2.7 - Lesson 2 Summary

In this lesson, we made a distinction among three types of large-sample hypothesis tests and related confidence intervals used in the analysis of categorical data: Wald, Likelihood-Ratio, and Score. The Wald test is the most widely used one. For example, we will see when we fit a logistic regression model that the z-statistic and the confidence intervals for the regression parameter estimates are Wald CIs.

Lesson 2 also introduced the goodness-of-fit test and the corresponding residuals. The distinction was made between the goodness-of-fit tests with known versus unknown population parameters. This idea of comparing the assumed model (H₀) to a distribution of the observed data, and assessing how close they fit, will be used throughout the course, as will these test statistics. For example, in the next lesson, we will see that the chi-square test of independence is just a goodness-of-fit test where the assumed model (H₀) of the independence of two random variables is compared to a saturated model, that is to the observed data.