AP Statistics 2017

(Marvins-Underground-K-12) #1

group of males. To simplify the example, suppose that we were only testing one level (say 500 mg) of the
drug versus a placebo. The experimental design, blocked by gender, could then be diagrammed as
follows.


Randomization and block designs each serve a purpose. It’s been said that you block to control for the
variables you know about and randomize to control for the ones you don’t. Note that your interest here is
in studying the effect of the treatment within the population of males and within the population of females,
not to compare the effects on men and women. Thus, there would be no additional comparison between
the blocks—that’s a different study.


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
on 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 posttest. A
score for each teacher is arrived at by subtracting their pretest score from their posttest 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
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