# Re: st: SP/RM[1,2] EMS

 From khigbee@stata.com To statalist@hsphsun2.harvard.edu Subject Re: st: SP/RM[1,2] EMS Date Fri, 22 Aug 2003 12:26:24 -0500

```David Airey <david.airey@vanderbilt.edu> wonders about what he thinks
is a difference between the example I show at

<http://www.stata.com/support/faqs/stat/anova2.html#anovat713>

and a similar problem he is working on.

The crux of the question is:

> Ken's command is:
>
> . anova score noise / subject|noise period noise*period /
>   period*subject|noise dial noise*dial / dial*subject|noise
>   period*dial noise*period*dial , repeated(period dial)
>
> My data are a little differently named but basically the same:
>
> between:
>      Ken has noise, I have "S"
> within:
>      Ken has dial, I have "I"
>      Ken has period, I have "P"
> random:
>      Ken has subject, I have "A"
>
> For EMSs I get:
>
> A|S   = piA + E
> S     = piA + apiS + E
> P     = asiP + iPA|S + E
> I     = aspI + pIA|S + E
> SP    = aiSP + iPA|S + E
> SI    = apSI + pIA|S + E
> PI    = asPI + E
> PA|S  = iPA|S + E
> IA|S  = pIA|S + E
> SPI   = PIA|S + E
> PIA|S = PIA|S + E
> E     = E
>
> So my F ratios to test are:
>
> MS(S) / MS(A|S)
> MS(P) / MS(PA|S)  <-- different --> Ken does MS(P) / MS(E)
> MS(I) / MS(IA|S)  <-- different --> Ken does MS(I) / MS(E)
> MS(SP) / MS(PA|S)
> MS(SI) / MS(IA|S)
> MS(PI) / MS(E)
> MS(SPI) / MS(E)
>
> My question is Ken tests each within subject factor over the error.
> What is different between testing over the error as Ken has done, vs
> testing over the terms I have determined above? It seems these terms
> are like the error as well.

David has misread the example in the FAQ.  He says that it uses
MS(E) for the test of P and I (his letters, or period and dial
the corresponding names for the example in the FAQ).

Look carefully at the -anova- command and at the output shown in
the FAQ.

term                 tested using
-----------------    --------------------
noise                subject|noise
period               period*subject|noise
noise*period         period*subject|noise
dial                 dial*subject|noise
noise*dial           dial*subject|noise
period*dial          residual
noise*period*dial    residual

If I am following the mapping from his names to the FAQ example
names correctly, it appears that we are in agreement.

By the way, what I present in the FAQ as Stata output of -anova-
agrees with what Winer, Brown, & Michels show in Table 7.16 where
they show the ANOVA table for the example dataset.

Ken Higbee    khigbee@stata.com
StataCorp     1-800-STATAPC

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```