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Chapter 25 Paired Samples and BlocksPaired Data Data are paired when the observations are collected in pairs or the observations in one group are naturally related to observations in the other. The simplest form of pairing is to measure each subject twice often before and after a treatment is applied.
The Lake County, IL Health Department experimented with a flexible fourday work week. For a year, the department recorded the mileage driven by 11 field workers on an ordinary fiveday work week. Then it changed to a flexible fourday work week and recorded the mileage for another year.
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Here are the data. The data are called paired because we have each worker's mileage before and after the work schedule change. The groups represent the same people at different times, so they can't be independent.
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Let's look at the difference in mileage for each worker as the work schedule changed.
Because it is the differences in mileage we care about, we'll treat them as if they were the data, ignoring the original two columns. Now that we have only one column of values to consider, we can use a simple onesample ttest. Mechanically a paired ttest is just a onesample ttest for the means of these pairwise differences.
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Assumptions and Conditions
Paired Data Assumption The data must be paired. You can't just decide to pair data when in fact the samples are independent. (Remember the twosample t methods are not valid without independent groups and paired groups are not independent.)
Independence Assumption If the data are paired, the groups are not independent. It's the differences that must be independent.
Randomization Condition In an experiment, the order of two treatments may be randomly assigned, or the treatments may be randomly assigned to one member of each pair.
10% Condition Applies to samples, not randomized experiments.
Nearly Normal Condition This condition can be checked with a histogram of the differences.
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HW p. 602; 2, 15, 17, 19 ANS
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