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Experiments and Observational Studies for AP Statistics (page 3)

By — McGraw-Hill Professional
Updated on Feb 5, 2011

Matched Pairs Design

A particular block design of interest is the matched pairs design. One possible matched pairs design involves before and after measurements on the same subjects. In this case, each subject becomes a block in which the experiment is conducted. Another type of matched pairs involves pairing the subjects in some way (matching on, say, height, race, age, etc.).

    example: A study is instituted to determine the effectiveness of training teachers to teach AP Statistics. A pretest is administered to each of 23 prospective teachers who subsequently undergo a training program. When the program is finished, the teachers are given a post-test. A score for each teacher is arrived at by subtracting their pretest score from their post-test score. This is a matched pairs design because two scores are paired for each teacher.
    example: One of the questions on the 1997 AP Exam in Statistics asked students to design a study to compare the effects of differing formulations of fish food on fish growth. Students were given a room with eight fish tanks. The room had a heater at the back of the room, a door at the front center of the room, and windows at the front sides of the room. The most correct design involved blocking so that the two tanks nearest the heater in the back of the room were in a single block, the two away from the heater in a second block, the two in the front near the door in a third, and the two in the front near the windows in a fourth. This matching had the effect of controlling for known environmental variations in the room caused by the heater, the door, and the windows. Within each block, one tank was randomly assigned to receive one type of fish food and the other tank received the other. The blocking controlled for the known effects of the environment in which the experiment was conducted. The randomization controlled for unknown influences that might be present in the various tank locations.
    You will need to recognize paired-data, as distinct from two independent sets of data, later on when we study inference. Even though two sets of data are generated in a matched-pairs study, it is the differences between the matched values that form the one-sample data used for statistical analysis.

Practice problems for these concepts can be found at:

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