Estimates of the standard deviation of a Single Measurement
http://www.tufts.edu/~gdallal/sizenotes.htm
Estimating the within group standard deviation, ,
When the Response Is a Difference
When the response being studied is change or a difference, the sample size formulas require the
standard deviation of the difference between measurements, not the standard deviation of the
individual measurements.
It is one thing to estimate the standard deviation of total cholesterol when many individuals are
measure once;
it is quite another
to estimate the standard deviation of the change in cholesterol levels when changes are measured.
One trick that might help: Often a good estimate of the standard deviation of the differences is
unavailable, but we have reasonable estimates of the standard deviation of a single measurement.
The standard deviations of the individual measurements will often be roughly equal. Call that
standard deviation . Then, the standard deviation of the paired differences is equal to
 (2[1-]),
where  is the correlation coefficient when the two measurements are plotted against each other.
If the correlation coefficient is a not terribly strong 0.50, the standard deviation of the
differences will be equal to  and gets smaller as the correlation increases.