In which circumstance would you use a Chi-square test?

The Chi-square test is specifically designed for analyzing the relationship between categorical variables. This statistical test evaluates whether there is a significant association between the observed frequencies in various categories compared to the expected frequencies if there were no association. It is particularly useful when dealing with nominal or ordinal data, allowing researchers to determine if the proportions of various outcomes differ between groups.

When using the Chi-square test, one typically constructs a contingency table that displays the distribution of the categorical variables. By calculating the Chi-square statistic, one can assess how likely it is to observe the data assuming no association exists. A significant result indicates that the variables may be related, guiding further analysis or research.

This makes option B the correct choice, as it aligns directly with the purpose and application of the Chi-square test in analyzing categorical data relationships. Other scenarios mentioned—like comparing means, assessing linear relationships, or examining variances—are better suited for different statistical tests, such as t-tests or ANOVA for means, Pearson correlation for continuous variables, and F-tests for variances, respectively.