Comparison of Two Groups

The purpose of statistical analysis is to clarify whether the observed difference of two groups, often called treatment and control group, is caused by an actual difference or by random variation. It is important to distinguish “independent” samples from “paired” samples because different methods of analysis are appropriate.

For unpaired samples, we impose an assumption of independence among all observations. This means that the observations come from two independent groups. This setup with independent groups corresponds to one-way analysis because different sources are compared and only one factor, treatment or control, is varied in the experiment.
“Paired” samples occur, for example, if two measurements are collected for each subject in the sample under different circumstances, or if measurements are taken on pairs of related observational units such as twins. In dietary studies with two diets under investigation, for example, it is common that the subjects try one drug in one period and the other drug in another period; thus, they are “dependent.” In the paired samples the pairwise differences of two measurements will be used.