On Wed, 12 Aug 2015 10:49:09 -0700 (PDT),
vivianhyl@gmail.com wrote:
The null hypothesis is: Sigma of population A = 2* (Sigma of population B)
We know the sample size of A is 11 and the observed standard deviation (true sigma is unknown).
Alpha=95%, beta=90%, and we want to know how much data from population B we need to collect for this test.
Any software can help compute this sample size?
If you are going to talk about power analyses, you need
to check ALL your terminology.
A power statement specifies
a) a given test statistic for
b) a particular H1 (not H0)
c) at a specific alpha (test size: often 0.05, never 0.95)
d) will require what N
e) for a given power (1-beta, not beta).
You mis-stated H1, alpha and beta, and did not mention
what test.
For non-experts to successfully find power from tables,
from a computer or from a text, they need explicit examples
of THEIR own task. I once had G-Power (I think it was called),
produced in Germany (if that helps identify it), which came with
a 30 or 50 page manual. I still relied on Jacob Cohen's book on
power.
Cohen's program could be used along with the last edition
of his textbook (else, be wary, he changed parameterization
for one Effect-size between editions).
I don't remember your problem being detailed. You might
be able to use one of the procedures if you understand
well enough the manipulation of noncentrality, since power
computations use the noncentral chisquared. One problem
of trying to apply "non-centrality", if you try to apply on-line
calculators for the non-central F, is that different authors
use 3 different versions of lambda. [See Wikip on non-central
chi-squared.]
What non-experts can do is simulation. You might use the
SPSS t-test procedure, which includes a test on variances.
(That is NOT the t-test, but the "test on variances".)
Generate, say, 100 samples with N1=11, N2= 11 to start.
(Number the samples; use SPLIT FILES to get parallel output.)
Use normal deviates, with SD1=1 and SD2=2 (your H1).
Then, move N2 up or down to converge to the desired outcome.
What you are looking for is the N2 that produces the desired power
of 90% for the 5% test; that is, 80% of the results should REJECT
"equality of variances" at the 5% test. If there are more (or fewer)
than 90% rejections, then you can decrease (or increase) N2.
Plot your results across N2 values, to see the regular increase
in power with increasing N2: extrapolate to find the smallest
N2 that should suffice.
When you are close to the right N2 and you want a really
solid number, run 1000 (or more) samples. This will be tedious
unless you know how to collect results.
--
Rich Ulrich
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)