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

 From David Airey To statalist@hsphsun2.harvard.edu Subject st: SP/RM[1,2] EMS Date Thu, 21 Aug 2003 17:22:36 -0500

I followed Neter et al.'s method to determine the expected mean squares for a split plot repeated measures ANOVA with 1 between-subject factor and 2 within-subject factors. What I got was close to what Ken Higbee uses in his FAQ online:

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

Here is his data:

----------------------------------------------------------------------
noise |
background |
and subject | 10 minute time periods and dial
nested in | ------- 1 ------ ------- 2 ------ ------- 3 ------
noise | 1 2 3 1 2 3 1 2 3
------------+---------------------------------------------------------
1 |
1 | 45 53 60 40 52 57 28 37 46
2 | 35 41 50 30 37 47 25 32 41
3 | 60 65 75 58 54 70 40 47 50
------------+---------------------------------------------------------
2 |
1 | 50 48 61 25 34 51 16 23 35
2 | 42 45 55 30 37 43 22 27 37
3 | 56 60 77 40 39 57 31 29 46
----------------------------------------------------------------------

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.

Can Ken or someone else comment? Of course all this assumes I followed Neter correctly, which I may not have. I did try.

-Dave

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