AP®︎ Statistics: Topic 3.15 Flashcards

Uses counts in a two-way table from one random sample to test whether two categorical variables are independent, or equivalently whether there is an association, in one population

Uses counts in a two-way table from two or more independent random samples or from a randomized experiment to test whether the distribution of one categorical variable is the same across populations or treatments

Count expected in a cell if H₀ is true; expected count = (row total × column total) / table total; expected counts need not be whole numbers

χ² = Σ (O − E)² / E over all non-total cells; measures total disagreement between observed and expected counts

Df = (r − 1)(c − 1), using the number of non-total rows and columns

If p-value ≤ α, reject H₀; if p-value > α, fail to reject H₀

Reject H₀: convincing evidence of an association between the two categorical variables in the population; fail to reject H₀: not convincing evidence of an association

Reject H₀: convincing evidence that the distribution of the categorical variable differs across the populations or treatments; fail to reject H₀: not convincing evidence that the distributions differ

Homogeneity and independence use the same expected counts, χ², degrees of freedom, and p-value; the study design determines the procedure name, hypotheses, and conclusion

Probability, assuming H₀ is true in context, of getting a chi-square statistic at least as large as the observed value; a chi-square test for homogeneity or independence is always right-tailed

Randomization; when sampling without replacement, each sample size is no more than 10% of its population; and every expected cell count is greater than 5, checked with expected counts, not observed counts

When sampling without replacement, each sample size must be no more than 10% of its population size; not required for a randomized experiment

Independence: random sample from one population; homogeneity: independent random samples from the populations or data from a randomized experiment