[R] Bug in power.anova.test?

[Prof Brian Ripley]

Two groups with a difference in mean of 20.6 have a between-group variance 
of 212.18 (as Minitab was given), not 424.36.

> var(c(0, 20.6))
[1] 212.18

(and the example on the help page shows this *is* what is meant by the 
variance).

On Mon, 8 Nov 2004, Peter Levy wrote:

> I think there is a bug in power.anova.test.  Firstly, n, the number of
> samples needed in each group, decreases as the number of groups
> increases.  Should the reverse not be the case?

No.  Think about having four groups, 2 with one mean and 2 with the 
another mean.  This is effectively a 2-group problem with twice the sample 
size.

> Secondly:
> 
> >      power.anova.test(groups = 2, between.var=424.36, within.var=256,
> sig.level= 0.1, power=.90)
> 
> gives the answer n = 5.986304 where n is number of samples needed in
> each group.
> 
> Four other sources give the answer n=12 (11.08 rounded up):
> 
> 1. One-way ANOVA with 2 groups should be the same as a t-test. 
> Power.t.test gives.
> >  power.t.test(n=NULL, delta=20.6, sd=16.0, sig.level=0.1, power=0.9,
> type=c("two.sample"), alternative=c("two.sided"), strict=FALSE)
> 
> 2. p35, example 2 in Steidl, R.J. and Thomas, L.  (2001)  Power
> analysis and experimental design.  In: Design and Analysis of Ecological
> Experiments, (eds S. M. Scheiner and J. Gurevitch), pp. 415. Open
> University Press, New York.
> http://www.oup-usa.org/sc/0195131878/c2_ex2a.html
> 
> 3. Minitab gives
> Power and Sample Size 
> One-way ANOVA
> Alpha = 0.1  Assumed standard deviation = 16  Number of Levels = 2
>           Sample  Target                   Maximum
> SS Means    Size   Power  Actual Power  Difference
>   212.18      12     0.9      0.920676        20.6
> The sample size is for each level.
> 
> 4. Minitab gives
> Power and Sample Size 
> 2-Sample t Test
> Testing mean 1 = mean 2 (versus not =)
> Calculating power for mean 1 = mean 2 + difference
> Alpha = 0.1  Assumed standard deviation = 16
>             Sample  Target
> Difference    Size   Power  Actual Power
>       20.6      12     0.9      0.920676
> The sample size is for each group.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595