Chapter 25: Two Categorical Variables: The Chi-Square Test

These flashcards cover essential concepts related to the Chi-Square Test for two categorical variables, including hypotheses, calculations, and interpretations.

What is the purpose of the Chi-Square Test in statistics?

To test the relationship between two categorical variables.

What hypotheses are tested in a Chi-Square Test?

Null hypothesis (H0): Two categorical variables are independent. Alternative hypothesis (Ha): Two categorical variables are not independent.

What data was analyzed in relation to Body Art and Class Rank?

The data set includes counts of undergraduates with and without body art across different class ranks (Freshman, Sophomore, Junior, Senior).

What is the expected count in a two-way table?

The expected count is calculated under the assumption that the null hypothesis is true, indicating independence between the categories.

What is the formula for the chi-square statistic?

χ² = Σ (observed count - expected count)² / expected count.

What are the conditions for using the Chi-Square Test?

Expected counts should be at least 1, no more than 20% of expected counts should be less than 5.

When is the chi-square test considered appropriate for analysis?

It is appropriate for independent samples from two or more populations classified according to two categorical variables.

What are the degrees of freedom for a chi-square test when analyzing two categorical variables?

Degrees of freedom = (r - 1)(c - 1), where r is the number of rows and c is the number of columns.

How is a chi-square distribution characterized?

It is skewed to the right and takes only non-negative values.