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problem about finding power in test about variances

3 messages · ati sundar, Uwe Ligges

ati sundar
# 
Hello All

I am new to this list. I have a problem where for a single sample drawn from normal population, null hypothesis is that variance = k (say). Alternative hypothesis is variance > k. Now if we know the true variance, then I would like to calculate the sample size required to produce certain power (for some
significance). How do I do this ? I thought of using pwr.chisq.test, and I contacted the author stephane champely, but he said his package can't do this. Does anybody have an idea ?

Thanks
Ati
Uwe Ligges
#
ati sundar wrote:
Perhaps you want to tell us more precisely what you are going to do 
rather than asking the same inprecise question again and again 
(including messages to single persons on the list).
Is k fixed or the variance? What are your data?  Specify a valid Null / 
Alternative combination. If you Null is variance = k (say) then you 
alternative is variance != k or if the alternative is variance > k, then 
your null is probably variance <= k

Uwe Ligges



  Alternative hypothesis is variance > k. Now if we know the true 
variance, then I would like to calculate the sample size required to 
produce certain power (for some
ati sundar
# 
Ok sorry Uwe.

Let me put a specific problem. I have some data for which sample size
n=15 and sample standard deviation s=0.008 mm. Now there are two parts of
the question. Here the random variable is diameter of rivet hole.
a) Is there a strong evidence to indicate that the standard deviation
of hole diameter exceeds 0.01 mm. Use aplha=0.05 .
 Now here Ho: variance = (0.01)^2 = 0.0001 mm
          H1: variance > 0.0001 mm
we can use test statistic  chisq = (n-1)*s^2 / 0.0001

Chisq has degree of freedom n-1=14. So using this test  statistic
we can check the null hypothesis. I can do this part. Now lets
look at the next part.

b)If true variance (sigma) is as large as 0.0125 mm, what sample size will
be required to detect this with power of at least 0.8 

Now this is the part where I am stuck and I want to use R to solve this
I know that R has power tests for other test statistics, but how do I solve this ?

Ati
--- On Thu, 4/30/09, Uwe Ligges <ligges at statistik.tu-dortmund.de> wrote: