|
    
|
 |
Power
Analysis - Controlling Power
Power is
the fourth element in this closed system - Given an effect size, and alpha,
and sample size, power is known. As noted above, a "convention"
exists that power should be set at 80% but this convention has no logical
basis. The appropriate level of power should be decided on a case-by-case
basis, taking into account the potential harm attendant on a Type I error,
the determination of a clinically important effect, the potential sample
size, as well as the importance of identifying an effect, should one exist.
Power analysis
- ethical issues
Some studies
involve putting patients at risk. At one extreme, the risk might involve
a loss of time spent completing a questionnaire. At the other extreme,
the risk might involve the use of an ineffective treatment for a potentially
fatal disease. These issues are clearly beyond the scope of this discussion,
but one point should be made here.
Ethical issues
play a role in power analysis. If a study to test a new drug will have
adequate power with a sample of 100 patients, then it would be inappropriate
to use a sample of 200 patients since the second 100 are being put at
risk unnecessarily. At the same time, if the study requires 200 patients
to yield adequate power, it would be inappropriate to use only 100. These
100 patients may consent to take part in the study on the assumption that
the study will yield useful results. If the study is under-powered, then
the 100 patients have been put at risk for no reason.
Of course,
the actual decision making process is complex. One can argue about whether
"adequate" power for the study is 80%, or 90%, or 99%. One can
argue about whether power should be set based on an improvement of 10
points, or 20 points, or 30 points. One can argue about the appropriate
balance between alpha and beta. The point being made here is that these
kinds of issues need to be addressed explicitly as part of the decision
making process.
The null
hypothesis vs. the nil hypothesis
Power analysis
focuses on the study's potential for rejecting the null hypothesis. In
most cases the null hypothesis is the null hypothesis of no effect (a.k.a.
the nil hypothesis). For example, the researcher is testing a null hypothesis
that the change score from time-1 to time-2 is zero. In some studies,
however, the researcher might attempt to disprove the null hypothesis
other than the nil. For example, "The intervention boosts the scores
by 20 points or more". The impact of this is to change the effect
size.
Previous | Next
|
