1 Chapter 11

2 FIGURE 11.1 Normal densities for male and for female femoral circumferences (in millimeters). The summary statistics for drawing these two densities are from Black (1978), and the vertical line is the “sectioning point” (at 57 mm) that could be used to sex individuals as male versus female. Copyright © 2013 Elsevier Inc. All rights reserved.

3 FIGURE 11.2 Normal densities for male and for female femoral circumferences (as in Figure 11.1), but with nine females to every one male. Note how this uneven sex ratio shifts the sectioning point up to 60.2 mm from the previous value of 57 mm. Copyright © 2013 Elsevier Inc. All rights reserved.

4 FIGURE 11.3 Simulation of 10,000 deaths from an exponential hazard model where the hazard is The histogram shows the “binned” ages from the simulation, while the dashed line shows the probability density function for age-at-death when the hazard is equal to Copyright © 2013 Elsevier Inc. All rights reserved.

5 FIGURE 11.4 Log hazards for each of the three components in a Siler model fit to Coale and Demeney’s (1983) Model West 1 for females. The unlabeled dashed line is the total log hazard. Copyright © 2013 Elsevier Inc. All rights reserved.

6 FIGURE 11.5 Hazard function, survivorship function, and probability density function (for age-at-death) from a negative and positive Gompertz model taken from Nagaoka et al.'s (2006) analysis of a Medieval Japanese archaeological skeletal collection. The final panel shows a simulation of 10,000 deaths from the modeled distribution. Copyright © 2013 Elsevier Inc. All rights reserved.

7 FIGURE 11.6 Plot of mean femoral length against age in boys. The filled points are from Maresh’s (1970) radiographic study, the dashed line was fit as a third-degree polynomial, and the solid line was fit using fractional polynomials. Copyright © 2013 Elsevier Inc. All rights reserved.

8 FIGURE 11.7 Plot of the predicted mean femoral length plus and minus two standard deviations across age. The open points are as in Figure 11.6, while the lines for the mean and plus and minus two standard deviations were drawn using fractional polynomials. Copyright © 2013 Elsevier Inc. All rights reserved.

9 FIGURE 11.8 Kaplan–Meier plot (Kaplan and Meier, 1958) of the survivorship from 250 simulated ages-at- death (solid line step function) and the 95% confidence intervals for survivorship estimated from the simulated femur length data (dashed smooth curves). Copyright © 2013 Elsevier Inc. All rights reserved.

10 FIGURE 11.9 Comparison of the empirical cumulative density function for 250 simulated femoral lengths (shown as a solid line step function) and the modeled cumulative density shown as a dashed line. Copyright © 2013 Elsevier Inc. All rights reserved.

11 FIGURE Plot of age estimates against femur lengths. The individual points are shown at centimeter intervals of femoral lengths from 8 to 20 cm and at millimeter intervals from 20 to 40 cm. There is one solid line shown that passes entirely through the points and is from a fractional polynomial fit. The additional line that departs from the points at greater femur lengths is from solving the regression of femur length on age. Copyright © 2013 Elsevier Inc. All rights reserved.

12 FIGURE Plot of standard error of age estimates against femur length. The solid line is from the calculation, while the dashed line is a fractional polynomial fit to the calculated values. Copyright © 2013 Elsevier Inc. All rights reserved.

13 FIGURE Plot of 250 simulated ages against femoral lengths. The solid lines show the 95% confidence intervals for age estimates, which contain 230 of 250 cases (92% of the data). Copyright © 2013 Elsevier Inc. All rights reserved.

14 FIGURE Plot of the actual coverage versus the stated coverage for the 250 individuals in the simulated sample (step function line). The diagonal line is the line of identity. Copyright © 2013 Elsevier Inc. All rights reserved.