Anecdotal evidence suggests that some individuals can tolerate alcohol better th

Question

Anecdotal evidence suggests that some individuals can tolerate alcohol better than others. As part of a traffic safety study, you arc planning an experiment to test for the presence of individual to individual variation. Volunteers will be recruited who have given their informed consent for participation after having been informed of the risks of the study. Each individual will participate in two sessions one week apart. In each session, the individual will arrive not having eaten for at least 4 hours. They will take a hand-eye coordination test, drink 12 ounces of beer, wait 15 minutes, and then take a second hand-eye coordination test. The score for a session is the change in hand-eye coordination. There are two sessions, so n = 2. We believe that the individual to individual variation sigma alpha 2 will be about the same size as the error a2. If we are testing at the 1% level, how many individuals should be tested to have power .9 for this setup? Do this problem twice. The first time, do it exactly as written in the textbook. Each individual participates in two sessions, so n = 2, and you need to find how many individuals are needed so power will be 0.9. The second time, suppose that each individual participates in three sessions, so n = 3. Now find the required number of individuals for power to be 0.9.

Explanation / Answer

Answer to the question)

The following calculation applies to n = 2

For power = 0.90 , we got Z = 1.282

Z for alpha = 0.01 is 2.575

Since it states that individual to individual variance is same as variance , we get Effect size ES = 1

Thus n = ( Zfor alpha + Zfor beta) ^2 / ES^2

n = [(1.282 + 2.575) / 1]^2

n = 14.8764

Thus the number of individuals need would be 15

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