1. Contingency Tables and Association
Lesson
Contingency Tables
and
Association

2. Objectives Compute the marginal distribution of a variable
Use the conditional distribution to identify association among categorical data

3. Vocabulary Contingency Table – relates to categories of data
Marginal Distribution – a frequency or relative frequency of either the row or column variable in the contingency table
Conditional Distribution – lists the relative frequency of each category of a variable, given a specific value of the other variable in the contingency table.

4. Requirements
To describe the association between two categorical variables, relative frequencies (percentages) must be used, because there will likely be different numbers of observations for each of the categories

5. Contingency Table Cat 2 Cat1 Plain Peanut Almond Total Red Blue Yellow
Conditional distributions
Cat 2
Cat1
Plain
Peanut
Almond
Total
Red
Blue
Yellow
Brown
Green
Totals by color of M&M
Totals by type of M&M
Marginal distributions

6. Conditional Distribution graph
Problem #11, page 650
Abortions in thousands completed in a year, by age and year
Percentages in total cells represents the marginal distributions
Percentages in other cells represent the conditional distributions (cell ⁄column total)
Total numbers going down; conditional % under 19 decreasing; conditional % over 25 increasing; conditional % between 20 – 24 pretty constant
Conditional Distribution graph
Age (yrs)
Year
Total
1990
1995
2000
≤ 19 % % % % % % % %
≥ 25 % % % %
1614
37.64% % %
4288
An alternative graph

7. Summary and Homework Summary Homework
Contingency tables are categorical data that have a specific structure
A row variable
A column variable
There are counts associated with each combination of row variable value and column variable value
Various row and column totals and row and column frequencies can be used to summarize this data
Homework
pg 647 – 651: 1, 3, 4, 7, 11, 13

8. Comments
Since the data is population data no inferential statistical comparisions are done.
Since many of the data is observational, beware of making any statements regarding causations.

9. Even Homework Answers
4: since each category could have different total numbers in them, the only safe way to compare is through percentages (or relative frequencies).