I'm using Pearson's chi-squared test to to compare the knowledge of two independent groups on knowledge about contact lens. But the number of respondents in group A is n = 200 and the number of respondents in group B is n = 2300.

Is Chi-squared test applicable for my study as it has fulfilled all the assumptions for chi-squared test to be carried out?

  • the question on knowledge about contact lens wear is dichotomous in nature.\

You will be fine. The Pearson $\chi^2$ test does not make any assumptions on the relative sizes of the two groups. The theory behind the test is based on asymptotic normality of maximum likelihood estimates which only depends on the total amount of data you have in each group. 200 and 2300 observations per group are probably more than enough.

Think about it intuitively: would you be better off if groups A and B both had 200 people?

One final note - you may be better off using Fisher's exact test.

  • $\begingroup$ Thank you MAB. I've seen 2 example of using two sample size with huge difference in the books which supports the use of Pearson's Chi-squared test in my case. From my knowledge, Fisher's exact is only applicable for small sample size or any cell with expected frequency of less than 5 which may not be appropriate for my study. $\endgroup$
    – Xuanli Tan
    Jan 8 '15 at 7:22
  • $\begingroup$ The Fisher Exact test, just as its name says, gives exact p-values, even if all the expected counts are greater than 5. The $\chi^2$ test gives approximate p-values, and these p-values are more accurate when you have lots of data and expected counts that aren't super low. I'd do both tests and check to make sure there aren't any huge discrepancies (there shouldn't be with the amount of data you have.) $\endgroup$
    – MAB
    Jan 9 '15 at 22:26

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