In general, a researcher can use half the number of participants in a counterbalanced crossover design and still retain the same statistical power as in the between-subjects design.

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In a counterbalanced crossover design, each participant acts as their own control by participating in both conditions of the experiment, which can increase statistical efficiency and allow for the same statistical power with fewer participants compared to a between-subjects design where each participant is only exposed to one condition.

In General, a Researcher Can Use Half the Number of Participants