Page 230 - Intermediate Statistics for Dummies

20_045206 ch13.qxd 2/1/07 10:21 AM Page 209
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 (qualitative) variables
Lis a very common goal for researchers. For example, many medical stud-
ies center on how some characteristic about a person either raises or lowers
his chance of getting some disease. Marketers ask questions like, “Who is
more likely to buy our product: males or females?” Sports stat freaks wonder
about things like “Does winning the coin toss at the beginning of a football
game increase your team’s chance of winning the game?”
To answer each of the above 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 was drawn. This last step needs the machin-
ery from Chapter 14 to accomplish it. The goals of this chapter are to under-
stand what it means for two qualitative 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 relationship between x and y.

Suppose you’re collecting data on cell-phone users, and you want to find out
whether more females use cell phones than males. A study of 508 randomly
selected male cell-phone users and 508 randomly selected female cell-phone
users conducted by a wireless company found that women tend to use their
phones for personal calls more than men (big shocker). The survey showed
that 427 of the women said they used their wireless phones primarily to talk
with friends and family, while only 325 of the men admitted to doing so.