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Abstract:
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Many students are initially exposed to the idea of a multivariate data when the topic of "paired samples" is introduced. The typical scenario is a set of measurements taken before and after some treatment. Most texts pay great tribute the reduction in variance that can be achieved when estimating the mean difference, so much so, that students often come away with the sense that paired, or multivariate measurements are always preferred over independent samples. We offer examples that help illustrate when independent samples are preferred over the matched samples. Also, we discuss how to handle issues of correlation that occur when independent samples, taken from finite populations, result in multiple measurements contributed by the same experimental unit.
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