L4.2: Association between two categorical variables - Introduction

​

Learning outcomes

• define association between two categorical variables
• read a two-way table
• distinguish joint counts and marginal totals
• interpret whether a pattern suggests association

​

Two-way tables

• A two-way table cross-classifies observations by two categorical variables.

​

Parts of the table

• Cell count: number in each category combination
• Row total: total for one row category
• Column total: total for one column category
• Grand total: total observations

​

What association means here

• If category distribution changes across the other variable, association may exist.
• If distributions look similar across groups, association may be weak or absent.

​

Reading the example

• CSE has more hostellers than day scholars.
• ME shows a different balance.
• That suggests possible association between department and residence type.

​

Exam hints and traps

• Raw counts alone can mislead when row or column totals differ strongly.
• First identify row totals and column totals before interpreting pattern.
• A two-way table is for two categorical variables, not two numerical variables.

​

Quick practice

1. In a two-way table, what does a cell count represent?
2. What is the difference between row total and grand total?
3. Why can raw counts alone sometimes mislead?

​

Answer key

1. Count for one combination of two categories
2. Row total is one row sum; grand total is total of all observations
3. Because groups may have different sizes