6.2 TWO FACTOR REPEATED MEASURES MODEL Y = S'|B|A

Analysis of terms: S|B|A - S*B*A

Data:

S	A	B	Y
1	1	1	 4.5924
2	1	1	-0.5488
3	1	1	 6.1605
4	1	1	 2.3374
1	1	2	 5.1873
2	1	2	 3.3579
3	1	2	 6.3092
4	1	2	 3.2831
1	2	1	 7.3809
2	2	1	 9.2085
3	2	1	13.1147
4	2	1	15.2654
1	2	2	12.4188
2	2	2	14.3951
3	2	2	 8.5986
4	2	2	 3.4945
1	3	1	21.3220
2	3	1	25.0426
3	3	1	22.6600
4	3	1	24.1283
1	3	2	16.5927
2	3	2	10.2129
3	3	2	 9.8934
4	3	2	10.0203


Model 6.2(i) A and B are fixed factors, S is a random subject:

                                 Restricted Unrestricted
  Source   DF       SS      MS      F      P      F      P
1 S         3     9.07    3.02      -      -   0.19  0.893*
2 A         2   745.36  372.68  67.58 <0.001  67.58 <0.001
3 B         1    91.65   91.65   4.13  0.135   4.13  0.135
4 B*A       2   186.37   93.18   7.82  0.021   7.82  0.021
5 S*A       6    33.09    5.51      -      -      -      -
6 S*B       3    66.51   22.17      -      -      -      -
7 S*B*A     6    71.51   11.92      -      -      -      -
8 P(S*B*A)  0        -       - 
  Total    23  1203.56

* Quasi F-ratio.


Model 6.2(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 S         3     9.07    3.02  0.14  0.932  0.19  0.893*
2 A         2   745.36  372.68  4.29  0.214* 4.29  0.214*
3 B         1    91.65   91.65  4.13  0.135  4.13  0.135*
4 B*A       2   186.37   93.18  7.82  0.021  7.82  0.021
5 S*A       6    33.09    5.51  0.46  0.815  0.46  0.815
6 S*B       3    66.51   22.17     -      -     -      -
7 S*B*A     6    71.51   11.92     -      -     -      -
8 P(S*B*A)  0        -       -
  Total    23  1203.56

* Quasi F-ratio.


Model 6.2(iii) A and B are random factors, S is a random subject:

  Source   DF       SS      MS     F      P
1 S         3     9.07    3.02  0.19  0.893*
2 A         2   745.36  372.68  4.29  0.214*
3 B         1    91.65   91.65  0.89  0.433*
4 B*A       2   186.37   93.18  7.82  0.021
5 S*A       6    33.09    5.51  0.46  0.815
6 S*B       3    66.51   22.17  1.86  0.237
7 S*B*A     6    71.51   11.92     -      -
8 P(S*B*A)  0        -       -
  Total    23  1203.56
 
* 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/