Which statistic is commonly used to analyze categorical data?

Which statistic is commonly used to analyze categorical data?

• A. Chi Square
• B. T-test
• C. ANOVA
• D. Repeated measures ANOVA

Answer: (A)

The key idea is that chi-square is designed for categorical data. When your data are counts in categories (nominal or ordinal), you’re interested in whether the observed frequencies differ from what would be expected under a certain hypothesis, such as no association between variables or a specific distribution across categories. The chi-square test does exactly that by comparing observed counts to expected counts in each category and producing a statistic that reflects how far the observed pattern is from the expectation. This approach is nonparametric and does not rely on normality or equal variances, which fits categorical data much better than methods that compare means. In contrast, the t-test and ANOVA are built to compare averages of a continuous outcome across groups, and even though there are repeated-measures versions, they still require a quantitative outcome. So when the data are about frequencies in categories, chi-square is the standard, most appropriate tool.

The key idea is that chi-square is designed for categorical data. When your data are counts in categories (nominal or ordinal), you’re interested in whether the observed frequencies differ from what would be expected under a certain hypothesis, such as no association between variables or a specific distribution across categories. The chi-square test does exactly that by comparing observed counts to expected counts in each category and producing a statistic that reflects how far the observed pattern is from the expectation.

This approach is nonparametric and does not rely on normality or equal variances, which fits categorical data much better than methods that compare means. In contrast, the t-test and ANOVA are built to compare averages of a continuous outcome across groups, and even though there are repeated-measures versions, they still require a quantitative outcome. So when the data are about frequencies in categories, chi-square is the standard, most appropriate tool.