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virtually the same number of 1s, 2s, 3s, 4s, 5s, and 6s), but the shorter
the run or the smaller the sample, the less we are able to truly sample
randomly from any population (6 rolls of an unbiased die are unlikely to
yield one of each possible value). In light of this, consider two scenarios,
which, although quite unlikely, could occur under random sampling:
We randomly sample 30 college students of the 600 students enrolled
in introductory psychology courses at a given university. When we
look at the sample, we note that we have only male students; that is,
females (representing at least half of the enrolled students) were not
sampled.
Clients in participating mental health settings have received 100
therapy sessions. We randomly sample four different amounts of
therapy sessions to examine treatment progress. When we look at
the sampled sessions, we note that we have sampled only sessions
1, 2, 3, and 4; that is, therapy sessions between 5 and 100 were not
sampled.
In principle, students and therapy sessions in the above two exam-
ples represent random effects. And in the statistical analysis we would
treat them as random effects (if we actually chose not to resample before
collecting any data). But how comfortable would researchers be in gener-
alizing their findings to introductory psychology students in general or to
therapy outcome, in general? Most researchers would feel very uncomfort-
able doing so and almost certainly would not choose to make any strong
inferences based on their data collection - they would rightfully wonder
the extent to which their findings would hold, respectively for each study,
for females and for clients who have more than a very few sessions of ther-
apy. Now, these are admittedly extreme examples, but we hope to have
made the point that, while we may follow a given experimental procedure
(randomly select levels of a variable), it is necessary to critically evaluate
the results of what we have done before overgeneralizing the findings from
any one study.
Most social and behavioral science research operates from a fixed effect
model perspective, because we often do not randomly select the levels of
our independent variables. The decision of which statistical model to use
is somewhat arbitrary, as Keppel and Wickens (2004) note:
There is some latitude in which model we assign to a particular factor, although
the choice should be made in a way that is consistent with the goals of the
research and will be accepted by those to whom it is to be presented. (p. 533)
The computational procedures involved in conducting a fixed effects
model versus a random effects model are comparable with one notable
exception. Selecting the appropriate error terms for random effects and
mixed effects models is more complicated than for the fixed effects models
that we have been discussing throughout this topic. Interested readers are
encouraged to review Clark (1973), Coleman (1964), Keppel (1973, 1991),
