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

Peter Dalgaard p.dalgaard at biostat.ku.dk
Thu Sep 23 22:03:43 CEST 2004

```meyerjp at 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)
>
> ______________________________________________
> R-devel at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>

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

```