In the chi-square test for two-way tables, if H₀ is true, we expect the joint probability of two outcomes to be equal to the product of the marginal probabilities for each outcome.

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In the chi-square test for independence in two-way tables, the null hypothesis (often denoted as H0) posits that two categorical variables are independent. If this hypothesis is true, the joint probability of any combination of outcomes for these variables should equal the product of their respective marginal probabilities, reflecting the assumption of independence between the variables.

In the Chi-Square Test for Two-Way Tables, If H0 Is

In the Chi-Square Test for Two-Way Tables, If H₀ Is