# Re: st: Sample size calculation

 From Ronán Conroy To Subject Re: st: Sample size calculation Date Thu, 27 Oct 2005 12:17:27 +0100

On 26 DFómh 2005, at 20:34, <slaowattana@pol.net> <slaowattana@pol.net> wrote:

Thanks. We plan to do the experiment in humans and they will be treated
with Rebif. The expected size of difference is 2 SD (to be clinically
significant) but my understanding is that to be able to calculate the
sample size (alpha = 0.05, beta = 0.20), we have to know estimated mean
and SD? Is this not true?
No, no. Sample size calculations are done on the difference between the two groups expressed in standard deviations. The actual size of the SD is irrelevant.

. sampsi 0 2, sd(1)

Estimated sample size for two-sample comparison of means

Test Ho: m1 = m2, where m1 is the mean in population 1
and m2 is the mean in population 2
Assumptions:

alpha = 0.0500 (two-sided)
power = 0.9000
m1 = 0
m2 = 2
sd1 = 1
sd2 = 1
n2/n1 = 1.00

Estimated required sample sizes:

n1 = 6
n2 = 6

. sampsi 0 20, sd(10)

Estimated sample size for two-sample comparison of means

Test Ho: m1 = m2, where m1 is the mean in population 1
and m2 is the mean in population 2
Assumptions:

alpha = 0.0500 (two-sided)
power = 0.9000
m1 = 0
m2 = 20
sd1 = 10
sd2 = 10
n2/n1 = 1.00

Estimated required sample sizes:

n1 = 6
n2 = 6

Two standard deviations is a lot. With a two standard deviation difference between your means,

. mwstati 2 1 1 , i
Mann-Whitney statistic for this situation is: 0.9214

The Mann-Whitney statistic is 0.92. In other words, there is a 92% chance that a person with MS taken at random will have a higher cytokyne measurement than a control taken at random. You might consider a Mann Whitney statistic of 0.75 to be more realistic as indicating a clinically important difference. This occurs with a difference of 1 standard deviation.

Ronán Conroy
rconroy@rcsi.ie

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