In the factorial plots (see Figure 2) in each panel, the 9 data points on
solid lines represent ratings for combinations of two relationship quality
factors. White bullets on double lines represent average ratings when a
single relationship quality factor is presented (uncombined condition). The 9
data points on dashed lines in the factorial plots represent mean happiness
ratings for combinations of all three relationship quality factors, averaged
over the 3 levels of the third factor (referred to with “FRav”,“PTav” and
“PRav” in the plots). Both dashed and solid lines in all three panels of
Figure 2 are well spread and show strong patterns of parallelism, indicatinglear main effects for the quality of the relations with a Partner, Friends and
Parents. These observations are confirmed by the corresponding ANOVAs
(See Table 1). In all three panels of Figure 2 the double line with white
bullets (uncombined condition) crosses the midmost solid line (2 factors
presented). Together with the parallelism in the solid lines this cross-over
indicates that the integration of information on two relationship qualities
follows an averaging model.
When considering the integration of information on 3 relationship
qualities presented simultaneously, the factorial graphs must be read slightly
differently. If the integration of a third factor with 2 other is additive, then it
should be expected that the dashed lines in Figure 2 would be parallel, but
offset from the solid lines. In case of averaging, however, it seems that 2
patterns can result. Either the dashed lines (3 factors presented, results
averaged over the third factor) have a lesser slope than the solid lines (2
factors presented), which results from the third factor that reduces the effect
of the first factor (on the ordinate), as in the right panel of Figure 2. Or, the
dashed lines are surrounded by solid lines, that is, on average, the third
factor reduces the effect of the second factor (as in the left and midmost
panel of Figure 2). It seems that averaging can in general explain how
information on 3 relationship qualities was integrated.