Statistical Inference for Two Populations

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 between the two groups is studied over several years. Other examples of studies between two groups include studies that compare various diet and exercise programs or politicians who compare the proportion of individuals from different income brackets who might vote for them.

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 interval or hypothesis test, following the same basic steps we have already learned but 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, which means that 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, which means 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.

“9.1 Introduction to Statistical Inference with Two Populations” from Introduction to Statistics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.