Page 237 - Statistics II for Dummies

Chapter 13

Forming Associations

with Two-Way Tables

In This Chapter
▶ Reading and interpreting two-way tables
▶ Figuring probabilities and checking for independence
▶ Watching out for Simpson’s Paradox

ooking for relationships between two categorical variables is a very
Lcommon goal for researchers. For example, many medical studies center
on how some characteristic about a person either raises or lowers his chance
of getting some disease. Marketers ask questions like, “Who’s more likely to
buy our product: males or females?” Sports stats freaks wonder about things
like, “Does winning the coin toss at the beginning of a football game increase
a team’s chance of winning the game?” ( I believe it does!)

To answer each of the preceding questions, you must first collect data (from
a random sample) on the two categorical variables being compared — call
them x and y. Then you organize that data into a table that contains columns
and rows, showing how many individuals from the sample appear in each
combination of x and y. Finally, you use the information in the table to con-
duct a hypothesis test (called the Chi-square test). Using the Chi-square test,
you can determine whether you can see a relationship between x and y in the
population from which the data were drawn. You need the machinery from
Chapter 14 to accomplish this last step.

The goals of this chapter are to help you to understand what it means for two
categorical variables (x and y) to be associated and to discover how to use
percentages to determine whether a sample data set appears to show a rela-
tionship between x and y.

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