Biology Reference
In-Depth Information
calibration, MA, and the ratio estimator are all fairly close to the anatomical reconstruction of
1,050 mm, while the inverse and RMA estimates are clearly too tall.”
This extreme case of extrapolation beyond the mean worked well with classical calibration
because it is the maximum likelihood estimator, in which the likelihood is proportional to
the probability that an individual with a certain stature would have a long bone length
that is identical to one existing in the actual population sample ( Konigsberg et al., 1998 ).
Therefore, the likelihood is proportional to the probability that the individual of stature x
(Lucy) has a long bone equal to one that has already been measured. Konigsberg et al.
(1998) make the argument that the femur/stature ratio, RMA, and MA can all be justified
as the maximum likelihood estimator. Classical calibration performed the best, and thus is
recommended in a case of extreme extrapolation. In most forensic cases, it is a fairly safe
bet that it does not involve extrapolation beyond the mean, but this could serve as a good
example for work in paleoanthropology or cases in which there is an individual with clear
signs of extreme stature reduction or gigantism.
In mathematical stature estimation, one interesting discovery was that the slope or regres-
sion coefficient in stature estimation formulae does not seem to vary much between popula-
tions. Recall from above that the standard regression equation using inverse calibration is
y ¼ mx þ b
, where y
¼
stature, x
¼
bone length, m
¼
slope or the regression coefficient, and
the y -intercept. 17 Jantz (1992) raises the point that the regression coefficient varies little
among populations andwithin populations, thus, you can use the regression coefficient estab-
lished by Trotter a n d Gl e ser (195 2) , an d then calculate new estimates for the y -intercept using
the equation
b
¼
are the population means. Jantz (1992) calculated the
mean femu r and tibia lengths from the Forensic Databank and inserted them into the above
formula as
b ¼ y mx
, where
y
and
x
using the regression coefficient from Trotter and Gleser as b . The new calculated
y- intercept could then be incorporated into the original Trotter and Gleser equation.
y
Fragmentary Remains
Incomplete bones are extremely commonplace in bioarchaeology and forensic studies.
How then do you estimate stature? Some studies have investigated the proportion of
different bone segments compared to the overall bone length; other studies directly compare
the bone segment length to stature. To estimate stature from fragmentary remains, it is first
necessary to determine which segments of the bones are the most reliable. Gertrude M ¨ ller
(1935) of Vienna first defined bone segments of the tibia (n
¼
100), humerus (n
¼
100), and
¼
radius (n
50), and calculated the proportion of each segment length compared to the entire
bone. The bone length estimates were then applied to Manouvrier tables to calculate stature.
This research paved the way for stature estimation from bone fragments by defining land-
marks on the bones to standardize the bone segments.
Steele and McKern (1969) reworked the M ¨ ller method but used the femur, tibia, and
humerus. They used the same model of standardized bone segments to estimate the length
of long bones from bone fragments. With the landmarks defined, the distance from one
17 In most statistical programs using statistical regression, the variables will be interpreted as stature
¼
(constant
independent variable)
þ
regression coefficient.
Search WWH ::




Custom Search