Re: [Rd] noncentrality paramter in power.anova.test (PR#7244)

From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>
Date: Fri 24 Sep 2004 - 06:03:43 EST

meyerjp@jmu.edu writes:

> Full_Name:
> Version: 1.9.0
> OS: Windows XP
> Submission from: (NULL) (134.126.93.191)
>
>
> I believe the noncentrality parameter, lambda, in power.anova.test is incorrect.
> The noncentrality paramter is defined as lambda <- (groups - 1) * n *
> (between.var/within.var). The n should not be there. The function pf defines the
> noncentrality parameter as the sum of squares of the means. Therefore, the
> noncentrality paramter, lambda, in power.anova.test should be lambda <- (groups
> - 1) * (between.var/within.var). The following code shows the difference in
> results. I've compared a few power computations using the new lambda to values
> from a text on power. The new lambda produces more correct values for power.

Correct by which measure? Surely not by consistency with power.t.test in the groups==2 case!

I think you're forgetting that there is a scale factor of n needed to make the variance of the sample means comparable to the sample variance. The means referred to in the definition of ncp for pf are only indirectly related to the actual group means.  

> groups <- 3
> n <- 5
> between.var <- 10.295
> within.var <- 1
> sig.level <- 0.05
>
>
> #The first, incorrect lambda is used in power.anova.test
> #incorrect labmda
> lambda <- (groups - 1) * n * (between.var/within.var)
> pf(qf(sig.level, groups - 1, (n - 1) * groups, lower = FALSE),
> groups - 1, (n - 1) * groups, lambda, lower = FALSE)
>
> #This correct lambda should be used instead
> lambda <- (groups - 1) * (between.var/within.var)
> pf(qf(sig.level, groups - 1, (n - 1) * groups, lower = FALSE),
> groups - 1, (n - 1) * groups, lambda, lower = FALSE)
>
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>

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907

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Received on Fri Sep 24 06:14:27 2004

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