Graphics Reference
In-Depth Information
Design Issues for the Two-way Interaction Plot
6.6.4
he two-way interaction plot, displayed in Fig.
.
, shows all the main effects and
two-way interactions for designs with two or more factors. he model in S nota-
tion is
wear ~ (filler + pretreat + raw)^2
.Weconstructthefigure
by analogy with the splom (scatterplot matrix). he rows and columns of the two-
way interaction plot are defined by the Cartesian product of the factors.
. Each main diagonal (SW-NE) panel shows a boxplot for the marginal effect of
afactor.
. Each off-diagonal panel is a standard interaction plot of the factors defining its
position inthe array.Eachpointinthe panelisthe mean ofthe responsevariable
conditional on the values of the two factors. Each line in the panel connects the
cell means for a constant level of the trace factor. Each vertically aligned set of
points in the panel shows the cell means for a constant value of the x-factor.
. Panels in mirror-image positions interchange the trace- and x-factors. his du-
plication is helpful rather than redundant because one of the orientations is fre-
quently much easier to interpret than the other.
. he rows are labeled with a key that shows the line type and color for the trace
factor by which the row is defined.
. Eachboxintheboxplotpanelshasthesamecolor,andoptionallythesameline
type, as the corresponding traces in its row.
. he columns are labeled by the x-factor.
Two-way Interaction Plots with Simple Efects
6.6.5
Figure
.
showedinteractionbetweenthe
strain
and
comb
factors.Consequently
the marginal main effects, showing the average effect of one factor over all levels of
the other, were not relevant. We redraw the two-way interaction plot, this time with
simple effects inthe main diagonal, in Fig.
.
.Simple effects of onefactor,
strain
for example, are conditional on a level of the other factor, in this case
comb
.Simple
effects areusually the correctset of means tolook at inthe presenceof interaction. In
theletpanelsofFig.
.
wespliteachboxinthemaindiagonal,andoffsetthematch-
ing points in the traces in the off-diagonal, to show the nesting of the combinations
within each strain. he extreme outliers in the
strain=5
are seen to occur entirely
in
comb="clover"
. In the right panels we split each box to show the nesting of
the strains within the combinations. he outliers in
comb="clover"
are seen to
be due primarily to
strain=5
.
he
boxesinthelower-letandupper-rightpanelsofFig.
.
areidentical, each
showing the distribution for one of the
strain-comb combinations. he order in
whichtheboxesappear,andthecolorsassignedtothem,differstoreflectthedifferent
nestings. he individual boxes are not labeled. Instead, the outer factor is labeled
and “rug fringes” for the inner factor are displayed. he reader can use the legend to
identify specific boxes.
