Paired versus Unpaired Data

If statistical methods are applied to analyze data from multiple groups and each individual data point comes from a separate and distinct source, the mathematics behind the statistics assumes an independence and randomness that would not be the same if the sources are highly related. As an example, consider a study of blood pressure in two groups of subjects, one treated with medication and the other untreated. Because blood pressure measurements can be widely scattered in distribution, depending on the subjects' previous medical condition, a small drug effect might be difficult to notice. However, if the same individuals were studied before and after therapy, the wide initial variations might cancel out and small effects would be noticed. In this latter study, the data points can be paired, one in each group, to detect these small effects. A study in which the data can be paired can be very sensitive in picking out small changes. Conversely, the erroneous use of paired statistics might suggest a statistically significant result when one does not exist.