Nested Designs - Scholar

other hand, have fixed effects. The investigator is interested in the effects of these five specific
hybrids. They are not randomly selected representatives of a larger population of hybrids. Thus,
their effects are fixed rather than random.
Ott and Longnecker (2001, Section 17.1) have these definitions:
In a fixed-effects model for an experiment, all the factors in the experiment have
a predetermined set of levels and the only inferences are for the levels of the
factors actually used in the experiment.
In a random effects model for an experiment, the levels of factors used in the
experiment are randomly selected from a population of possible levels. The
inferences from the data in the experiment are for all levels of the factors in the
population from which the levels were selected and not only the levels used in the
experiment.
In a mixed effects model for an experiment, the levels of some of the factors used
in the experiment are randomly selected from a population of possible levels,
whereas the levels of the other factors in the experiment are predetermined. The
inferences from the data in the experiment concerning the factors with fixed levels
are only for the levels if the factors used in the experiment, whereas inferences
concerning factors with randomly selected levels are for all levels of the factors in
the population from which the levels were selected.
D e , or by
Notation. It would make sense to denote the random effect of leaf l by ijkl
D , B, C eijkl
, or even by e eijklbecause
it is a nested effect just like B and C. But the
ijkl
l ijk
fact is that all of the error terms in Anova are always random effects, and, being replicates, are
necessarily nested within other effects.
It is traditional to represent fixed effects by Greek letters and random effects by English letters.
nested01.docx 4 4/5/2012
l ijk