Elementary Statistics JMP Assignment 01

198

Performing Contingency Analysis

Chapter 6

3

Performing Contingency Analysis

Using the Fit Y by X or Contingency Platform

(1) Click on the Help tab in JMP and select Sample Data.

(2) Click on the following option: See an Alphabetical List of all Sample Data Files

(3) Click on the Car Poll.jmp sample data table

Make an attempt to answer the following questions and if you find that you will take more than 60 seconds then look at the section below on Contingency Table.

(1) What is the number of cars that are both large and come from America?

(2) What is the percentage of all cars that are both large and come from America?

(3) What is the percentage of large cars that come from America?

(4) What is the percentage of American cars that are large?

Contingency Table

The Contingency Table is a two-way frequency table. There is a row for each factor level and a column for each response level.

To produce the plot shown in Figure 6.1, follow the instructions in the example below:

The Contingency or Fit Y by X platform lets you explore the distribution of a categorical (nominal or ordinal) variable Y across the levels of a second categorical variable X. The Contingency platform is the categorical by categorical personality of the Fit Y by X platform. The analysis results include a mosaic plot, frequency counts, and proportions.

Figure 6.1 A Contingency Table

Example of Contingency Analysis

This example uses the Car Poll.jmp sample data table, which contains data collected from car polls. The data includes aspects about the individual polled, such as their sex, marital status, and age. The data also includes aspects about the car that they own, such as the country of origin, the size, and the type. Examine the relationship between car sizes (small, medium, and large) and the cars’ country of origin.

1. Using the open Car Poll.jmp sample data table.

2. Select Analyze > Fit Y by X.

3. Select size and click Y, Response.

4. Select country and click X, Factor.

5. Click OK.

The following table explains the conclusions that you can make about these cars using the Contingency Table.

Number Description Label in Table

36 Number of cars that are both large and come from America Count

11.88% Percentage of all cars that are both large and come from America (36/303)a.

85.71% Percentage of large cars that come from America (36/42)b

31.30% Percentage of American cars that are large (36/115)c.

Total%

Col%

Row%

Mosaic Plot The mosaic plot is a graphical representation of the two-way frequency table or Contingency Table. A mosaic plot is divided into rectangles, so that the area of each rectangle is proportional to the proportions of the Y variable in each level of the X variable

Note the following about the mosaic plot in the Figure above:

· The proportions on the x-axis represent the number of observations for each level of the X variable, which is country.

· The proportions on the y-axis at right represent the overall proportions of Small, Medium, and Large cars for the combined levels (American, European, and Japanese).

·

From the mosaic plot and legend in the Figure above, notice the following:

· Very few Japanese cars fall into the Large size category.

· The majority of the European cars fall into the Small and Medium size categories.

· The majority of the American cars fall into the Large and Medium size categories.