Advanced Topics in Analysis of Variance - Analysis of Variance Designs - page 491

factor independent variables could be client dysfunction level (severe,
moderate, minor), word concreteness (high, medium, low), or population
of the area in which people reside (large city, small town, rural commu-
nity). Each of these examples depicts independent variables whose levels
could be easily replicated in a subsequent study.
17.2.2 RANDOM EFFECTS
Random effects or factors use levels of the independent variables that have
been randomly and unsystematically selected from the overall popula-
tion of all possible independent variable levels. For example, a researcher
defines an independent variable as the number of therapy sessions com-
pleted by clients. Assume that the clients in the population to be studied
had between 1 and 100 therapy sessions. Because of resource availability,
the researchers wish to study therapy progress on four different amounts
of therapy. Under a random effect model, the researchers would ran-
domly select those four different amounts of therapy (e.g., 10, 27, 44, and
82 sessions completed) and designate them as the levels of the indepen-
dent variable. Because the four sessions are randomly chosen, amount of
therapy sessions is defined as a random factor in the data analysis. In a
subsequent replication study, a different random selection might net the
following four levels: 6, 16, 55, and 60.
As another example, assume that individuals participating in a study
are recruited from a larger population of all students taking an introduc-
tory psychology course at a given university. But selection of those who
agree to participate is not under the control of the researcher. From the
researcher's perspective, those who participate in the study represent an
unpredictable (haphazard or perhaps quasirandom) subset of the popu-
lation. Only a certain subset actually volunteered, although anyone in the
population (at least theoretically) could have participated. By this reason-
ing, participants can be viewed as a random effect, and this is why SAS
Enterprise Guide elected to treat the subjects as a random effect in the
repeated measures analysis model.
17.2.3 MIXED EFFECTS
A mixed effects model contains at least one independent variable that rep-
resents a fixed effect and at least one independent variable that represents
a random effect. Note that although we require at least two independent
variables to qualify for a mixed effects model, there is no constraint on
(a) whether those variables must be between-subjects or within-subjects
variables, and (b) which represents the fixed effect and which represents
the random effect.
17.2.4 GENERALIZABILITY ISSUES
The main advantage of employing a random effects model over a fixed
effect model lies in the degree to which a researcher may generalize
the results of the study. With a fixed effects model, the researchers can