6.3 TWO FACTOR MODEL WITH REPEATED MEASURES ON ONE CROSS FACTOR Y = B|S'(A)

Analysis of terms: B|A + B|S(A) - B*S(A)

Data:

S	A	B	Y
1	1	1	-3.8558
2	1	1	 4.4076
3	1	1	-4.1752
4	1	1	 1.4913
1	1	2	 5.9699
2	1	2	 5.2141
3	1	2	 9.1467
4	1	2	 5.8209
1	2	1	 9.4082
2	2	1	 6.0296
3	2	1	15.3014
4	2	1	12.1900
1	2	2	 6.9754
2	2	2	14.3012
3	2	2	10.4266
4	2	2	 2.3707
1	3	1	19.1834
2	3	1	18.3855
3	3	1	23.3385
4	3	1	21.9134
1	3	2	16.4482
2	3	2	11.6765
3	3	2	17.9727
4	3	2	15.1760


Model 6.3(i) A and B are fixed factors, S is a random subject:

                                  Restricted  Unrestricted
  Source   DF       SS      MS      F      P      F      P
1 A         2   905.27  452.63  48.17 <0.001  48.17 <0.001
2 S(A)      9    84.56    9.40      -      -   0.61  0.766
3 B         1     0.19    0.19   0.01  0.915   0.01  0.915
4 B*A       2   167.65   83.82   5.41  0.029   5.41  0.029
5 B*S(A)    9   139.47   15.50      -      -      -      -
6 P(B*S(A)) 0        -       -
  Total    23  1297.13


Model 6.3(ii) A is a fixed factor, B is a random factor, S is a random subject:


                                 Restricted Unrestricted       
  Source   DF       SS      MS     F      P     F      P
1 A         2   905.27  452.63  5.82  0.173* 5.82  0.173* 
2 S(A)      9    84.56    9.40  0.61  0.766  0.61  0.766
3 B         1     0.19    0.19  0.01  0.915  0.00  0.967
4 B*A       2   167.65   83.82  5.41  0.029  5.41  0.029
5 B*S(A)    9   139.47   15.50     -      -     -      -
6 P(B*S(A)) 0        -       -
  Total    23  1297.13

* Quasi F-ratio.


Model 6.3(iii) A is a random factor, B is a fixed factor, S is a random subject:

                                  Restricted Unrestricted
  Source   DF       SS      MS      F      P     F      P
1 A         2   905.27  452.63  48.17  0.000  5.82  0.173*
2 S(A)      9    84.56    9.40      -      -  0.61  0.766
3 B         1     0.19    0.19   0.00  0.967  0.00  0.967
4 B*A       2   167.65   83.82   5.41  0.029  5.41  0.029
5 B*S(A)    9   139.47   15.50      -      -     -      -
6 P(B*S(A)) 0        -       -
  Total    23  1297.13

* Quasi F-ratio.


Model 6.3(iv) A and B are random factors, S is a random subject:

  Source   DF       SS      MS     F      P
1 A         2   905.27  452.63  5.82  0.173*
2 S(A)      9    84.56    9.40  0.61  0.766
3 B         1     0.19    0.19  0.00  0.967
4 B*A       2   167.65   83.82  5.41  0.029
5 B*S(A)    9   139.47   15.50     -      -
6 P(B*S(A)) 0        -       -
  Total    23  1297.13 

* Quasi F-ratio.


__________________________________________________________________

Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and
Covariance: How to Choose and Construct Models for the Life Sciences.
Cambridge: Cambridge University Press.
http://southampton.likn.co/~cpd/anovas/datasets/