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is independent). But because stature is the more difficult variable, and bone length the more
easily attainable measure, inverse calibration has become the norm for physical anthropology
since first developed by Pearson (1899) .
Konigsberg and colleagues (1998) point out that this inverse calibration is essentially
a Bayesian statistical approach, in which an assumption is made that the stature distribution
of the reference sample (that which was used to create the formula) is a reasonable prior.
Another way to state this is as follows: it is reasonable to presume that the individual for
whom we estimate stature likely is a member of the population used to pull the reference
sample. If the goal is to estimate stature for an individual that likely comes from the same
population, the inverse calibration regression performs with the least amount of bias. The
inverse calibration equation shown below in Equation 6.2 does not look like the simple equa-
tion of a line presented earlier, because it explicitly includes the population means for femur
length and stature, the covariance between stature and femur length, and the variance of
femur length. The equation is as follows:
x i ¼ x þ b xy ðy i
(6.2)
x
In this equation, x is stature (the independent variable),
is th e stature sought;
x
is the pop-
ulation mean, y is the bone length (the dependent variable),
y
is the population mean femur
length in which
, and cov( x,y ) is the covariance between stature
and femur length with V y being the variance of femur length. Stature is essentially estimated
by ordinary least squares.
According to this same statistical review ( Konigsberg et al., 1998 ), classical calibration is
the regression of bone length on stature, and then solving for stature or x
b xy
is equal to
covðx; yÞ=V y
( y-b )/ m .This
statistical model is the approach taken in allometry studies and is shown below in Equa-
tion 6.3 below. Note that the only difference between equations 6.2 and 6.3 is the negative
exponent, hence the “inversion” of the former:
¼
x i ¼ x þ b xy 1 ðy i
(6.3)
Classical calibration works best when the case involves extrapolation beyond the reference
sample limits (e.g., very tall, very short, or proportions different than the reference sample).
An example of this might be estimating stature of a fossil hominid or a bioarchaeological
specimen when there is not a sizeable or appropriate reference sample for comparison.
This could also be necessary in a forensic case when the individual does not come from
the reference sample and the proportions could be drastically different. For most forensic
cases, however, we can make a strong Bayesian assumption that the stature likely falls within
the distribution of some modern contemporary reference sample.
There are three other statistical models that can be used: Major Axis (MA), Reduced
Major Axis (RMA) or a long bone/stature ratio model. Konigsberg and colleagues
( Konigsberg et al., 1998; Hens et al., 2000 ) tested all of the above statistical models on
a case with extreme extrapolation d estimating the stature of the Australopithecus afarensis
fossil AL 288-1, also known as ”Lucy.“ Lucy's stature was calculated using a modern human
reference sample that included a sample of Mbutu Pygmies fromWest Africa. Lucy's ”actual
stature” was calculated from a reconstruction of the fossil, comparable to the Fully anatom-
ical method. Konigsberg and colleagues (1998) stated, “The estimates from classical
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