A certain lake has been designated for pollution clean-up. One way to assess the effectiveness of the clean-up measures is to randomly select a number n of locations from which water samples are taken and analyzed both before and after the cleanup.

The n randomly chosen locations are the experimental units, each of which yields two measurements. This results in paired data. Another way of designing the comparative study is to select a random sample of n1 locations from which water samples are taken to assess the water quality before the clean-up measures, and a different random sample of n2 locations which will serve to assess the water quality after the clean-up measures. The second sampling design will result in two independent samples, one from each population.