Chi-square Test for Homogeneity

Definition

The chi-square test for homogeneity is a statistical test used to determine if there is a significant difference in the proportions or distributions of a categorical variable across two or more independent groups or populations. It evaluates whether the observed frequencies in each category are consistent with the expected frequencies under the null hypothesis of homogeneity.

5 Must Know Facts For Your Next Test

1. The chi-square test for homogeneity is used to determine if there is a significant difference in the proportions or distributions of a categorical variable across two or more independent groups or populations.
2. The null hypothesis for the chi-square test for homogeneity is that the proportions or distributions of the categorical variable are the same across the independent groups or populations being compared.
3. The test statistic for the chi-square test for homogeneity is calculated by summing the squared differences between the observed and expected frequencies in each cell of the contingency table, divided by the expected frequencies.
4. The degrees of freedom for a chi-square test for homogeneity are calculated as (r-1)(c-1), where r is the number of rows (categories) and c is the number of columns (groups) in the contingency table.
5. The p-value from the chi-square test for homogeneity represents the probability of observing the given test statistic or a more extreme value under the null hypothesis of homogeneity.

Review Questions

• Explain the purpose of the chi-square test for homogeneity and the null hypothesis it tests.
  • The chi-square test for homogeneity is used to determine if there is a significant difference in the proportions or distributions of a categorical variable across two or more independent groups or populations. The null hypothesis for this test states that the proportions or distributions of the categorical variable are the same across the independent groups or populations being compared. In other words, the test evaluates whether the observed frequencies in each category are consistent with the expected frequencies under the assumption of homogeneity.
• Describe how the test statistic and degrees of freedom are calculated for the chi-square test for homogeneity.
  • The test statistic for the chi-square test for homogeneity is calculated by summing the squared differences between the observed and expected frequencies in each cell of the contingency table, divided by the expected frequencies. The degrees of freedom for this test are calculated as (r-1)(c-1), where r is the number of rows (categories) and c is the number of columns (groups) in the contingency table. The degrees of freedom represent the number of independent values that can vary in the final calculation of the test statistic.
• Explain how the p-value from the chi-square test for homogeneity is interpreted and used to draw conclusions about the null hypothesis.
  • The p-value from the chi-square test for homogeneity represents the probability of observing the given test statistic or a more extreme value under the null hypothesis of homogeneity. If the p-value is less than the chosen significance level (e.g., 0.05), the null hypothesis is rejected, indicating that there is a statistically significant difference in the proportions or distributions of the categorical variable across the independent groups or populations being compared. Conversely, if the p-value is greater than the significance level, the null hypothesis of homogeneity is not rejected, suggesting that the observed differences are likely due to chance.

Related terms

Null Hypothesis:

The null hypothesis for a chi-square test for homogeneity states that the proportions or distributions of the categorical variable are the same across the independent groups or populations being compared.

Degrees of Freedom:

The degrees of freedom for a chi-square test for homogeneity are calculated as (r-1)(c-1), where r is the number of rows (categories) and c is the number of columns (groups) in the contingency table.

Contingency Table:

A contingency table is a tabular format used to display the observed frequencies of the categorical variable across the different groups or populations being compared in a chi-square test for homogeneity.