# Re: st: Sample size for ttest - (am I wrong?)

 From Ronan Conroy To "statalist hsphsun2.harvard.edu" Subject Re: st: Sample size for ttest - (am I wrong?) Date Wed, 19 Feb 2003 11:39:31 +0000

```on 18/02/2003 9:44 pm, Ricardo Ovaldia at ovaldia@yahoo.com wrote:

> Thank you David and Ronan. I'm confused by the
> apparent contradictions in the two posts. I understood
> how Ronan calculated the power but its this valid? Or
> is the problem (as I originally suspected) that a
> "difference of 1.5 SD" doesn't mean anything without
> knowing something about the distribution of the two
> groups? Am I missing something?

I don't think there's a contradiction. What we are saying is that the maths
is all right, but as we all know power calculation is the application of
precise statistical procedures to wild assumptions.

The first thing to note is that we don't even know how how the researcher is
measuring Cox2. In several of the papers I have been involved in, Cox2 has
been measured on an ordinal scale, with expression rated in four categories
from none to intense. If this is the case, then talking about means and
standard deviations is nonsense.

Cox2 can also be measured as a percentage expression. This may be what your
researcher is doing. However, even if this is the case, there is the issue
of what constitutes a clinically significant difference between groups.

Let's look at the issue of 1.5 standard deviations. In the case of Cox2,
with an average expression of 50%, the standard deviation is about 30%. So a
difference of 1.5 standard deviations between groups corresponds to a 45%
difference in mean expression! Clearly, differences a lot smaller than this
are clinically interesting. We did some work on Cox2 and polyp type and the
results were considered clinically interesting enough to get a major journal
publication though the actual size of the mean difference in Cox2 expression
was less than 10%! A difference of about 10% would be clinically
interesting, which corresponds to a third of a standard deviation.

. sampsi 50 60, sd(30)

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 =       50
m2 =       60
sd1 =       30
sd2 =       30
n2/n1 =     1.00

Estimated required sample sizes:

n1 =      190
n2 =      190

Ooof! 90% power applied to what we know about the real life distribution of
Cox2 produces a horrifying picture: two groups of 190!

Your colleague's parroting of (literally) correct power calculations just
underlines the concerns that David voiced more articulately than I, and
which I repeat:

power calculation is the application of precise statistical procedures to
wild assumptions

When the researcher is not even aware of what these assumptions are, then
the ethics committee should send them away to reconsider. But you may draw
comfort from the fact that your hunch was very right. Cox2 is going to need
sample sizes waaaaay bigger than 8!

Ronan M Conroy (rconroy@rcsi.ie)
Lecturer in Biostatistics
Royal College of Surgeons
Dublin 2, Ireland
+353 1 402 2431 (fax 2764)

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