9.1 Introduction to Statistical Inference with Two Populations

This is a photo of a plate with a large pile of eggs in the foreground and six slices of toast in the background. There is a small dish of red jam sitting near the toast on the plate.
If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when conducting a hypothesis test. Photo by Chloe Lim, CC BY 4.0.

Studies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is given a placebo. Then, the heart attack rate is studied over several years.

There are other situations that deal with the comparison of two groups. For example, studies compare various diet and exercise programs. Politicians compare the proportion of individuals from different income brackets who might vote for them. Students are interested in whether SAT or GRE preparatory courses really help raise their test scores.

Previously, we learned to conduct confidence intervals and hypothesis tests on single means and single proportions. We will extend these ideas in this chapter so that we can compare two means or two proportions to each other. The general procedures are similar to any confidence or hypothesis test, following the same basic steps we have already learned, just expanded to include the cases of studying two population parameters.

To compare two means or two proportions, we work with two populations. The groups are classified either as independent or matched pairs. Independent groups consist of two samples that are independent.  That is, one population is independent of the other if the sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. That is, there is some relationship between the samples selected from the two populations.  In this book, independent groups are used for either two population means or two population proportions and matched pairs are for two population means.

Attribution

“Chapter 10 Introduction” in Introductory Statistics by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Introduction to Statistics Copyright © 2022 by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.