Questions: A researcher is using a chi-square test for independence to evaluate the relationship between birth-order position and self esteem. Each individual is classified as being 1st born, 2nd born, or 3rd born, and self-esteem is categorized as either high or low. For this study, what is the df value for the chi-square statistic? 1 2 3 4

Solution Steps

In a chi-square test for independence, the degrees of freedom (df) is calculated based on the number of categories for each variable. In this problem, we have two variables:

1. Birth-order position: 1st born, 2nd born, 3rd born (3 categories)
2. Self-esteem: High, Low (2 categories)

The formula for calculating the degrees of freedom for a chi-square test for independence is:

\[ df = (r - 1) \times (c - 1) \]

where \( r \) is the number of categories for the first variable, and \( c \) is the number of categories for the second variable.

Substituting the given values:

\[ df = (3 - 1) \times (2 - 1) = 2 \times 1 = 2 \]

Final Answer