Information Technology Reference
In-Depth Information
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TNF-alpha
FIGURE 9.3
Relation Between Two Inflammatory Reaction Mediators in
Response to Silicone Exposure.
Data taken from Mena et al. [1995].
The data in Figure 9.3 are taken from Mena et al. [1995]. These
authors reported in their abstract that, “The correlation . . . between
IL-6 and TNF-alpha was .77 . . . statistically significant at a
p
-value
less than .01.” Would you have reached the same conclusion?
With more complicated models, particularly those like Model IV that
are nonlinear, it is advisable to calculate several values that fall outside the
observed range. If the results appear to defy common sense (or the laws of
physics, market forces, etc.), the nonlinear approach should be abandoned
and a simpler model utilized.
Often it can be difficult to distinguish which variable is the cause and
which one is the effect. But if the values of one of the variables are fixed
in advance, then this variable should always be treated as the so-called
independent variable or cause, the
X
in the equation
Y
=
a
+
bX
+ e.
Here is why:
When we write
Y
=
a
+
bx
+ e, we actually mean
Y
=
E
(
Y
|
x
) + e, where
E
(
Y
|
X
) =
a
+
bx
is the expected value of an indefinite number of indepen-
dent observations of
Y
when
X
=
x
. If
X
is fixed, the inverse equation
x
=
(
E
(
x
|
Y
) -
a
)/
b
+ e¢=makes little sense.
Confounding Variables
If the effects of additional variables other than
X
on
Y
are suspected, these
additional effects should be accounted for either by stratifying or by perform-
ing a multivariate regression.
