7.2 THREE FACTOR CROSS FACTORED UNREPLICATED MODEL Y = C|B|A

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

Data:

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

Model 7.2(i) A, B and C are all fixed factors:

  Source   DF       SS      MS      F      P
1 A         2   745.36  372.68      -      -
2 B         1    91.65   91.65      -      -
3 B*A       2   186.37   93.18      -      -
4 C         3     9.07    3.02      -      -
5 C*A       6    33.09    5.51      -      -
6 C*B       3    66.51   22.17      -      -
7 C*B*A     6    71.51   11.92      -      -
8 S(C*B*A)  0        -       -
  Total    23  1203.56


Model 7.2(ii) A and C are fixed factors, B is a random factor:
 
                                   Restricted  Unrestricted
  Source   DF        SS      MS      F      P      F      P
1 A	    2    745.36  372.68   4.00  0.200   4.00  0.200
2 B	    1     91.65   91.65      -      -   0.89  0.433*
3 B*A	    2    186.37   93.18      -      -   7.82  0.021
4 C	    3      9.07    3.02   0.14  0.932   0.14  0.932
5 C*A	    6     33.09    5.51   0.46  0.815   0.46  0.815
6 C*B	    3     66.51   22.17      -      -   1.86  0.237
7 C*B*A	    6     71.51   11.92      -      -      -      -
8 S(C*B*A)  0         -       -				
  Total	   23   1203.56					

* Quasi F-ratio.


Model 7.2(iii) A is a fixed factor, B and C are random factors:

                                   Restricted  Unrestricted
  Source   DF        SS      MS      F      P      F      P
1 A	    2    745.36  372.68   4.29  0.214*  4.29  0.214*
2 B	    1     91.65   91.65   4.13  0.135   0.89  0.433*
3 B*A	    2    186.37   93.18   7.82  0.021   7.82  0.021
4 C	    3      9.07    3.02   0.14  0.932   0.19  0.893*
5 C*A	    6     33.09    5.51   0.46  0.815   0.46  0.815
6 C*B	    3     66.51   22.17      -      -   1.86  0.237
7 C*B*A	    6     71.51   11.92      -      -      -      -
8 S(C*B*A)  0         -       -				
  Total	   23   1203.56					

* Quasi F-ratio.


  Model 7.2(iv) A, B and C are all random factors:

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