Bug in power.anova.test?
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