Unit 7 of 12
Categorical Data Inference
- 4 lessons
- Videos 52 to 55
Categorical outcomes are summarized by counts, risks and odds. This unit compares risks and odds and tests tables of counts with chi-square, Fisher's exact and McNemar tests.
Risk differences, risk ratios and odds ratios describe the same table in different ways, and a case-control study can estimate an odds ratio but not the risks themselves. Chi-square tests compare observed counts with the counts expected under a model, such as a specified set of category probabilities, independence in a two-way table or the same distribution in several groups. When counts are small, Fisher's exact test conditions on the margins of the table, and when the same people give two binary answers, McNemar's test is based on the discordant pairs.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Risk and Odds
Risk, Odds and Relative Effects
How risks, risk differences, risk ratios and odds ratios describe one table, why the baseline risk matters, what a case-control study can estimate, and how to build a log-scale interval for a ratio.
Video 52
Chi-Square and Exact Tests
Chi-Square Goodness-of-Fit Tests
How a chi-square goodness-of-fit test compares observed counts with the expected frequencies of a multinomial model, and how parameters estimated from the data reduce the degrees of freedom.
Video 53
Chi-Square Independence and Homogeneity
How expected counts from the margins of a contingency table give the chi-square tests of independence and homogeneity, how Pearson residuals locate a discrepancy, and how Cramér's V measures its size.
Video 54
Sparse Tables, Fisher's Exact Test and Paired Binary Data
How Fisher's exact test conditions on the margins of a small 2 by 2 table, how two-sided exact p-values are defined, and how McNemar's test uses discordant pairs to test marginal homogeneity in paired binary data.
Video 55