Re: Sample size for chi-square test
- From: Richard Ulrich <Rich.Ulrich@xxxxxxxxxxx>
- Date: Mon, 12 Dec 2005 18:48:59 -0500
On Mon, 12 Dec 2005 15:57:03 +0100, "ecciù" <non_me_la@xxxxxxxx>
wrote:
> Hello.
>
> I need your help for calculate the sample size in order to
> perform a chi-square test (goodness-of-fit).
>
> Specifically, i'm trying to test if my observations follow
> a gamma distribution.
>
> Question: is there a formula for calculate the sample size?
>
Chi-squared GOF tests are not necessarily a good choice,
but I don't know anything about testing for gamma.
The sample size will undoubtedly depend on the alternative
hypothesis: what the shape of the other distribution is
(in addition to "how you are testing it").
Then your GOF test is going to have a certain amount of
power, for a certain N, against that particular alternative.
Changing the bins or changing the shape that you want
to detect will change the power.
If you "dummy-up" your alternative data, you can get
a test for that configuration -- using that shape of the data,
the configuration of bins you are counting, and N; then
compute that GOF test. Presumably, you can compute the
"non-centrality parameter" by dividing the test by N.
(This would be a term "w-squared" rather than "w", until
you take the square root.)
Since chi-squared tables with non-centrality are generally
available in the context of computing power, that's probably
what you need. Enter the table with the give d.f., p-value,
desired power, and noncentrality, in order to obtain the
sample size you need.
For checking your results: Increase the dummied-up N
(by multiplying cells by the same constant) so that the test
is just-barely significant: That gives a baseline table where
the power is approximately 50%.
If this doesn't help, you might need to read more about
statistical power analysis. Jacob Cohen's book includes
some discussions, along with numerous tables.
--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.
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