Question

Which test (Chi-Square or Fisher’s Exact Test) is most appropriate for 2x2 table AND how to determine  there a significant difference in the test?

Answer 1

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Which test (Chi-Square or Fisher’s Exact Test) is most appropriate for 2x2 table​​​​​

Generally, Fisher’s exact test is preferable to the chi-squared test because it is an exact test. The chi-squared test should be particularly avoided if there are few observations (e.g. less than 10) for individual cells.

how to determine Chi-Square and Fisher’s Exact Test significant difference in the test?

The chi-squared test applies an approximation assuming the sample is large, while the Fisher's exact test runs an exact procedure especially for small-sized samples.

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