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drug were affecting their performance. We can think of this situation as
representing measurement error for at least two converging reasons:
Because we cannot identify the factors that are responsible for these
individual differences (our data set contains only two pieces of infor-
mation: the patient's group and his or her score on the dependent
variable), this variation in their scores despite the fact that they were
under the same drug condition is treated as measurement error.
Knowing that these patients were under the drug condition would
not allow perfect prediction of their scores. Even if the drug had a
clear effect, and we knew the average improvement of the patients
as a group, there would still be some margin of error involved in
predicting their actual scores in the study.
5.2.2 THE MEANING OF INDEPENDENCE OF ERRORS
The first statistical assumption underlying ANOVA is that the residual or
error component of the
Y
i
scores (the difference between these scores and
the group mean) is random and independent across individual observa-
tions. Hence, no systematic pattern of errors is assumed to be present
among the
Y
i
scores both within and between treatment groups. This
means that the measurements representing one case in the study are inde-
pendent of the data collected from all of the other cases in the study (Hays,
1981).
Dependence occurs when one
Y
i
contains information about another
score. An example of
dependence
- signifying a systematic violation of the
independence assumption - would be observed if the dependent variable
showed larger residual error for the scores in one group and smaller errors
for the scores in another group. This would be indicative of a statistical
relationship between the errors and the scores. To the extent that we could
predict the values of the residuals better than chance from a knowledge of
the group to which a case belonged would indicate that the assumption
of independence of errors has been violated. Examples of dependence in
research situations are discussed next.
5.2.3 SITUATIONS PRODUCING VIOLATIONS OF ERROR
INDEPENDENCE
Several research design situations foster dependence or correlated obser-
vations. One important source of potential bias occurs when participants
within one treatment condition are tested in small or intact groups or
participants enter a treatment condition with previous affiliations (out-
side of the study) that affect how they may perform as measured on the
dependent variable. This “grouping” effect can produce differential error
components among the basic scores or observations. Examples of such sit-
uations might be evaluating improvement in coping behaviors in patients
comprising a single group in group therapy and measuring the effects of
a program of instruction in a class of school children.