AP®︎ Statistics (pre-2026): Unit 8 Flashcards
Master key terms and definitions for Unit 8 of AP Statistics (pre-2026) – Inference for Categorical Data: Chi-Square to help you prep for quizzes and the AP exam.
Statistically Significant Difference
A result unlikely to occur by chance alone if the original claim were true.
A result unlikely to occur by chance alone if the original claim were true.
Larger samples produce less variability, making unusual departures from expectation easier to detect.
As sample size increases, sample results tend to get closer to the true population value.
Observed counts are actual totals, and expected counts are model-predicted totals for comparison.
A question of whether differences from expectation are due to chance or a false claim.
The probability, assuming the null hypothesis is true, of getting a test statistic at least as extreme as the one observed.
The number of categories minus 1, which determines the specific chi-square distribution used.
The set of population proportions across all categories of a single categorical variable.
Use a random sample or randomized experiment, and if sampling without replacement, require n over N at most 0.10.
All expected counts should be at least 5 for the chi-square approximation to be reliable.
The true population proportion for each category of the categorical variable being studied.
A right-skewed distribution of positive values that becomes less skewed as degrees of freedom increase.
A chi-square test that assesses whether one categorical variable from a single sample matches a stated or theoretical distribution of proportions.
The sum of (observed minus expected) squared divided by expected across all categories.
The predicted count under the null hypothesis for a category or table cell.
The actual count observed in a category or table cell from the data.
The distribution of test statistics expected if the null hypothesis and probability model are true.
Use simulation under the null or use a chi-square model when a probability model is assumed true.
Use the chi-square table or computer output with the test statistic and degrees of freedom.
Larger chi-square values show greater disagreement between observed and expected counts, so only the right tail matters.
State whether to reject or fail to reject and interpret the result in context.
For a chi-square goodness-of-fit test, the degrees of freedom equal the number of categories minus 1.
Reject the null hypothesis if the p-value is less than alpha; otherwise, fail to reject the null hypothesis.
Multiply the row total by the column total, then divide by the table total.
A table of expected frequencies found by applying the expected count formula to every cell.
A chi-square test that compares the distribution of a categorical variable across two or more independent populations or treatments.
A chi-square test that assesses whether two categorical variables are associated in a single population using one sample.
Independence uses one sample from one population; homogeneity compares distributions across separate populations or treatments.
A table that displays counts for combinations of two categorical variables.
Use the proper random process, check n/N ≤ 10% when needed, and ensure all expected counts exceed 5.
Calculated as (number of rows minus 1)(number of columns minus 1).
Independence: evidence of association; homogeneity: evidence distributions differ across populations.
State the decision and evidence in terms of the variables or populations studied.
A non-significant result means fail to reject the null, not prove it true.
The sum of (observed minus expected) squared divided by expected over all cells in a two-way table.
Use the chi-square distribution with the appropriate degrees of freedom, via a table or technology, to find the p-value.
One-way tables summarize one categorical variable; two-way tables summarize two categorical variables together.
Null states no difference or no association; alternative states a difference in distributions or an association.
Use z procedures for two-category proportions and chi-square procedures for variables with multiple categories.
Use goodness of fit for one sample and one variable, independence for one sample and two variables, and homogeneity for multiple samples and one variable.
The null hypothesis states that the population distribution for the categorical variable matches the stated or theoretical proportions; the alternative is that at least one true proportion differs.
The null hypothesis states that the distributions of the categorical variable are the same across populations or treatments; the alternative is that at least one distribution differs.
The null hypothesis states that two categorical variables are independent in the population; the alternative is that they are associated.
