st: SP/RM[1,2] EMS

[David Airey <david.airey@vanderbilt.edu>]

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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