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CHAPTER THREE
Elements of ANOVA
3.1 PARTITIONING OF THE VARIANCE
The term
analysis of variance
is very descriptive of the process we use in the
statistical treatment of the data. In a general sense, to analyze something is
to examine the individual elements of a whole. In ANOVA, we start with
a totality and break it apart - partition it - into portions that we then
examine separately.
The totality that we break apart in ANOVA, as you might suspect from
the name of the procedure, is the variance of the scores on the dependent
variable. As you recall from Chapter 2, variance is equal to the sum of
squares - the sum of the squared deviations from the mean - divided by
the degrees of freedom. In an ANOVA design, it is the variance of the total
set of scores that is being partitioned. The various ANOVA designs are
different precisely because they allow this total variance to be partitioned
in different ways.
ANOVA is a statistical procedure that allows us to
partition
(divide) the
total variance
measured in the study into its sources or component parts.
This total measured variance is the variance of the scores that we have
obtained when participants were measured on the dependent variable.
Therefore, whenever we talk about the variance associated with a given
partition or whenever we talk about the total variance, we are always
referring to the variance of the dependent variable.
3.2 A SIMPLE EXAMPLE STUDY
3.2.1 A DESCRIPTION OF THE STUDY
To keep this chapter's discussion somewhat concrete, we will flesh out
the example introduced in Chapter 1, a hypothetical two-group design.
Assume that a set of researchers wished to learn if the room color in
which college students are asked to respond to questions assessing their
mood can affect their reported mood. A total of fourteen participants
were randomly assigned to one of two groups. The students were asked
to complete an inventory that assessed their current mood. One group
of seven students answered the questions in a room painted a soft shade
of blue (Blue Room group); this color was expected to exert a calming
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