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Chapter 1: Q 33. (page 26)

Marginal distributions aren鈥檛 the whole story Here are the row and column totals for a two-way table with two rows and two columns:

Find two different sets of counts a,b,c, and d for the body of the table that gives these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

Short Answer

Expert verified
203050

401050
401050

203050
6040100

6040100
104050

50050
50050

104050
6040100

6040100

Step by step solution

01

Given information

The table is

ab50
cd50
6040100
02

Concept

The distribution of a category variable is displayed using pie charts and bar graphs. Any set of quantities measured in the same units can be compared using bar graphs. It's a good idea to ask yourself, "What do I see?" when looking at any graph.

03

Explanation

Below is an alternate set of counts a,b,c,anddfor the table's body that provides the same totals:

ab50

302050
cd50

302050
6040100

6040100
203050

401050
401050

203050
6040100

6040100
104050

50050
50050

104050
6040100

6040100

This explains why the relationship between two variables cannot be determined solely by looking at the two individual variables.

As a result, the two different sets of counts have been discovered.

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