[R] aov() and anova() making faulty F-tests

[PatGauthier]

Dear useRs, 

I've just encountered a serious problem involving the F-test being carried
out in aov() and anova(). In the provided example, aov() is not making the
correct F-test for an hypothesis involving the expected mean square (EMS) of
a factor divided by the EMS of another factor (i.e., instead of the error
EMS). 

Here is the example:


                  Expected Mean Square            df
Mi                     σ2+18σ2M                              1
Ij                  σ2+6σ2MI+12Ф(I)                      2
MIij                   σ2+6σ2MI                              2
ε(ijk)l                        σ2                                   30

The clear test for Ij is EMS(I) / EMS(MI) -  F(2,2)

However, observe the following example carried out in R, 

M <- rep(c("M1", "M2"), each = 18)
I <- as.ordered(rep(rep(c(5,10,15), each = 6), 2))
y <-
c(44,39,48,40,43,41,27,20,25,21,28,22,35,30,29,34,31,38,12,7,6,11,7,12,15,10,12,17,11,13,22,15,27,22,21,19)
dat <- data.frame(M, I, y)
summary(aov(y~M*I, data = dat))
                       Df    Sum Sq       Mean Sq         F value       
Pr(>F)    
m                     1     3136.0           3136.0            295.85      <
2e-16 ***
i                        2      513.7              256.9              24.23     
5.45e-07 ***
m:i                   2      969.5              484.7              45.73     
7.77e-10 ***
Residuals   30       318.0                10.6                     
---

In this example aov has taken the F-ratio of MS(I) / MS(ε) -  F(2,30) =
24.23 with F-crit = qf(0.95,2,3) = 9.55 -- significant

However, as stated above,  the correct F-ratio is MS(I) / MS(MI) -  F(2,2) =
0.53 with F-crit = qf(0.95,2,2) = 19 -- non-significant

Why is aov() miscalculating the F-ratio, and is there a way to fix this
without prior knowledge of the appropriate test (e.g., EMS(I)/EMS(MI)?

Thanks for your help, 

Patrick





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