Unequal n example from Neter Wasserman & Kutner, p.763, 768

MTB > name c1 'sex' c2 'devpt' c3 'observat' c4 'growth'
MTB > read c1-c4
DATA> 1 1 1 1.4
DATA> 1 1 2 2.4
DATA> 1 1 3 2.2
DATA> 2 1 1 2.4
DATA> 1 2 1 2.1
DATA> 1 2 2 1.7
DATA> 2 2 1 2.5
DATA> 2 2 2 1.8
DATA> 2 2 3 2.0
DATA> 1 3 1 0.7
DATA> 1 3 2 1.1
DATA> 2 3 1 0.5
DATA> 2 3 2 0.9
DATA> 2 3 3 1.3
DATA> end
     14 ROWS READ

******RUN GLM Solution for Unbalanced Design  MTver7 manual 8-27
MTB > glm growth = sex | devpt

Factor   Levels Values
sex           2     1     2
devpt         3     1     2     3

Analysis of Variance for growth  

Source      DF     Seq SS     Adj SS     Adj MS       F
sex          1     0.0029     0.1200     0.1200    0.74
devpt        2     4.3960     4.1897     2.0949   12.89
sex*devpt    2     0.0754     0.0754     0.0377    0.23
Error        8     1.3000     1.3000     0.1625
Total       13     5.7743  

Unusual Observations for growth  

Obs.   growth       Fit Stdev.Fit  Residual   St.Resid
  4   2.40000   2.40000   0.40311   0.00000         * X

X denotes an obs. whose X value gives it large influence.

*********************************************
 note: these agree with NWK pg. 753   Table 20.4 Adj SS, MS, test statistics
********************************************
MTB > glm growth = devpt | sex

Factor   Levels Values
devpt         3     1     2     3
sex           2     1     2

Analysis of Variance for growth  

Source      DF     Seq SS     Adj SS     Adj MS       F
devpt        2     4.3063     4.1897     2.0949   12.89
sex          1     0.0926     0.1200     0.1200    0.74
devpt*sex    2     0.0754     0.0754     0.0377    0.23
Error        8     1.3000     1.3000     0.1625
Total       13     5.7743  

Unusual Observations for growth  

Obs.   growth       Fit Stdev.Fit  Residual   St.Resid
  4   2.40000   2.40000   0.40311   0.00000         * X

X denotes an obs. whose X value gives it large influence.
-------------------------------------------------------------------------
NOW CONSIDER APPROXIMATE SOLUTION FROM MILLER-- 2-way on cell means

  2.0  1  1
  1.9  1  2
  0.9  1  3
  2.4  2  1
  2.1  2  2
  0.9  2  3

TWOWAY on CELL MEANS for APPROX Procedure
 
MTB > twoway c1, c2 c3
 
 ANALYSIS OF VARIANCE  C1      
 
 SOURCE        DF        SS        MS
 C2             1    0.0600    0.0600
 C3             2    1.9600    0.9800
 ERROR          2    0.0400    0.0200
 TOTAL          5    2.0600
 
 MTB > note ERROR is really interaction

Here are the points of difference between Miller's approximate solutions
and the glm exact one.

GLM shows very clearly (by looking at the sequential sums of squares) that
the order of entering the factor makes a difference. Thus for comparison
we look at the adjusted sums of squares in the glm runs:

      MILLER                         GLM
SS            MS       Source      SS(Adj)     MS(Adj)
0.12          0.12     Gender       0.1200      0.1200
3.92          1.96     Development  4.1897      2.0949
0.08          0.04     Interaction  0.0754      0.0377

The differences are small, and the F-tests yield the same conclusions.