Biology Reference
In-Depth Information
TABLE 3.6 Variances and Standard Deviation
Within-Indicator Variance
Between-Indicator Variance
Total Variance
Standard Deviation
0.040891
0.07354
0.114431
0.338276
to the actual ages for the hold out sample. Ninety-five of the 100 individuals had ages that fell
within the 95% highest posterior density regions, indicating proper coverage. However, the
widths of the 95% highest posterior density regions were sometimes quite considerable,
reaching a maximum of 50 years for anyone in the final phase for all three indicators,
reemphasizing the point that aging is variable, especially for older adults.
In practice, the reference tables (
Tables 3.2
e
3.4
) can be used to estimate ages on a case-by-
case basis with age indicators assessed according to methods that anthropologists are already
familiar with (i.e., Suchey
e
Brooks pubic symphysis phases, Lovejoy et al. auricular surface
phases, and I¸can et al. sternal rib phases).
As an example, consider a set of remains that score as a Suchey
e
Brooks (pubic symphysis)
phase 3, a Lovejoy et al. (auricular surface) phase 2, and an I¸can et al. (fourth sternal rib end)
phase 5. Looking at the reference tables, the mean ages (on a log scale) are 3.154550, 3.638586,
and 3.608466, respectively. The overall mean log age (across the three indicators) is found by
summing the products of the individual mean log ages times the individual precisions
(83.73803) and dividing by the sum of the individual precisions (24.45524). The mean log
age in this case is 3.424138 years (
Table 3.5
). In order to integrate these separate estimates
we need to know the within and between variance of the estimates. The precisions, given
in the tables, are the inverse of the variance of each mean log age. If you sum the three preci-
sions of each indicator for the scored phase (in this case, 10.341600, 6.189976, and 7.923664,
respectively [
Tables 3.2
e
3.4
]) and take the inverse you have the within-indicator variance.
The between-indicator variance is the variance of the three mean log ages for the indicators,
and the total variance is the sum of the within-and between-indicator variance (
Table 3.6
).
The standard deviation is the square root of the total variance; to obtain 95% confidence
intervals for normally distributed data you multiply the standard deviation (calculated as
0.338276 for this case) by 1.96 (a standard scaling variable for how wide a curve will be
when normally distributed) and add and subtract that from the overall mean log age. The
final step is to exponentiate (convert from log numbers to regular numbers) the endpoints
of the interval and the mean log age to convert it from log years to actual years. In this
example, 3.424138 (mean log age)
0.663020 gives us a range of 2.761117
e
4.087159. When
these numbers are exponentiated we have a final range of 15.81751 years to 59.57044 years
with a mean of 30.69606.
CONCLUSION
The skeleton offers a wealth of information related to age-at-death in both juveniles and
adults. Anthropologists continue to strive for a better understanding of skeletal develop-
ment, including the influence of population and sex differences, so that epiphyseal fusion,
