19  Comparing Groups

Module IV built the inferential machinery: how to draw a sample worth trusting, how a statistic varies across samples, how to estimate a parameter with honest uncertainty, and how to test a claim about it. Every one of those chapters worked with a single mean or proportion.

Almost no real question stops there. Businesses and researchers compare: this branch against that one, the new process against the old, three suppliers against each other, spend against tenure. This module turns the one-sample machinery into the comparisons that applied work actually runs on.

Chapter 17 compares two groups, and distinguishes the independent design from the paired one. Chapter 18 handles outcomes that are categories rather than measurements, where the question becomes whether two classifications are associated. Chapter 19 extends comparison to three or more groups at once, and explains why running three separate t-tests is not an acceptable substitute. Chapter 20 adds a second factor, where the interaction between the two is usually the most interesting term in the table, and handles designs in which the same units are measured more than once.

The statistical logic never changes from Chapter 16: state a null, measure how far the data sits from it in standard errors, and ask how often chance alone would produce a gap that large. What changes is the statistic, and each chapter is largely about choosing the right one for the shape of the question.