Test for homogeneity

Definition

A test for homogeneity evaluates whether different populations have the same distribution of a categorical variable. It is a type of chi-square test used to compare the frequencies of categories across multiple groups.

5 Must Know Facts For Your Next Test

1. The null hypothesis states that all populations have the same distribution of the categorical variable.
2. It requires categorical data from two or more independent samples or populations.
3. The test statistic follows the chi-square distribution with degrees of freedom calculated as $(r-1)(c-1)$, where $r$ is the number of rows and $c$ is the number of columns in the contingency table.
4. A significant result indicates that at least one population has a different distribution compared to others.
5. Expected frequencies should be sufficiently large (generally at least 5) to ensure validity.

Review Questions

• What does the null hypothesis state in a test for homogeneity?
• How are degrees of freedom calculated for this test?
• What would you conclude if your test statistic exceeds the critical value from the chi-square distribution table?

Related terms

Chi-Square Test: A statistical test used to determine if there is a significant association between two categorical variables.

Contingency Table: A table used to display the frequency distribution of variables and analyze relationships between them.

$p$-Value: The probability that observed results occurred by chance, used to determine significance in hypothesis testing.