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In a matched pairs design, subjects are matched in pairs and each treatment is given to one
subject in each pair. Another situation calling for matched pairs is beforeandafter observations
on the same subjects.
Matched pairs t procedures: To compare the responses to the two treatments in a matched pairs
design, find the difference between the responses within each pair. Then apply the onesample t
procedures to these differences.
The parameter µ in a matched pairs t procedure is the mean difference in the responses to the two
treatments within matched pairs of subjects in the entire population.
We turn matched pairs data into singlesample data by taking differences within each pair. We
are making inferences about a single population, the population of all differences within matched
pairs.
The t confidence interval and test are exactly correct when the distribution of the population is
exactly Normal and SRS. No real data are exactly Normal. The usefulness of the t procedures in
practice therefore depends on how strongly they are affected by lack of Normality.
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 Winter '11
 PattiColling

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