# Block designs and matched pairs designs

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Block designs and matched pairs designs
AP Statistics

Double Blind Experiments
Neither the subjects nor the people who have contact with them know which treatment a subject received.

Matched pairs designs Matched pairs designs compare two treatments ONLY. We choose blocks of two units that are as closely matched as possible. We assign one of the treatments to each unit by tossing a coin or reading odd and even digits from Table B. ALTERNATIVELY, each block in a matched pairs design may consist of just one subject who gets both treatments one after the other. Each subject serves as his or her own control. The order of the treatments can influence the subject’s response, so we randomize the order for each subject by a coin toss. YOU MUST HAVE INDEPENDENT OBSERVATIONS FOR A MATCHED PAIRS DESIGN

We erect a pole at each location to hold the boards.
Example 5.16 p 301 Are cereal leaf beetles more strongly attracted by the color yellow or by the color green? Agriculture researchers want to know, because they detect the presence of the pests in farm fields by mounting sticky boards to trap insects that land on them. The board color should attract beetles as strongly as possible. We must design an experiment to compare yellow and green by mounting boards on poles in a large field of oats. WE can do this with a matched pairs design. The experimental units are locations in the field far enough apart to represent independent observations. We erect a pole at each location to hold the boards. We will mount a board of each color on both poles. We will have to randomly select the color that goes on top and on the bottom by a coin toss or using odd digits in table B. We compare the number of trapped beetles on the green board with the number of trapped beetles on the yellow board on the SAME POLE!

A Block Design a group of experimental units or subjects that are known before the experiment to be similar in some way that is expected to affect the response to the treatments. In a block design, the random assignment of units to treatments is carried out separately within each block.

Here is a mapping of this experiment:
Example 5.17 Comparing cancer therapies  The progress of a type of cancer differs in women and in men. A clinical experiment to compare three therapies for this cancer therefore treats sex as a blocking variable. Two separate randomizations are done. One assigning the female subjects and the other assigning the male subjects. They are groups of subjects that differ in some way (sex in this case) that is apparent BEFORE the experiment. Here is a mapping of this experiment:

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