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It is usually explained in biostatistics textbooks that to do a z-test for the difference of two proportions, it is necessary that p*n and (1-p)*n are both equal to or above five for both samples. However, I did not find any explanation of what to do when this condition is not met?

So I have this table below, and I need to test if there is a significant difference in fuzzy drinks consumption between genders. As you can see, there are only 4 females in the non-consumption category, so the condition for z-testing is not met. What should I do?

Consumption of fuzzy drinks by gender

Ammar Aldawoodyeh
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  • The 4 is not relevant to the calculation. The p in this case would be the estimated proportion under the null hypothesis – Glen_b Mar 24 '18 at 10:18
  • The chi square test in spss makes the assumption that non of the cells contain an expected value less than 5. the expected value for this cell is 3.7, so the assumption is violated. So I need to know what to do in this case. – Ammar Aldawoodyeh Mar 24 '18 at 10:24
  • Indeed; this is the same issue for both tests. The problem of small expected values in a chi-square on a 2x2 table has been asked about many times before. – Glen_b Mar 24 '18 at 11:04
  • Could you provide the links or the titles of the questions? I would be thankful as I need to have a look at them. or could you mention what was the answers? – Ammar Aldawoodyeh Mar 24 '18 at 11:08
  • https://stats.stackexchange.com/questions/35657/applicability-of-chi-square-test-if-many-cells-have-frequencies-less-than-5 https://stats.stackexchange.com/questions/60076/why-are-5-expected-frequencies-needed-in-pearsons-chi-square https://stats.stackexchange.com/questions/14226/given-the-power-of-computers-these-days-is-there-ever-a-reason-to-do-a-chi-squa https://stats.stackexchange.com/questions/44622/what-to-do-when-assumptions-are-not-met-in-a-chi-squared-test https://stats.stackexchange.com/questions/93212/what-to-do-when-i-have-expected-count-5-warning-for-a-chi-squared-test – Glen_b Mar 24 '18 at 11:28
  • These should give you a fair coverage of the different things people have to say. Using the search facility may turn up some additional points. – Glen_b Mar 24 '18 at 11:29

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