A statistical test used instead of chi-square when sample size is small is:

A statistical test used instead of chi-square when sample size is small is:

• A. Z-Test
• B. Fisher Exact
• C. T-Test
• D. Mann-Whitney U

Answer: (B)

When sample sizes are small, the chi-square test’s approximation can be unreliable because the expected counts in some cells may be too low for the chi-square distribution to be a good fit. Fisher Exact test handles this by calculating the exact probability of the observed arrangement under the null hypothesis, using the hypergeometric distribution. This yields an exact p-value for a 2x2 contingency table, making it the appropriate choice when counts are small. Other options are meant for different situations: a Z-test relies on a large-sample normal approximation for proportions; a T-test compares means between two groups; and the Mann-Whitney U test compares distributions for two independent samples on ordinal or non-normal data. These do not directly replace chi-square for testing associations in small-sample categorical data, hence Fisher Exact is the best fit.

When sample sizes are small, the chi-square test’s approximation can be unreliable because the expected counts in some cells may be too low for the chi-square distribution to be a good fit. Fisher Exact test handles this by calculating the exact probability of the observed arrangement under the null hypothesis, using the hypergeometric distribution. This yields an exact p-value for a 2x2 contingency table, making it the appropriate choice when counts are small.

Other options are meant for different situations: a Z-test relies on a large-sample normal approximation for proportions; a T-test compares means between two groups; and the Mann-Whitney U test compares distributions for two independent samples on ordinal or non-normal data. These do not directly replace chi-square for testing associations in small-sample categorical data, hence Fisher Exact is the best fit.