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generalize the results of the study only to the specific levels of the inde-
pendent variables used in the study. For most situations in the social and
behavioral sciences, this constraint on generalizability is not a major detri-
ment to using fixed factor designs. This is true because many independent
variables exhaust the possible pool of alternative levels, and investigators
typically choose levels that they deem to be representative of the indepen-
dent variable (Keppel, 1973, 1991).
With a random effects model a researcher can generalize the results to
many more, perhaps even all possible, levels of the independent variable.
The rationale upon which this rests is analogous to why we prefer to ran-
domly sample participants in a research study. Recall that SAS Enterprise
Guide treats subjects in a repeated measures or mixed design as a random
effect, and for very good reason. When we are able to obtain a random
sample it means, all else equal, that every member of the population had
the same chances of participating. Under such a circumstance, any one
subset from this population is presumed to react to the treatment in a
manner similar to any other subset. This, in turn, allows us to general-
ize our findings based on the obtained sample to other members of the
population.
The same reasoning can be applied to other independent variables that
are treated, or can be conceived, as representing a random effect. If the
levels of a variable have been randomly selected from a set or population of
levels, then we should be able to generalize our findings to other members
of that population. Thompson (2006, pp. 345-346) expresses the idea as
follows:
Logically, if the random sampling of participants generates data that support
generalization to a larger field of participants, why could we not randomly
samplelevels...fromawiderpopulationofpotentiallevels,andtherebyachieve
generalization beyond the levels . . . actually used in the study? . . . A random
effect presumes a representative sample of levels from the more numerous
potential levels on the way, along with interest in generalizing from the sampled
levels to the population of all possible levels.
Keppel (1991, p. 486) makes the case as follows:
Generalizations based on fixed effects are restricted to the specific levels or con-
ditions actually included in the experiment. On the other hand, generalizations
based on random effects may be extended beyond those levels included in the
experiment to the population or pool of levels from which they were randomly
selected.
We should note that the generalizability of the results to all possible
levels of the independent variable should not be carried out in a blind and
uninformed manner (not that Thompson and Keppel have suggested this),
but our inferences must be tempered by both common sense and critical
thinking. Random sampling is a theoretical ideal but falls short when
applied in the empirical world. We can approximate random sampling
with very long series (10,000 rolls of an unbiased die should result in
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