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sessions, followed by a free recall test after each encoding (study) session.
In order to control for the possible confounding effects of the presenta-
tion order of the musical stimuli, we give each participant a presentation
sequence depicted by each row of the Latin square in Figure 17.4. Hence,
one participant receives the order rock, pop, classical, jazz, a second par-
ticipant receives the order pop, jazz, rock, classical, and so on. Such an
arrangement neutralizes the potentially confounding effect of stimulus
presentation order, by spreading it evenly across all participants.
The statistical analyses associated with Latin square designs and their
derivatives can be quite complex. We recommend the interested reader
to consult Anderson (2001), Keppel (1991), Keppel and Wickens (2004),
and Winer et al. (1991).
17.5 UNEQUAL SAMPLE SIZE
Most of the analyses we have covered throughout this topic, particu-
larly the computations, have been predicated on the expectation of equal
numbers of participants assigned to each treatment condition. When par-
ticipants contribute equally to each treatment or treatment combination,
statistical assumption violations (which were covered in Chapter 5) are
less likely to occur. Thus, it makes good research sense to strive for equal
treatment group sample sizes. Unfortunately, during the course of our
research practice we will encounter unequal sample sizes as a result of
the loss of participants from our study, or as a result of the realities of
conducting real-world archival or field research.
Anderson (2001) offers five possible causes for unequal sample sizes,
allofwhichcanaffecthowweconductanANOVA.Thecriticalissue
common to all five potential causes is whether the unequal samples are
independent or related to the treatment itself.
Accidental participant loss: Participants are lost as a result of schedul-
ing errors or equipment malfunctions, unrelated to the treatment.
Such loss does not bias the individual treatment means.
Planned unequal samples: Additional or fewer participants are ran-
domly assigned to treatments. This can occur with specialized con-
trol groups, or unusual, rare subpopulations that have unique his-
tories or qualities. Such differential sample sizes should not bias the
observed treatment means.
Treatment-related participant loss: Animals may die or become
incapacitated as a result of medical intervention. Task demands
may encourage participant fatigue, demoralization, and subsequent
dropout. Mean differences assessed with ANOVA procedures, under
these circumstances, may be biased and should be noted.
Unknown participant loss: For the most part, participant loss or
attrition is ultimately an experimental or research design issue.
Tighter controls, clearer instructions, more realistic or relevant task
