Page 257 - Statistics II for Dummies

Chapter 14

Being Independent Enough

for the Chi-Square Test

In This Chapter
▶ Testing for independence in the population (not just the sample)
▶ Using the Chi-square distribution
▶ Discovering the connection between the Z-test and the Chi-square test

Y ou’ve seen these hasty judgments before — people who collect one

sample of data and try to use it to make conclusions about the whole
population. When it comes to two categorical variables (where data fall into
categories and don’t represent measurements), the problem seems to be
even more widespread.

For example, a TV news show finds that out of 1,000 presidential voters, 200
females are voting Republican, 300 females are voting Democrat, 300 males
are voting Republican, and 200 males are voting Democrat. The news anchor
shows the data and then states that 30 percent (300 ÷ 1,000) of all presiden-
tial voters are females voting Democrat (and so on for the other counts).
This conclusion is misleading. It’s true that in this sample of 1,000 voters, 30
percent of them are females voting Democrat. However, this result doesn’t
automatically mean that 30 percent of the entire population of voters is
females voting Democrat. Results change from sample to sample.

In this chapter, you see how to move beyond just summarizing the sample
results from a two-way table (discussed in Chapter 13) to using those results
in a hypothesis test to make conclusions about an entire population. This
process requires a new probability distribution called the Chi-square dis-
tribution. You also find out how to answer a very popular question among
researchers: Are these two categorical variables independent (not related to
each other) in the entire population?

21_466469-ch14.indd 241 7/24/09 9:51:28 AM