What is the chi-square test for independence used for?

What is the chi-square test for independence used for?

• A. To test whether two categorical variables are independent in a contingency table.
• B. To estimate the difference between two means.
• C. To measure association between two continuous variables with correlation.
• D. To test whether sample variances are equal.

Answer: (A)

The chi-square test for independence checks whether two categorical variables are related or independent by looking at a contingency table of observed counts. If the variables are independent, the distribution of counts in each cell is determined by the row totals and column totals. The test compares what we observe to what we'd expect if the variables were independent: Eij = (row_i total × column_j total) / grand total. The test statistic sums over all cells the value (Oij − Eij)² / Eij, where Oij is the observed count and Eij the expected count. A large value indicates that the observed pattern of counts deviates from what independence would predict, suggesting an association between the variables. The p-value is obtained from the chi-square distribution with degrees of freedom (number of rows − 1) × (number of columns − 1). Key assumptions include using counts from a random sample, categories that are mutually exclusive, independent observations, and sufficiently large expected cell counts (typically at least 5). If counts are too small, a Fisher’s exact test is a better choice. This isn’t about comparing means, measuring association between two continuous variables, or testing equality of variances, so those approaches would address different questions.

The chi-square test for independence checks whether two categorical variables are related or independent by looking at a contingency table of observed counts. If the variables are independent, the distribution of counts in each cell is determined by the row totals and column totals. The test compares what we observe to what we'd expect if the variables were independent: Eij = (row_i total × column_j total) / grand total.

The test statistic sums over all cells the value (Oij − Eij)² / Eij, where Oij is the observed count and Eij the expected count. A large value indicates that the observed pattern of counts deviates from what independence would predict, suggesting an association between the variables. The p-value is obtained from the chi-square distribution with degrees of freedom (number of rows − 1) × (number of columns − 1).

Key assumptions include using counts from a random sample, categories that are mutually exclusive, independent observations, and sufficiently large expected cell counts (typically at least 5). If counts are too small, a Fisher’s exact test is a better choice.

This isn’t about comparing means, measuring association between two continuous variables, or testing equality of variances, so those approaches would address different questions.