Power Analysis for the Matched Pairs Design
Recent events suggest that Army generals are likely to engage in behaviors that are
associated with high levels of testosterone. Can you imagine that? We proposed research to test the
hypothesis that elevated testosterone makes males more likely to engage in extra-pair copulations.
After our proposal to use military officers as the subjects in our research was rejected by the DOD,
we obtained a grant from a pharmaceutical firm to test the effect of their testosterone patches. Our
university IRB declined to approve our proposal to use male college students as the subjects, which
is just as well, as it would be better to employ subjects from species know to be (relatively)
monogamous. The corresponding committee for animal research did approve our alternative
procedure.
Our proposed procedure called for the identification, in the field, of twenty pairs of male
animals (one pair for each of twenty species considered to be monogamous). Within each pair, one
male was randomly assigned to the treatment group and one to the control group. Testosterone
patches were applied to the treatment group and placebo patches to the control group, and their
behavior was monitored by video for thirty consecutive days during their breeding season. The
dependent variable was number of extra-pair copulations during the test period.
If the effect of testosterone were medium in size (the treatment population has a mean onehalf of a standard deviation greater than that of the control population) and if the correlation due to
matching by species were 0.8, what is the probability that we would obtain significant results, using
the traditional .05 criterion of statistical significance?
d Diff 
1  2
d
1/ 2


 .791
 Diff
2(1  12 )
2(1  .8)
  dDiff n  .791 20  3.54
From the table in Howell,
if  = 3.50, then power = .94.
if  = 3.60, then power = .95.
Power = .94 + .4(.01) = .944.
Karl L. Wuensch, November, 2012