Which test compares observed frequencies with expected frequencies in categorical data?

Which test compares observed frequencies with expected frequencies in categorical data?

• A. Chi-Square Test
• B. T-Test
• C. ANOVA
• D. Mann-Whitney U

Answer: (A)

When you have categorical data and want to know if the observed counts in each category match what you’d expect under a specified hypothesis, you use the chi-square test of goodness-of-fit. It builds a statistic from how far the observed frequencies are from the expected frequencies in each category, typically by summing (observed − expected)²/expected across all categories. A small value means the observed counts align with the expectations, while a large value suggests the distribution differs from what was expected, indicating the hypothesis may not hold. The other tests focus on different kinds of questions. A t-test compares means of a continuous outcome between two groups. ANOVA extends that idea to compare means across three or more groups. Mann-Whitney U compares the distribution of a continuous or ordinal outcome between two independent groups. None of these directly assess whether observed category counts match expected frequencies in categorical data.

When you have categorical data and want to know if the observed counts in each category match what you’d expect under a specified hypothesis, you use the chi-square test of goodness-of-fit. It builds a statistic from how far the observed frequencies are from the expected frequencies in each category, typically by summing (observed − expected)²/expected across all categories. A small value means the observed counts align with the expectations, while a large value suggests the distribution differs from what was expected, indicating the hypothesis may not hold.

The other tests focus on different kinds of questions. A t-test compares means of a continuous outcome between two groups. ANOVA extends that idea to compare means across three or more groups. Mann-Whitney U compares the distribution of a continuous or ordinal outcome between two independent groups. None of these directly assess whether observed category counts match expected frequencies in categorical data.