THEANALYSIS OF VARIANCE(ANOVA)has long enjoyed the status of being the most used
(some would say abused) statistical technique in psychological research. The popularity
and usefulness of this technique can be attributed to two sources. First, the analysis of vari-
ance, like t, deals with differences between or among sample means; unlike t, it imposes
no restriction on the number of means. Instead of asking whether two means differ, we can
ask whether three, four, five, or kmeans differ. The analysis of variance also allows us to
deal with two or more independent variables simultaneously, asking not only about the in-
dividual effects of each variable separately but also about the interacting effects of two or
more variables.
This chapter will be concerned with the underlying logic of the analysis of variance and
the analysis of results of experiments employing only one independent variable. We will
also examine a number of related topics that are most easily understood in the context of a
one-way(one-variable) analysis of variance. Subsequent chapters will deal with compar-
isons among individual sample means, with the analysis of experiments involving two or
more independent variables, and with designs in which repeated measurements are made
on each subject.11.1 An Example
Many features of the analysis of variance can be best illustrated by a simple example, so we
will begin with a study by M. W. Eysenck (1974) on recall of verbal material as a function
of the level of processing. The data we will use have the same group means and standard de-
viations as those reported by Eysenck, but the individual observations are fictional. The
study may be an old one, but it still has important things to tell us and is still widely cited.
Craik and Lockhart (1972) proposed as a model of memory that the degree to which
verbal material is remembered by the subject is a function of the degree to which it was
processed when it was initially presented. Thus, for example, if you were trying to memo-
rize a list of words, repeating a word to yourself (a low level of processing) would not lead
to as good recall as thinking about the word and trying to form associations between that
word and some other word. Eysenck (1974) was interested in testing this model and, more
important, in looking to see whether it could help to explain reported differences between
young and old subjects in their ability to recall verbal material. An examination of
Eysenck’s data on age differences will be postponed until Chapter 13; we will concentrate
here on differences due to the level of processing.
Eysenck randomly assigned 50 subjects between the ages of 55 and 65 years to one of
five groups—four incidental-learning groups and one intentional-learning group. (Inciden-
tal learning is learning in the absence of the expectation that the material will later need to
be recalled.) The Counting group was asked to read through a list of words and simply
count the number of letters in each word. This involved the lowest level of processing, be-
cause subjects did not need to deal with each word as anything more than a collection of
letters. The Rhyming group was asked to read each word and think of a word that rhymed
with it. This task involved considering the sound of each word, but not its meaning. The
Adjective group had to process the words to the extent of giving an adjective that could rea-
sonably be used to modify each word on the list. The Imagery group was instructed to try
to form vivid images of each word. This was assumed to require the deepest level of pro-
cessing of the four incidental conditions. None of these four groups were told that they
would later be asked for recall of the items. Finally, the Intentional group was told to read
through the list and to memorize the words for later recall. After subjects had gone through
the list of 27 items three times, they were given a sheet of paper and asked to write down all
of the words they could remember. If learning involves nothing more than being exposed to318 Chapter 11 Simple Analysis of Variance
analysis of
variance (ANOVA)
one-way analysis
of variance