What does the chi-square test examine in research?

The chi-square test is specifically designed to assess whether there is a significant association or relationship between two categorical variables. It operates on the principle of comparing observed frequencies in each category of a contingency table with the frequencies that would be expected if there was no association between the variables. By doing so, researchers can determine if the distribution of one variable differs significantly across the categories of another variable. This makes the chi-square test a valuable tool for analyzing data when both variables are nominal or ordinal in nature, providing insights into underlying relationships in categorical data.

In contrast, the other options pertain to different types of statistical relationships or analyses that do not align with the aims of the chi-square test. For instance, evaluating average differences () concerns continuous variables and typically involves tests like t-tests or ANOVA. Trends over time () would likely use time-series analysis or regression techniques to examine how a variable changes over a period. Lastly, analyzing individual impacts of variables () suggests a focus on causal analysis often associated with multiple regression or other modeling techniques that evaluate how predictors influence a dependent variable. Thus, the chi-square test's focus on relationships between categorical variables is what distinguishes it and confirms why the choice related to examining categorical variables is correct.