1. Inference for Two Way Tables
14.2
Inference for Two Way Tables

2. To compare two proportions, we use a 2-Proportion Z Test or a 2-Proportion T Test. If we want to compare three or more proportions, we need a new procedure.

3. The first step in the overall test for comparing several proportions is to arrange the data in a two-way table.

4. Think of the counts as elements of a matrix with r rows and c columns
Think of the counts as elements of a matrix with r rows and c columns. This is called an r x c table with (r)(c) cells.

5. Our null hypothesis is that there is no difference among the proportions. The alternative hypothesis is that there is some difference among the proportions.
We will use the chi-square test to measure how far the observed values are from the expected values

6. To calculate the expected counts, multiply the row total by the column total, and divide by the table total:

7. The chi-square statistic is the sum over all r x c cells in the table:

8. The degrees of freedom is (r – 1)(c – 1)
The degrees of freedom is (r – 1)(c – 1). The P-value is the area to the right of the statistic under the chi-square density curve.

9. The chi-square test can also be used to show evidence that there is a relationship between two categorical variables
Use this if you have independent SRSs from several populations where one variable is categorical and the other is the sample number
Or, if you have a single SRS with each individual classified according to two categorical variables
Or, if you have an entire population with each individual classified according to two categorical variables