Biology Reference
In-Depth Information
where
is the best estimate of age from Equation
11.20
. We have plotted the square roots of
the variances from Equation
11.22
as individual points connected by a solid line in
Figure 11.11
, which looks very much like
Figure 11.10
. The fractional polynomial fit to these
points, shown as a dashed line in
Figure 11.11
, gives us a standard error of the estimate of age
as equal to
expð7:647 þ 2:145
m
p
FL
p
FL
logðFLÞÞ
. We then use these standard
errors to calculate 95% confidence intervals for ages-at-death, following the same procedure
as with sex ratio confidence intervals.
Figure 11.12
plots the 95% confidence intervals for age-at-death given femur length.
Although these intervals should include 95% of the data or about 238 out of 250 individuals,
they actually include only 92% of the data, or 230 of 250 cases. Additionally, the 50% confi-
dence interval, which should include 125 individuals, actually includes 51.6% of the data
or 129 cases. This type of wobble is to be expected for relatively small sample sizes, and it
is important in these cases to assess whether or not the calculated confidence intervals are
themselves reliable. We do this by examining the coverage for the sample at all possible confi-
dence limits.
Figure 11.13
shows a plot of the actual coverage versus the stated coverage for
the 250 individuals in the simulated sample. The stated coverage is simply the claimed confi-
dence interval, formed from percentage values of 1/250, 2/250, 3/250
0:238
249/225, 250/250
and shown in this graph as a diagonal line of identity. The actual coverage is the number
of cases (counted up and converted into a percentage) that fall within the stated confidence
.
FIGURE 11.11
Plot of
standard error of age esti-
mates against femur length.
The solid line is from the
calculation, while the
dashed line is a fractional
polynomial fit to the calcu-
lated values.
10
15
20
25
30
35
40
Femur Length (cm)
