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In a matched pairs design, each subject is paired with another subject that shares key characteristics. This minimizes variability between groups and ensures each pair is as similar as possible. The matched pairs design is especially useful in experiments where it is crucial to control individual differences that could impact the results. For example, in the HIV vaccine experiment involving 80 pairs of twins, each pair of twins serves as a natural matched pair. Twins generally share genetic make-up and environmental factors, making this design ideal. By using matched pairs, we can directly compare the effects of the two different vaccines within each twin pair. One twin receives the DNA vaccine, and the other receives the adenoviral vector vaccine. This way, each twin acts as a control for the other, given their shared characteristics. This approach helps to attribute any differences in vaccine effectiveness specifically to the vaccines themselves, rather than to other variables.

The randomized block design groups subjects into blocks based on a certain characteristic before randomly assigning treatments. This design helps control for variability within the blocks that might affect the outcome. For instance, in an experimental study, blocks can be formed based on subjects' gender, age, or other relevant traits. Once grouped, subjects within each block are randomly assigned different treatments. This ensures balance and comparability across treatment groups. Although not used in the HIV vaccine twin study, this design would have required forming blocks of subjects with similar characteristics before random treatment assignments. While this method helps control for confounding variables, it is less beneficial when natural pairs, like twins, are already available, as they inherently control for many variables.

A completely randomized design assigns treatments to all subjects entirely by chance, without considering individual characteristics aside from randomness. This design is straightforward and helps prevent systematic bias. It's suitable for studies where subjects are not naturally paired or blocked. In the HIV vaccine study context, a completely randomized design would involve assigning the DNA and adenoviral vector vaccines to subjects purely by random selection, irrespective of their twin status. However, this method could introduce more variability into the results, making it harder to discern the true effect of the vaccines due to the broader range of subject differences. Thus, while easy to implement, this design is less precise when compared to the matched pairs design, especially in scenarios involving naturally matched subjects like twins.