I am hoping to perform a chi-square test of independence on data in a 2x2 contingency table with the following values:
Group A: 627 successes, 28 failures Group B: 59 successes, 2 failures
I understand that this is a small collection of observations, and I wish to determine the minimum number of observations required for a chi-squared test at 0.05 significance, 0.8 power. However, it seems that the normal approximation of the binomial distribution that is generally used for power analysis among comparisons of proportions is not appropriate here for at least two reasons:
- p(success) is nowhere near 0.5 for the populations AND
- the expected number for Group B Failures, (2+59)*(2+28)/716 = 2.56, is below the guideline of 5 for all cells in chi-square power analysis.
Any constructive guidance on how to perform this test of independence (or reference to other questions I may have overlooked) is greatly appreciated.