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One hundred people were recruited in two sessions and randomly assigned to one of two groups. Some information about the design and analysis:

  • In Session 1, participants were given gum to chew whilst doing a series of tasks to complete.

  • In Session 2, participants were not given gum to chew and did the same tasks in the same order as the first session.

  • A series of independent sample t tests were carried out, one for each task, and were then compared across the two sessions.

My question is this: Is an independent sample t-test correct in this scenario as a testing method? Or should it be a multiple paired sample t test, whereby the test is done within subjects?

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For the experiment described in the first paragraph, a two-sample t-test is indeed appropriate, as the participants are independent. For the crossover experiment you describe next, the paired t-test is indeed most appropriate. Both setups and analysis methods are correct and will give you unbiased estimation of the effect of gum.

Yet the crossover setup has the advantage of conditioning on the participant, eliminating variability between participants and thus giving you better power and more precise estimation. Yet it hinges on the assumption that there is no effect of having chewed gum in the first session on the concentration on the second session, where the participants do not get to chew gum.

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  • $\begingroup$ so would you suggest that doing a multiple paired sample t test might be a better option for this experiment? $\endgroup$
    – user400775
    Commented Nov 16, 2023 at 9:50
  • $\begingroup$ The test you do should correspond to the design. And it seems like the paired design is indeed the best choice here. $\endgroup$
    – Knarpie
    Commented Nov 17, 2023 at 8:57

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