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# Experiments and Observational Studies for AP Statistics

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Practice problems for these concepts can be found at:

### Completely Randomized Design

A completely randomized design for a study involves three essential elements: random allocation of subjects to treatment and control groups; administration of different treatments to each randomized group (in this sense we are calling a control group a "treatment"); and some sort of comparison of the outcomes from the various groups. A standard diagram of this situation is the following:

There may be several different treatment groups (different levels of a new drug, for example) in which case the diagram could be modified. The control group can either be an older treatment (like a medication currently on the market) or a placebo, a dummy treatment. A diagram for an experiment with more than two treatment groups might look something like this:

Remember that each group must have enough subjects so that the replication condition is met. The purpose of the placebo is to separate genuine treatment effects from possible subject responses due to simply being part of an experiment. Placebos are not necessary if a new treatment is being compared to a treatment whose effects have been previously experimentally established. In that case, the old treatment can serve as the control. A new cream to reduce acne (the treatment), for example, might be compared to an already-on-the-market cream (the control) whose effectiveness has long been established.

example: Three hundred graduate students in psychology (by the way, a huge percentage of subjects in published studies are psychology graduate students) volunteer to be subjects in an experiment whose purpose is to determine what dosage level of a new drug has the most positive effect on a performance test. There are three levels of the drug to be tested: 200 mg, 500 mg, and 750 mg. Design a completely randomized study to test the effectiveness of the various drug levels.
solution: There are three levels of the drug to be tested: 200 mg, 500 mg, and 750 mg. A placebo control can be included although, strictly speaking, it isn't necessary is our purpose is to compare the three dosage levels. We need to randomly allocate the 300 students to each of four groups of 75 each: one group will receive the 200 mg dosage; one will receive the 500 mg dosage; one will receive the 750 mg dosage; and one will receive a placebo (if included). No group will know which treatment its members are receiving (all the pills look the same), nor will the test personnel who come in contact with them know which subjects received which pill (see the definition of "double-blind" given below). Each group will complete the performance test and the results of the various groups will be compared. This design can be diagramed as follows:

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