Nested Designs - Scholar

differs from the mean transpiration rate i of hybrid i. But we are not interested in the 15
effects (2) of these 15 randomly selected pots specifically, because they are 15 of a huge
population of pots that we could have used and in which we are equally interested Indeed,
we are not interest in any of the pots specifically. And the same is true for the random
plants within the pots, and random leaves within the plants and pots. Rather we are
interested in the distribution of the random effects and random means, because the
distribution describes the entire populations, and the distributions of the random effects
affect transpiration rates.
The random effects of each random factor are assumed to have
o (central location) mean = 0, thus,
E B E C E e
0
j i k i, j l i, j, k
o (dispersion) variance homogeneous over levels, thus
ji
ki , j
li , j, k
2
Var B for all ,
B i j
2
Var C for all , ,
o (shape) normal distribution, thus
C i j k
2
Var e for all , , ,
e i j k l
Bji
2
Normal 0, B
ki , j
2
Normal 0, C
, ,
2
Normal 0, e
C
e
l i j k
This implies that the responses Y ijkl have the following distribution
o (central location)
EY
ijkl i
nested01.docx 6 4/5/2012