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# Experiments and Observational Studies for AP Statistics (page 2)

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

### Double-Blind Experiments

In the example above, it was explained that neither the subjects nor the researchers knew who was receiving which dosage, or the placebo. A study is said to be double-blind when neither the subjects (or experimental units) nor the researchers know which group(s) is/are receiving each treatment or control. The reason for this is that, on the part of subjects, simply knowing that they are part of a study may affect the way they respond, and, on the part of the researchers, knowing which group is receiving which treatment can influence the way in which they evaluate the outcomes. Our worry is that the individual treatment and control groups will differ by something other than the treatment unless the study is double-blind. A double-blind study further controls for the placebo effect.

### Randomization

There are two main procedures for performing a randomization. They are:

• Tables of random digits. Most textbooks contain tables of random digits. These are usually tables where the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 appear in random order (well, as random as most things get, anyhow). That means that, as you move through the table, each digit should appear with probability 1/10, and each entry is independent of the others (knowing what came before doesn't help you make predictions about what comes next).
• Calculator "rand" functions. The TI-83/84 calculator has several random functions: rand, randInt (which will generate a list of random integers in a specified range), randNorm (which will generate random values from a normal distribution with mean μ and standard deviation s), and randBin (which will generate random values from a binomial distribution with n trials and fixed probability p—see Chapter 10). If you wanted to generate a list of 50 random digits similar to the random digit table described above, you could enter randInt(0,9) and press ENTER 50 times. A more efficient way would be to enter randInt(0,9,50). If you wanted these 50 random integers stored in a list (say L1), you would enter andInt(0,9,10) →L1 (remembering that the → is obtained by pressing STO).

We will use tables of random digits and/or the calculator in Chapter 9 when we discuss simulation.

### Block Design

Earlier we discussed the need for control in a study and identified randomization as the main method to control for lurking variables—variables that might influence the outcomes in some way but are not considered in the design of the study (usually because we aren't aware of them). Another type of control involves variables we think might influence the outcome of a study. Suppose we suspect, as in our previous example, that the performance test varies by gender as well as by dosage level of the test drug. That is, we suspect that gender is a confounding variable (its effects cannot be separated from the effects of the drug). To control for the effects of gender on the performance test, we utilize what is known as a block design. A block design involves doing a completely randomized experiment within each block. In this case, that means that each level of the drug would be tested within the group of females and within the 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 diagramed 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 so that there would be no additional comparison between the blocks—that's a different study.

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