demographics in two different patient groups and seeing if it is more common in one or the another. Another thing I didn't understand is what the bonferri correction has to do with sample size. When I actually run the test the P-value i will adjust based on the #of tests, but should I do anything else with regards to the sample size? I really appreciate it, thanks! $\endgroup$
    – Rahim Ahmed
    Commented Nov 28, 2020 at 2:28

1 Answer 1

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Amending my comment: The df will be 1 since it amounts to a test of two proportions. If you are willing to assume that tests for var1–var3 are independant, a very simple yet conservative procedure would be to use Bonferroni correction.

I don't think power analysis is required (1) in the case of a retrospective study and (2) when the variables in question are probably not the main outcome.

  1. Contrary to a prospective study, using information from the sample data, rather than expected effect size--fixed a priori, in a retrospective study is controversial. Post-hoc power analysis has been discussed at length on this site, but see, e.g., Thomas, L. (1997). Retrospective Power Analysis, Conservation Biology, 11(1), 276–280.

  2. Secondary endpoints are usually treated separately. Anyway, the following two references discuss the case of multiple tests in relation to power analysis: Bang, H., S.-H. Jung, and S. George (2005). Sample size calculation for simulation-based multiple-testing procedures. Journal of Biopharmaceutical Statistics, 15, 957–967; Senn, S. and F. Bretz (2007). Power and sample size when multiple endpoints are considered. Pharmaceutical Statistics, 6, 161–170. Note, however, that in both cases those papers focus on randomized clinical trials with multiple endpoints or correlated outcomes.

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