the material (the way most of us read a newspaper or, heaven forbid, a class assignment),
then the five groups should have shown equal recall—after all, they all saw all of the
words. If the level of processing of the material is important, then there should have been
noticeable differences among the group means. The data are presented in Table 11.1.
11.2 The Underlying Model
The analysis of variance, as all statistical procedures, is built on an underlying model. I am
not going to beat the model to death and discuss all of its ramifications, but a general un-
derstanding of that model is important for understanding what the analysis of variance is
all about and for understanding more complex models that follow in subsequent chapters.
To start with an example that has a clear physical referent, suppose that the average
height of all American adults is 5'7" and that adult males tend to be about 2 inches taller
than adults in general. Suppose further that you are an adult male. I could break your height
into three components, one of which is the mean height of all American adults, one of
which is a component due to your sex, and one of which is your own unique contribution.
Thus I could specify that your height is 5'7" plus 2 inches extra for being a male, plus or
minus a couple of inches to account for the fact that there is variability in height for males.
(We could make this model even more complicated by allowing for height differences
among different nationalities, but we won’t do that here.) We can write this model as
Height 5 5'7" 1 2" 1 uniqueness
where “uniqueness” represents your deviation from the average for males. Another way to
write it would be
Height 5 grand mean 1 gender component 1 uniqueness
If we want to represent the above statement in more general terms, we can let mstand
for the mean height of the population of all American adults, stand for the extra com-
ponent due to being a male ( ), and be your unique contribution to
the model. Then our model becomes
Xij=m1tmale1 ́you
tmale=mmale2m ́you
tmale
Section 11.2 The Underlying Model 319
Table 11.1 Number of words recalled as a function of level of processing
Counting Rhyming Adjective Imagery Intentional Total
9 7 11 12 10
8 9 13 11 19
6681614
86611 5
10 6 14 9 10
4111123 11
6 6 13 12 14
5 3 13 10 15
7 8 10 19 11
7 7 11 11 11
Mean 7.00 6.90 11.00 13.40 12.00 10.06
St. Dev. 1.83 2.13 2.49 4.50 3.74 4.01
Variance 3.33 4.54 6.22 20.27 14.00 16.058
