Precision
- Overview
The discussion
to this point has focused on power analysis, which is the logical precursor
to a test of significance. If the researcher designing a study to test
the null hypothesis, then the study design should ensure, to a high degree
of certainty, that the study will be able to provide an adequate (i.e.
powerful) testing of the null hypothesis.
The study
may be designed with another goal as well. In addition to (or instead
of) testing the null hypothesis the researcher might use the study to
estimate the magnitude of the effect - to report, for example that the
treatment increases the cure rate by 10 points, or by 20 points, or by
30 points. In this case, study planning would focus not on the study's
ability to reject the null hypothesis but rather on the precision with
which it will allow us to estimate the magnitude of the effect.
Assume, for
example, that we are planning to compare the response rates for treatments,
and anticipate that these rates will differ from each other by 20 percentage
points. We would like to be able to report the rate difference with a
precision of plus/minus 10 points.
The precision
with which we will be able to report the rate difference is a function
of the confidence level required, the sample size, and the variance of
the outcome index. Except in the indirect manner discussed below, it is
not affected by the effect size.
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