Independent vs. Paired Samples

When you are interested in estimating a difference in population means, you usually start with data from samples from each of the populations of interest. There are two different strategies for selecting the two samples. One strategy is to select a sample from one population and then independently select a sample from the second population. Using this strategy results in two samples where the individuals selected for the first sample do not influence the individuals selected for the second sample. This would be the case if you took a random sample from each population. Samples selected in this way are said to be independent samples.

The second strategy is to select samples where each observation in one sample is paired in a logical way with a particular observation in the second sample. In the question above, the observations would be paired by student—there is a before keyboarding class typing speed and an after keyboarding class typing speed for each student. If samples are chosen in a way that results in the observations in one sample being paired with the observations in the other sample, the samples are said to be paired samples or matched pairs. Paired samples are also sometimes called dependent samples.

One common process that results in paired samples is when data are collected both before and after some intervention (like the keyboarding class). But there are other data collection methods that can result in paired samples. One example would be if participants in a study to evaluate the effect of exercise (light vs. moderate exercise) were paired by weight prior to the study, and then one person from each pair was assigned to each exercise group. This would result in exercise groups that were similar with respect to weight, and the two samples would be paired because there is a logical way to match an observation from the light exercise group with a particular observation from the moderate exercise group.

It is important to make a distinction between independent samples and paired samples because the way the data from the samples are analyzed is different for these two cases.