Question

You are considering testing a new drug that is supposed to facilitate learning in mentally retarded children. Based on preliminary research, you have some idea about the size of the drug's effect. Because of your work schedule you can either do the test with 15 subjects or with 20. You would like to only run 15 subjects, but if running 20 will make power at least 20% higher, you will run 20 subjects. Calculate power for the following conditions: a. N = 15, a = .051 tail, Preal = 0.70. b. N = 20, a = .051 tail, Preal = 0.70. c. Based on your calculations, how many subjects will you test?

Answer 1

A new drug that is supposed to facilitate learning in mentally retarded children. Based on preliminary research, you have some idea about the size of the drug's effect. Because of your work schedule you can either do the test with 15 subjects or with 20. You would like to only run 15 subjects, but if running 20 will make power at least 20% higher, you will run 20 subjects. Calculate power for the following conditions: a. N = 15, a = .051 tail, Preal = 0.70. b. N = 20, a = .051 tail, Preal = 0.70. c.

Given that we are considering testing a new drug that is supposed to facilitate learning in mentally retarded children. Because there is relatively little known about the drug, we plan to use a non-directional alternative hypothesis. Since resources are limited, we can test only 15 subjects. The subjects will be run in a repeated measures design and the data analyzed with the sign test using .

Given that the drug has a medium effect on learning such that . We have to find the probability that we will detect it when doing the experiment.

Calculating Power. There are two steps in the calculation of power.

Step 1: Assume the null hypothesis is true and determine the possible sample outcomes that will allow to be rejected.

From the Binomial distribution table with and we get

Beginning at the extreme and moving towards the middle of the distribution, we find that we can reject if we obtain 3 or 12 pluses in the sample. Therefore, the outcomes that will allow rejection of are 0, 1, 2, 3, 12, 13, 14 or 15 pluses.

Step 2: For , determine the probability of getting any of the above said sample outcomes. This probability is the power of the experiment to detect this hypothesized real effect.

From the Binomial distribution table with and we get

if independent variable has a real effect

The probability of type II error,