Information Technology Reference
In-Depth Information
Ta b l e 3 . 2 .
Summary table for the analysis of the data contained in Table 3.1
Between-subjects effects
Sources of variance
SS
df MS
F
ratio
Probability
Eta squared (
η
2
)
Between groups (Factor
A
)
87.50
1
87.50
18.75
.001
.610
Within groups (Error or
S
/
A
)
56.00
12
4.67
Total variance
143.50
13
sum of squares, degrees of freedom, and mean square (
MS
) in the remain-
ing portion of this chapter. In the following chapter, we will address the
F
ratio, the probability associated with the
F
ratio, statistical significance,
the eta squared (
2
) statistic, and statistical power.
η
3.3 SOURCES OF VARIANCE
The first column of the summary table is labeled “Sources of variance.”
A “source” of variance represents a portion or partition of the total vari-
ance. As shown in Table 3.2, the
total
variance occupying the last row is
partitioned into
between-groups
variance and
within-groups
variance. The
details concerning these sources of variance will be explicated when we
discuss the sum of squares column in Section 3.4. For the moment, here
is an overview of each of these sources of variance:
The between-groups portion of the variance deals with the differ-
ences between the group means. In the notation system that we
will be using, independent variables, often called
effects
,
factors
,or
treatments
, are designated by uppercase letters in alphabetic order
starting with
A
. With only one independent variable in the study, its
effect is noted as Factor
A
. If there were two independent variables,
the effect of one (arbitrarily determined) would be called “Factor
A
”
and the effect of the other would be called “Factor
B
.”
The within-groups portion of the variance deals with the variation
of the scores within each of the experimental groups. It is referred to
as error variance for reasons we will discuss shortly. In our notation
system we designate it as
S
A
; this notation stands for the expression
“subjects within the levels of Factor
A
.”
The total variance of the dependent variable deals with the variation
of all the scores taken together (regardless of group membership).
/
3.4 SUMS OF SQUARES
3.4.1 TOTAL SUM OF SQUARES
The total variability of the scores can be seen in pictorial form in Figure 3.1.
The data in the circle are the values of the dependent variable taken from
Table 3.1. There are fourteen scores in the set - each score in the study is
