[R] Bug in power.anova.test?

[Peter Levy]

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?
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.

 


 


Peter Levy
Centre for Ecology and Hydrology
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Midlothian, EH26 0QB, UK
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E-mail: plevy at ceh.ac.uk