Chi-square test is used to assess whether observed frequencies differ from what would be expected by chance.

• A. Compare means of two groups.
• B. Measure strength of linear relationship.
• C. Assess association between two continuous variables.
• D. Assess whether observed frequencies differ from expected frequencies by chance.

Answer: (D)

Chi-square is used with categorical data to see if what we observe in each category matches what we would expect by chance under a specific null hypothesis. It compares the actual frequencies to the expected frequencies (based on assumptions like equal distribution or independence) and asks whether any differences are large enough to unlikely occur by random variation. If the observed counts differ from the expected counts more than would be expected by chance, the chi-square statistic is large and the p-value is small, suggesting a real effect or association. This differs from choices that focus on comparing means of groups (that uses tests like t-tests or ANOVA), measuring a linear relationship between continuous variables (that uses correlation), or assessing associations between two continuous variables (which involves regression or correlation). Chi-square specifically targets frequencies in categories, not means or continuous relationships, and can also be used to test independence between two categorical variables or goodness-of-fit for a single categorical variable.