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Question 882:

8. For the preceding problem you should find that
there are significant differences among the three
treatments. The primary reason for the significance
is that the mean for treatment I is substantially
smaller than the means for the other
two treatments. To create the following data,
we started with the values from problem 7 and
added 3 points to each score in treatment I.
Recall that adding a constant causes the mean
to change but has no influence on the variability
of the sample. In the resulting data the mean
differences are much smaller than those in
problem 7.
I II III
n  6 n  6 n  6
M  4 M  5 M  6 N  18
T  24 T  30 T  36 G  90
SS  30 SS  35 SS  40 ΣX2  567
a. Before you begin any calculations, predict how
the change in the data should influence the
outcome of the analysis. That is, how will the
F-ratio and the value of η2 for these data compare
with the values obtained in problem 7?
b. Use an ANOVA with α  .05 to determine
whether there are any significant differences
among the three treatment means. (Does your
answer agree with your prediction in part a?)
c. Calculate η2 to measure the effect size for this
study. (Does your answer agree with your
prediction in part a?)

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