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The rationale behind determining the sample size for a given
eperiment is statistical power. Statistical power is basically
the likelihood of determining a significant treatment effect
when one really exists. So that a sufficiently large sample
size (i.e. the number of patients in each group) will allow
enough statistical power so that there is a good likelihood
that a significant treatment effect will be detected (i.e. by
a t-test) if one exists, and this provides a good reason for
conducting the study.
Since your study design indicates that if the measured
parameter is normally distributed a t-test would be an appropriate
statistical test, a power chart for a t-test could be used
to determine the necessary sample size. If the size of the change
you expect to detect is about the same size as the standard
deviation of the parameter in the population, then the sample
size to obtain statistical power above 80% is around 20 patients
per group. However, if the expected change or treatment effect
is only about 50% of the standard deviation of the parameter in
the population, then the required sample size ot obtain 80%
statistical power would be about 50 per group.
The same reasoning applies to analysis of variance but a
noncentrality parameter is calculated to determine statistical power
rather than just phi=delta/sigma in the case of the t-test.
Noncentrality parameter (phi):
eg for delta/sigma= 1 and n=25, k= 3 treatment groups
phi= (1)SQRT(25/6)= (1)(2.04)= 2.04
Consulting a power chart for analysis of variance indicates that
a sample size of about 25 per treatment group would provide the
sufficient 80% statistical power given a delta/sigma of 1 and and k=3
At any rate, the idea would be to determine the magnitude of
change you are expecting to find, compare this to the standard
deviation of the parameter in the patient population, and then
consult a power chart to determine the necessary sample size to
achieve statistical power of 80%. The power chart you consult
depends on the statistical test you intend to perform.
One good reference for this would be Glantz's Primer of
Biostatistics from McGraw-Hill.
Mike Leibold, PharmD, RPh
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Copyright 1995-2010 David W. A. Bourne (email@example.com)