What does the chi-square test for independence assess?

What does the chi-square test for independence assess?

• A. Whether a sample comes from a normal distribution.
• B. Whether two categorical variables are related.
• C. Whether variances are equal across groups.
• D. Whether there is a linear relationship.

Answer: (B)

The main idea is that the chi-square test for independence checks whether two categorical variables are related rather than independent. You organize the data in a contingency table of observed counts for each combination of categories. If the variables are independent, the distribution of counts in each cell should follow what you’d expect from the marginal totals: the expected count for a cell is (row total × column total) divided by the grand total. You then compute the chi-square statistic by summing (observed minus expected) squared over the expected value for every cell. This statistic is compared to a chi-square distribution with degrees of freedom (number of rows − 1) × (number of columns − 1). A small p-value means the observed pattern of counts is unlikely under independence, so you conclude the variables are related; a large p-value suggests no evidence of association. Keep in mind this test is for categorical data and is nonparametric, unlike tests that assess normality, equal variances, or linear relationships. If the sample is small, some conditions about expected counts aren’t met, in which case other methods like Fisher’s exact test might be used.

The main idea is that the chi-square test for independence checks whether two categorical variables are related rather than independent. You organize the data in a contingency table of observed counts for each combination of categories. If the variables are independent, the distribution of counts in each cell should follow what you’d expect from the marginal totals: the expected count for a cell is (row total × column total) divided by the grand total.

You then compute the chi-square statistic by summing (observed minus expected) squared over the expected value for every cell. This statistic is compared to a chi-square distribution with degrees of freedom (number of rows − 1) × (number of columns − 1). A small p-value means the observed pattern of counts is unlikely under independence, so you conclude the variables are related; a large p-value suggests no evidence of association.

Keep in mind this test is for categorical data and is nonparametric, unlike tests that assess normality, equal variances, or linear relationships. If the sample is small, some conditions about expected counts aren’t met, in which case other methods like Fisher’s exact test might be used.