What statistical test is used when the data set is small?

What statistical test is used when the data set is small?

• A. Chi-square
• B. T-test
• C. Fisher's exact
• D. ANOVA

Answer: (C)

When the data set is small, an exact method is needed to assess association between two categorical variables in a 2x2 table. Fisher's exact test calculates the exact probability of the observed arrangement under the null hypothesis of no association, using the hypergeometric distribution. Because it doesn't rely on the large-sample approximation, it remains valid even with very small counts or when expected frequencies are below 5. In contrast, the chi-square test relies on an approximation that becomes unreliable with small samples or sparse data. The t-test and ANOVA are designed for comparing means of a continuous outcome and rely on assumptions like normality and equal variances; they aren't appropriate for analyzing small categorical data. Therefore, Fisher's exact test is the most appropriate choice for a small data set.

When the data set is small, an exact method is needed to assess association between two categorical variables in a 2x2 table. Fisher's exact test calculates the exact probability of the observed arrangement under the null hypothesis of no association, using the hypergeometric distribution. Because it doesn't rely on the large-sample approximation, it remains valid even with very small counts or when expected frequencies are below 5. In contrast, the chi-square test relies on an approximation that becomes unreliable with small samples or sparse data. The t-test and ANOVA are designed for comparing means of a continuous outcome and rely on assumptions like normality and equal variances; they aren't appropriate for analyzing small categorical data. Therefore, Fisher's exact test is the most appropriate choice for a small data set.