What is the null hypothesis for a chi-square test?

Sourav PanSeptember 10, 2024

Answered

The null hypothesis for a Chi-Square test depends on the type of Chi-Square test being conducted. Here are the null hypotheses for the various types of Chi-Square tests:

1. Chi-Square Test for Independence:
   • Null Hypothesis (H₀): There is no association between the two categorical variables. In other words, the variables are independent of each other.
2. Chi-Square Test for Goodness of Fit:
   • Null Hypothesis (H₀): The observed frequencies of the categorical data match the expected frequencies under the specified theoretical distribution.
3. Chi-Square Test for Homogeneity:
   • Null Hypothesis (H₀): The distribution of a categorical variable is the same across different populations or groups. In other words, the proportions are homogeneous across the groups.
4. Chi-Square Test for a Contingency Table:
   • Null Hypothesis (H₀): There is no relationship between the variables represented in the contingency table. The distribution of one variable is independent of the distribution of the other variable.
5. Chi-Square Test for Population Proportions:
   • Null Hypothesis (H₀): The proportions of the categorical outcomes are the same across the different groups or categories being compared.