AP®︎ Statistics: Topic 3.14 Flashcards

Compares the distribution of one categorical variable across two or more populations or treatment groups

Determines whether two categorical variables are associated within one population, using one random sample with both variables recorded on each individual

The actual count recorded in a cell of the two-way table

The count expected in a cell if H₀ is true; expected count = (row total × column total) / table total

Measures overall distance between observed and expected counts relative to expected counts; sum of (O − E)² / E over all cells

A family of right-skewed distributions with only nonnegative values; skew decreases as degrees of freedom increase

H₀: the distribution of the categorical variable is the same across populations or treatments; Hₐ: the distributions are not all the same

H₀: the two categorical variables are independent, or there is no association, in the population; Hₐ: they are not independent, or there is an association

For independence: data come from a random sample from one population; for homogeneity: data come from independent random samples from the populations being compared or from a randomized experiment

When sampling without replacement, n ≤ 10% of N; for homogeneity with separate samples, check each sample against its population; not needed for a randomized experiment

Every expected cell count must be greater than 5

One sample from one population, with two categorical variables measured on each individual → chi-square test for independence; separate samples from populations or separate randomized treatment groups, with one categorical response recorded → chi-square test for homogeneity

The cells of the two-way table must contain counts, not percentages, proportions, measurements, or summary statistics