- On 15 Aug 2000 at 10:06:26, ml11439.-a-.goodnet.com sent the message

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Brian,

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):

phi= (delta/sigma)SQRT(n/2k)

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

treatment groups.

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.

Good Luck!!

Mike Leibold, PharmD, RPh

ML11439.aaa.goodnet.com

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