2.1 TWO FACTOR NESTED MODEL Y = B(A) + e

Analysis of Cortisol response (Y) in terms of Food (A) and Pen (B): 
A + B(A)

Data:

A	B	Y
1	1	15.5
1	1	16.2
1	1	15.0
1	2	18.7
1	2	15.0
1	2	20.8
1	3	12.0
1	3	15.0
1	3	13.2
1	4	12.4
1	4	10.4
1	4	 9.5
2	1	16.1
2	1	 7.3
2	1	10.5
2	2	 7.5
2	2	 7.2
2	2	10.8
2	3	 5.2
2	3	 9.4
2	3	 5.5
2	4	 8.8
2	4	10.3
2	4	 9.9

Model 2.1(i) A is a fixed factor, B is a random factor:

  Source  DF       SS      MS     F      P
1 A        1   177.13  177.13  8.64  0.026
2 B(A)     6   122.99   20.50  3.78  0.016
3 Error   16    86.79    5.42
  Total   23   386.90

COMMENT: With this model, the coding of Pen B describes four pens 
nested in the even food treatment (level 1 of A) and four (different) 
pens nested in the patchy food treatment (level 2 of A).


__________________________________________________________________

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://www.southampton.ac.uk/~cpd/anovas/datasets/