Chapter 5: Association between Categorical Variables (Chi-Squared Test)

Vocabulary flashcards covering key terms and definitions from the Chi-Squared Test of Independence and contingency tables.

Contingency table

A table displaying counts of observations for all combinations of two categorical variables; row totals and column totals are called marginal distributions.

Marginal distribution

The row totals or the column totals in a contingency table.

Conditional distribution

The distribution of one variable given a fixed category of the other variable; used to assess independence.

Statistical independence

The population conditional distributions on one variable are identical across all categories of the other variable; probabilities are the same across levels.

Statistical dependence

The conditional distributions differ across categories, indicating an association between the variables.

Null hypothesis (H0) of independence

The two categorical variables are statistically independent.

Alternative hypothesis (Ha) of dependence

The two categorical variables are statistically dependent.

Observed frequency f0

The count actually observed in a cell of the contingency table.

Expected frequency fe

The count expected in a cell if the variables were independent; fe = (row total × column total) / overall sample size.

Pearson chi-squared statistic

χ2 = sum over all cells of (f0 − fe)² / fe; measures discrepancy between observed and expected frequencies under H0.

Degrees of freedom

df = (r − 1)(c − 1) for an r × c contingency table.

P-value

The right-tail probability of observing a χ2 as large or larger than the observed value under H0.

Significance level (α)

The threshold for rejecting H0; if P ≤ α, reject H0.

Large-sample condition

For the chi-squared test, each cell should have fe > 5 to rely on the χ2 approximation.

Fisher’s exact test

An exact test used for small samples when the chi-squared approximation may be unreliable.

Randomization

Assumption that the sample is random, ensuring valid inference for the chi-squared test.

2×3 contingency table

A table with 2 rows and 3 columns used to illustrate cross-classification of two variables (e.g., gender and party ID).

Chi-squared test of independence

A test comparing observed frequencies to expected frequencies under independence to determine if two categorical variables are related.

Interpretation caution: association vs strength

A large χ2 indicates evidence of association but does not quantify the strength; examine conditional distributions for strength.