Chapter 9: Inference for Two–Way Tables

Introduction

From previous sections, we know how to compare two populations. What if we wanted to compare more than two populations or more than two samples?!

The problem of multiple comparisons

There are two parts to multiple comparisons:

1. an overall test to see if there is any evidence of differences AMONG parameters
2. follow-up tests to decide which of the parameters differs by how much

In this course, we will focus on the former.

Section 9.1: Two–Way Tables

A table with r rows and c columns of data is called an r × c table. The table contains r·c cells which contain the data. This table shows the relationship between categroical variables. The r × c cells are combinations of explanatory and response variables.

Expected counts

In hypothesis testing, we compare observed counts with expected counts.

The expected count (when H₀ is true) is determined by:

expected count_{for cell r,c} .