Information Technology Reference
In-Depth Information
Table 12.1.
Summary tables for within-subjects and between-subjects effects
for the three-way numerical example
Within-subjects variance
Source
2
SS
df MS
F
Sig.
η
Box color (
A
)
138.889
1
138.889
0.872
0.393
A
×
S
796.278
5
159.256
Granules (
B
)
578.000
1
578.000
7.717
0.039
.028
B
×
S
374.800
5
74.900
Powder color (
C
)
9,780.333
2
4,890.167
126.579
0.000
.475
C
×
S
386.333
10
38.633
A
×
B
1,720.889
1
1,720.889
25.486
0.004
.084
A
×
B
×
S
337.611
5
67.522
A
×
C
2,441.444
2
1,220.722
77.808
0.000
.119
A
×
C
×
S
156.889
10
15.689
B
×
C
2,712.333
2
1,356.167
116.243
0.000
.132
B
×
C
×
S
116.667
10
11.667
A
×
B
×
C
677.444
2
338.722
9.394
0.005
.033
A
×
B
×
C
×
S
360.556
10
36.056
Total within subjects
2,0578.466
Between-subjects variance
Source
SS
df
MS
Subject differences (S)
495.833
5
99.167
interaction supercedes the two-way interactions, which, in turn, supersede
the main effects.
As can be seen from Table 12.1, with the exception of the main effect of
box color, all of the effects of interest are statistically significant. Although
it is not the strongest effect as indexed by eta squared, the significant
three-way interaction informs us that satisfaction with the detergent is a
function of all three independent variables; that is, satisfaction is related to
the particular combinations of box color, presence or absence of granules,
and color of the powder. We would therefore graph that interaction to see
the interrelationships of the variables.
There are several ways to construct a graphic representation of this
interaction. We opt to place all three independent variables within a single
set of axes, partly because there is no pressing theoretical reason to break
apart one of the variables, and partly because it seems desirable to see
them together so that the manufacturer will be in a better position to
decide on what the product will look like.
Placing all the data points on one axis set does have the drawback of
driving the pictorial representation toward complexity, making it more
difficult for readers to discern the pattern. If we are going to use just one
set of axes, we want to select a type of plot that will help readers process
the information. We note that all three of our variables are categorical and
thus do not cry out for a line graph to convey the functional relationship
