Biology Reference
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were known. They revised their earlier hypothesis to be that there exists some population
variation in the femur/stature ratio. The femur/stature ratio for Africans (27.25%) was
significantly different than that for “Europeans” (26.64%) or “Asians” (26.31%), but there
was much variation within the “African” samples. When they used an ancestry-specific
ratio for a known specimen, however, the results were only slightly better than when using
the generic formula (
Feldesman and Fountain, 1996
). If the population affinity was
unknown, they recommended using the generic ratio. Ultimately, the femur/stature ratio
works best for individuals around the mean (those individuals in the middle of the distri-
bution) and does not perform well with outliers; it underestimates stature for shorter indi-
viduals and overestimates stature for taller individuals.
Mathematical Methods: Regression Theory
Manouvrier's earlier method from 1893 was quickly replaced by a mathematical method by
the BritishbiometricianKarl Pearson. LikeManouvrier, PearsonusedRollet'sdata (
Rollet, 1888
)
to establish a newmethod based on regression theory (
Pearson, 1899
). Under regression theory,
the independent and dependent variables are “fit” to the equation of a line:
y ¼ mx þ b
(6.1)
where
y
is stature or the independent variable,
m
is the slope of the regression line,
x
is the
bone length, and
b
is the intercept of the regression line.
If these variables are positively and closely correlated to each other, the data will plot along
a line. See
Figure 6.1
. The regression line is the best estimation of the conditional mean for the
dependent variable corresponding to each independent variable (
Freedman, 1978
). Regres-
sion theory uses standard deviation for the long bones and coefficients of correlation
between the long bones and stature. Least squares regression is the resulting line that
runs through the center of the population (
Steele and McKern, 1969
). Pearson set up the
dependent variable to be stature and the independent variable to be bone length. The conse-
quences of this early designation of stature as the dependent variable will be discussed later.
Pearson's regression was the first true ”mathematical model.” Unlike Manouvrier,
Pearson did not omit any of the older aged individuals from his sample. He created two sepa-
rate equations: one for cadaver (wet) and one for dry bones. From Rollet's data, Pearson sub-
tracted the thickness of the cartilage and accounted for the increase in length when soaked in
water (based on the dissertation of Heinrich Werner from 1897) (
Pearson, 1899
). Pearson
came up with three rules for developing stature estimation equations. First, calculate the
mean and standard deviation for the entire sample and determine the correlation with
stature. Second, measure as many bones of the skeleton as possible. Third, there is an effect
of time (i.e., secular change) and climate/environment on dimensions of body proportions
(
Krogman and I¸can, 1986
). According to
Pearson (1899)
, if stature correlations with a partic-
ular bone are high, then only 50
e
100 individuals may be needed to develop an equation. In
other cases, several hundred individuals may be necessary. It is important to note that there
are inherent errors in stature estimation when combining incongruent data of dry and fleshed
specimens to living individuals (
Krogman and I¸can, 1986
).
In 1929, Paul Stevenson was the first researcher to test Pearson's statistical method of
stature estimation on an independent sample. Stevenson worked as a professor in China
