Test of independence

Definition

A test of independence evaluates whether two categorical variables are statistically independent. It uses the chi-square statistic to measure the association between the variables.

5 Must Know Facts For Your Next Test

1. The null hypothesis states that the two categorical variables are independent.
2. The alternative hypothesis states that there is a significant association between the variables.
3. The expected frequency for each cell in a contingency table must be at least 5 for the chi-square approximation to be valid.
4. The degrees of freedom for the test are calculated as $(\text{number of rows} - 1) \times (\text{number of columns} - 1)$.
5. A large chi-square statistic relative to the critical value indicates rejection of the null hypothesis.

Review Questions

Related terms

Chi-Square Distribution:

A probability distribution used in tests involving categorical data, especially goodness-of-fit and tests of independence.

Contingency Table:

A table used to display the frequency distribution of variables and analyze their relationships.

Degrees of Freedom:

The number of values in a calculation that are free to vary, often denoted as $df$.