On Mar 6, 2013, at 03:56 , Rolf Turner wrote:
>
>
> Your subject line is patent nonsense. The aov() and anova() functions
> have been around for decades. If they were doing something wrong
> it would have been noticed long since.
>
> You should realize that the fault is in your understanding, not in these
> functions.
>
> I cannot really follow your convoluted and messy code, but it would
> appear that you want to consider "M" and "I" to be random effects.
Only M and M:I, AFAICT. And, yes, it is messy; in particular, I refuse to
believe that y~M*I has generated output with lowercase m and i!
>
> Where have you informed aov() as to the presence of these
> random effects?
To be specific, try y~I + Error(M + M:I). Without the random effects, aov() is
just telling you that there is a highly significant interaction between M and
I, and beyond that, no sensible comparisons can be made.
>
> cheers,
>
> Rolf Turner
>
> On 03/06/2013 03:36 PM, PatGauthier wrote:
>> 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,
>
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--
Peter Dalgaard, Professor
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd....@cbs.dk Priv: pda...@gmail.com
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