Confidence Interval Estimation
We have looked at creating a confidence interval for the difference between two population means using independent samples, meaning that the data from the two samples have no influence on each other. However, sometimes situations arise when the data sets are dependent. In this section, we will discuss how to construct a confidence interval for the difference between two population means using dependent samples where the observations in one sample uniquely correspond with observations in the second sample. Two dependent data sets, in which the observations from one data set are matched directly to the observations from the other data set, are called paired data.
So how do you decide when to design an experiment that will give you paired data? In general, you should select to use paired data when you want to compare two subgroups of a population that are logically connected. Each member of the first subgroup is systematically paired with a single member of the second subgroup either by matching characteristics or by using a preexisting connection, for example, twins. Here are some specific situations in which paired data would be used.
Pretest/posttest studies on the same subjects: For instance, suppose researchers wanted to study whether a person's sleeping habits changed when taking a new drug. Data would be taken from a number of participants both before the drug was administered and after. The data from each participant would then be paired together.
Pairing subjects with similar characteristics: The same research on sleep could occur by recruiting subjects as pairs by matching variables such as age, ethnicity, work environment, and so forth, and then giving one group a treatment (that is, the new drug) and the other a placebo.
Pairing subjects who have a specific connection that is of interest: For instance, parent/child pairings or sibling/twin pairings could reveal how certain genetic traits are related to patients' responses to the new drug.