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Unit 8: Inference for Categorical Data: Chi-Square

7 dot points across 7 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you compute the chi-square statistic and P-value and conclude a goodness-of-fit test?

Topic 8.3 Carrying Out a Chi-Square Test for Goodness of Fit: compute the chi-square statistic from observed and expected counts, find the P-value using k minus 1 degrees of freedom, and state a conclusion in context.
A focused answer to AP Statistics Topic 8.3, on computing the chi-square statistic from observed and expected counts, finding the P-value with k minus 1 degrees of freedom, and stating a conclusion in context, with a full worked test.
11 min answer →

How do you compute the chi-square statistic and P-value and conclude a test of homogeneity or independence?

Topic 8.6 Carrying Out a Chi-Square Test for Homogeneity or Independence: compute the chi-square statistic from a two-way table, find the P-value using (rows minus 1)(columns minus 1) degrees of freedom, and state a conclusion in context.
A focused answer to AP Statistics Topic 8.6, on computing the chi-square statistic from a two-way table, finding the P-value with (r minus 1)(c minus 1) degrees of freedom, and stating a conclusion in context, with a full worked test.
11 min answer →

How do you compute expected counts in a two-way table under the assumption of no association?

Topic 8.4 Expected Counts in Two-Way Tables: compute the expected count for each cell of a two-way table under the null hypothesis using the row total times column total divided by the grand total.
A focused answer to AP Statistics Topic 8.4, on computing expected counts in a two-way table under the null of no association, using row total times column total over the grand total, and why this formula encodes independence.
9 min answer →

When a categorical variable has more than two categories, how do we judge whether observed counts depart from what was expected?

Topic 8.1 Introducing Statistics: Are My Results Unexpected?: explain why comparing observed counts across several categories to expected counts motivates the chi-square family of tests.
A focused answer to AP Statistics Topic 8.1, on why comparing observed counts across several categories to expected counts motivates chi-square tests, extending proportion inference to variables with more than two categories.
9 min answer →

How do you choose the correct inference procedure for a categorical-data scenario?

Topic 8.7 Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data: choose among the one-proportion, two-proportion, and chi-square (goodness of fit, homogeneity, independence) procedures based on the scenario.
A focused answer to AP Statistics Topic 8.7, on choosing among one-proportion, two-proportion, and chi-square (goodness of fit, homogeneity, independence) procedures for categorical data, based on the number of variables, categories, and samples, with a worked decision.
10 min answer →

How do you state the hypotheses, compute expected counts, and check conditions for a chi-square goodness-of-fit test?

Topic 8.2 Setting Up a Chi-Square Goodness of Fit Test: state the hypotheses for a goodness-of-fit test, compute expected counts from a claimed distribution, and verify the conditions.
A focused answer to AP Statistics Topic 8.2, on stating the hypotheses for a goodness-of-fit test, computing expected counts from a claimed distribution, and checking the random, large-counts (expected at least 5), and 10% conditions.
9 min answer →

How do you state the hypotheses and decide between a chi-square test of homogeneity and one of independence?

Topic 8.5 Setting Up a Chi-Square Test for Homogeneity or Independence: distinguish a test of homogeneity from a test of independence based on the design, state the appropriate hypotheses, and check the conditions.
A focused answer to AP Statistics Topic 8.5, on distinguishing a chi-square test of homogeneity (several groups, same variable) from a test of independence (one sample, two variables), stating the right hypotheses, and checking the conditions.
9 min answer →