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Large
Small
Rural
15
38
42
20
43
48
Female
10
M = 15
33
M = 38
36
M = 42
M = 31.67
21
46
49
9
30
35
16
28
10
22
34
16
Male
10
M = 16
22
M = 28
4
M = 10
M = 18
21
35
15
11
21
5
M = 15.5
M = 33
M = 26
Figure 8.2
Data for example.
are interested in feelings of loneliness experienced by adults who are living
alone. We sample individuals from three different types of population
centers: large metropolitan cities, small municipalities or towns, and rural
communities (coded as 1, 2, and 3 in the data file). Recognizing that
gender might be an important factor here, we separately code for female
and male participants (coded as 1 and 2, respectively).
Further assume that participants are randomly selected from the pop-
ulation of singles representing the respective demographic category. They
are each asked to complete a loneliness inventory, the score from which
will serve as the dependent variable. A score of zero means that a person
has experienced no loneliness whatsoever, whereas the maximum score of
60 reflects repeated and intense feelings of loneliness.
The data for thirty respondents, shown in Figure 8.2, are organized
into a 2
3 between-subjects design. Each cell contains five individuals
of one gender living in one type of community. We show the cell means
as well as the means for the rows (levels of
A
) and columns (levels of
B
) in the figure. For example, the average loneliness score for females
living in small towns is 38.00, the overall loneliness score for all of the
females in the sample is 31.67, and the average loneliness score for all of
those in the sample living in rural communities is 26.00.
×
8.3 PARTITIONING THE VARIANCE INTO ITS SOURCES
8.3.1 THE SUMMARY TABLE
As was true of the one-way between-subjects design, the total variance of
the dependent variable in a two-way design is partitioned into its sepa-
rate sources. These sources are the ones associated with the independent
variables and their interaction, which are usually referred to as the effects,
and the variance which is not accounted for, which is usually referred to as
within-groups variance or error variance. We have computed the ANOVA
for the data shown in our numerical example. The summary table of the
results may be seen in Table 8.1.
As can be seen from Table 8.1, the total variance is partitioned into four
parts. The partitions representing single independent variables are known
