Chapters 9 and 10 focused on comparing independent groups. But often, dependent groups are compared instead. Imagine, for example, that a training program for increasing endurance is under investigation, the endurance of participants is measured before training starts, they undergo the training program for 4 weeks, and then their endurance is measured again. This is an example of what is called a repeated measures or within subjects design, simply meaning that the same individuals are repeatedly measured over time. An issue is whether there has been a change in the average endurance, but because the same participants are measured both before and after training, it is unreasonable to assume that these two measures are independent. If they are dependent, Welch's test and the two-sample Student's c11-math-0001 test for comparing means, described in Chapter 9, are no longer valid. (They use the wrong standard error.)

As another example, consider again the study where the goal is to assess the effects of ozone on weight gain among rats. Now, however, rather than randomly sampling rats, pairs of rats from the same litter are sampled, one is assigned to the ozone-free group and the other is exposed to ozone. Because these pairs of rats are related, it is unreasonable to assume that their reactions to their environment are independent.

As a final example, consider ...

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