In chapter 11 we saw how to we could test a hypothesis by comparing a single sample proportion to a fixed proportion. The fixed proportion value was either established through practice, or over time, or was simply a given. It could also be an assumed value or one that someone claimed as being true and we wanted to test it. However, often we want to compare two population proportions.
For example, suppose that a physical therapist has developed a new treatment that she believes will reduce injuries of a certain type. In this situation the researcher is interested in the difference between proportion of injuries observed by those who receive the treatment, versus the proportion of injuries observed by those who do not receive the treatment.
Generally, to compare two population proportions, we need two groups to compare to each other. Examples include:
Women compared to men.
People with children compared to people without children
People in college compared to people not in college
People who exercise regularly compared to people who don’t exercise at all
People who prefer dogs compared to people who prefer cats
We also need two or more choices for the groups. Some things we could survey people about include:
Diet soda compared to regular soda
Will vote in the upcoming election compared to will not compared to undecided
Preference for beer compared to wine vs. mixed drinks
Favorite type of music
Opinion of a public figure, political topic, etc.
Brand preference
As with comparing two means, comparing two proportions is common in the data-driven disciplines, and this chapter introduces the hypothesis test and confidence interval for making inferences on two proportions.