Jacobson et al.: Measurement errors in body size of Placopecten magellanicus 
247 
Shell height (mm) 
Appendix Figure 2 
Bootstrap distributions (1000 iterations) for Atlantic sea scal- 
lop ( Placopecten magellanicus ) shell-height data obtained from 
measurement boards (A) and video (B), with measurement 
errors. The solid line shows the actual caliper-derived shell- 
height data in experiment 2. 
ments), their mean (bias), and variance were 
used to calculate the bootstrap measurement er- 
ror matrix and its inverse. Finally, the original 
video shell-height composition data used in ex- 
periment 2 (expressed as proportions) were then 
multiplied by the bootstrap inverse matrix (Eq. 
A4) to remove measurement errors and obtain a 
bootstrap estimate of the true shell-height com- 
position. There were 1000 bootstrap iterations 
for both the video and measurement board data. 
The variability among bootstrap estimates of the 
true shell-height composition was due entirely to 
errors in the measurement error matrix E and 
its inverse . 
As expected, based on condition factors (see 
above) and measurement error statistics (Table 
2), bootstrap estimates of true caliper shell- 
height composition data from video data were 
highly variable and predicted proportions ranged 
from -188 to 195 (i.e., outside the feasible range 
for proportions). Bootstrap estimates from mea- 
surement board data resembled the correspond- 
ing true caliper measurements. However, the 
estimated proportions for both measurement 
methods were often negative and infeasible (Ap- 
pdx. Fig. 1). 
We used a similar bootstrap procedure to eval- 
uate effects of uncertainty in predicted length 
compositions with measurement errors (Eq. A3 
in Appdx. 1), which is the approach used in the 
CASA model. In this bootstrap analysis, the 
caliper shell height composition data from ex- 
periment 2 were assumed to be true and error 
matrices were generated by bootstrapping the 
experimental and video and measuring board 
data as described above. The sample size was 
n=172 for both video and measuring boards and 
the same as the number of individual specimens 
in experiment 2. This lower bound estimate of 
the effective sample size was used in order to 
overstate effects of uncertainty in error matrices. Re- 
sults indicated that the calculations used in the CASA 
model for measurement errors were robust to uncer- 
tainty about the error matrices and the magnitude of 
the errors because variability in predicted shell height 
compositions was relatively minor (Appdx. Fig. 2). 
