Now Playing: Multiple Comparisons of Treatments vs. a Control (3:29)
An integrated health system would like to compare 3 new methods to the current method of treatment for a specific subset of high-risk pregnancies. One of the primary responses of interest is the infant birth weight.
The average birth weight under the current treatment is 4.7 pounds. The average birth weights under the 3 new treatments will be assumed to be 4.9, 5.1, and 5.2 pounds.
The researchers would like to examine the power that is achieved for group sample sizes ranging from 50 to 1,000.
Two types of power will be considered. All-pairs power describes the probability that all 3 treatment differences will be detected. Any-pairs power describes the probability of detecting at least one of the 3 new methods as being different from the current method.
The assumed standard deviation within all groups is 1.2 pounds.
As Normality will be assumed, the Dunnett Test will be used rather than the nonparametric alternative.
In the output, the any-pairs power and the all-pairs power is given for each sample size.
The power curve for the all-pairs power shows the gradual increase in the ability to detect all 3 differences, for larger and larger sample sizes.
The any-pair power curve shows that the power to detect at least one difference is already over 90% when group sample sizes reach 150 per group.
The comparative plots at the end show the power that would be lost if the nonparametric test were used instead.
When distributions other than the Normal distribution are assumed, the power for the nonparametric test is often higher than the Dunnett test power. We have found the Tukey [Too-Key] G-H distribution to be a very useful distribution for simulations, in that it transforms a Normal distribution to a desired skewness and elongation. Many other distributions are also available.