Section 1.3 Design of Experiments 21 Solution This experiment is not double-blind, because the teachers know whether they are using the new method or the old method. Randomized block experiments The type of randomized experiment we have discussed is sometimes called a completely randomized experiment, because there is no restriction on which subjects may be assigned which treatment. In some situations, it is desirable to restrict the randomization a bit. For example, imagine that two reading programs are to be tested in an elementary school that has children in grades 1 through 4. If children are assigned at random to the programs, it is possible that one of the programs will end up with more fourth graders while the other one will end up with more first graders. Since fourth graders tend to be better readers, this will give an advantage to the program that happens to end up with more of them. This possibility can be avoided by randomizing the students within each grade separately. In other words, we randomly assign exactly half of the students within each grade to each reading program. This type of experiment is called a randomized block experiment. In the example just discussed, each grade constitutes a block. In a randomized block experiment, the subjects are divided into blocks in such a way that the subjects in each block are the same or similar with regard to a variable that is related to the outcome. Age and gender are commonly used blocking variables. Then the subjects within each block are randomly assigned a treatment. Observational Studies Recall that an observational study is one in which the investigators do not assign the treatments. In most observational studies, the subjects choose their own treatments. Observational studies are less reliable than randomized experiments. To see why, imagine a study that is intended to determine whether smoking increases the risk of heart attack. Imagine that a group of smokers and a group of nonsmokers are observed for several years, and during that time a higher percentage of the smoking group experiences a heart attack. Does this prove that smoking increases the risk of heart attack? No. The problem is that the smoking group will differ from the nonsmoking group in many ways other than smoking, and these other differences may be responsible for differences in the rate of heart attacks. For example, smoking is more prevalent among men than among women. Therefore, the smoking group will contain a higher percentage of men than the nonsmoking group. It is known that men have a higher risk of heart attack than women. So the higher rate of heart attacks in the smoking group could be due to the fact that there are more men in the smoking group, and not to the smoking itself. Objective 3 Understand how confounding can affect the results of an observational study Confounding The preceding example illustrates the major problem with observational studies. It is difficult to tell whether a difference in the outcome is due to the treatment or to some other difference between the treatment and control groups. This is known as confounding. In the preceding example, gender was a confounder. Gender is related to smoking (men are more likely to smoke) and to heart attacks (men are more likely to have heart attacks). For this reason, it is difficult to determine whether the difference in heart attack rates is due to differences in Explain It Again smoking (the treatment) or differences in gender (the confounder). Another way to describe a confounder: A confounder is something other than the treatment that can cause the treatment groups to have different outcomes. SUMMARY A confounder is a variable that is related to both the treatment and the outcome. When a confounder is present, it is difficult to determine whether differences in the outcome are due to the treatment or to the confounder.
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