Graphics Reference
In-Depth Information
he mechanics of scale control in Fig.
.
differ for S-Plus and R. In S-Plus, we
needed to draw eight graphs and give each one its own
xlim
and
ylim
arguments.
In R, the
xlim
and
ylim
arguments can take a list and therefore all eight panels on
the top can be drawn with a single call to the HH function
xysplom
.
he
xysplom
has an option to display pairwise correlations in the strip labels.
We use that capability in Fig.
.
.
Ladder of Powers Plot - Wool Data
6.3.7
A power transformation oten succeeds in changing from a skewed distribution to
one more closely resembling a symmetric unimodal distribution. Such transforma-
tions are basic items in analysts' toolkits because many standard statistical analyses
require variables to be approximately normally distributed.
hefamilyofpowertransformations T
p
(
x
)
,otencalled Box-Cox transformations
Boxand Cox (
), isgiven by
x
p
(
p
)
,
T
p
(
x
)=
(
.
)
ln
(
x
)(
p
=
)
,
x
p
−
(
p
<
)
.
heladder of powersisthesequentialsetofpowertransformationswiththeparticular
choice of powers p
,
,
,
,
.
Inastudy of the “plasticity ofwool,”Ripa andSpeakman (
)reprinted inTukey
(
), interest lies in relating
diam
, the coe
cient of variation of the diameter of
a wool fiber, to the amount of
time
in minutes the fiber is stretched under a pre-
scribed load. Figure
.
displays an xysplom of the set of ladder of powers transfor-
mations of
diam
against the ladder of powers transformations of
time
.Suppose
the goal is to model some transformation of a variable y as a linear function of some
transformation of x.hisisbestaccomplished ifwecanfindatransformation ofeach
variable such that the two transformed variables are closely linearly related. We ex-
amine this plot for the pair of transformations that best renders a linear relationship.
Clearly the best transformation for
time
is the square root. Careful examination
of the figure suggests that leaving
diam
untransformed is slightly better than us-
ing a square root transformation for
diam
. At this stage of the analysis, we would
ordinarily ask the client which of these two transformations is more readily inter-
pretable.
=−
,
−
