Jacobson et al.: Measurement errors in body size of Placopecten magellanicus 
243 
50 100 
Mean shell height (mm) 
Figure 5 
Bland-Altman plots for Atlantic sea scallop ( Placopecten mag- 
ellanicus) meat weights calculated from experimental shell- 
height measurements in experiment 2 (measuring boards in 
panel A and video in panel B). The y-axis shows the difference 
between the meat weights calculated from the experimental 
(video or measuring board) shell height measurements and the 
meat weights calculated from caliper measurements. The x-axis 
shows the average of the experimental and caliper-derived 
measurements. 
tributions of measurement errors directly in er- 
ror matrices, particularly if experimental sample 
sizes are large. 
Drouineau et al. (2008) used simulation analy- 
sis to show the importance of alternative as- 
sumptions about the distribution of individuals 
within size groups and the statistical distribu- 
tion of growth increments in length-structured 
models like the CASA (catch-at-size-analysis) 
model. Our experience indicates that the same 
types of assumptions are important in calcu- 
lating body-size measurement-error matrices. 
In particular, it was important to assume that 
individuals were uniformly distributed within 
size groups, to make realistic assumptions about 
the distributions of measurement errors, and to 
be careful in programming to ensure consistent 
calculations at the boundaries of length bins for 
calculating error matrices and for the stock as- 
sessment model. 
Statistical methods for repeated measurements 
or random effects may be suitable for analysis of 
our experimental data. We made allowances for 
repeated measures in bootstrap calculations (Ap- 
pendix 2) and in calculating P-values for skew- 
ness and kurtosis tests, but not in calculating 
other statistics (Tables 1-3). 
Our experiments were conducted under ideal 
conditions with tiles and shell valves, rather 
than live sea scallops. Our results may under- 
estimate the magnitude of errors under more 
realistic field conditions. 
Model results may depend on shell-height bin 
width such that larger shell height bins would 
cause measurement errors to have a greater im- 
pact on biomass and mortality estimates. We 
used 5-mm SH bins for sea scallops because 5- 
mm is the resolution and approximate accuracy 
for the survey shell-height data. In general, it 
may be important to consider the magnitude of 
measurement errors in making decisions about size bins 
used in stock assessment modeling. 
Body-size measurement errors 
Random measurement errors are unavoidable. One may 
conclude that it is incumbent on the researcher to search 
out and correct sources of bias, whatever the source. We 
suggest that it may be more cost effective to quantify 
measurement errors experimentally and to accommodate 
them in modeling. Time series with consistent body-size 
measurement errors are probably easiest to interpret. 
Models may become overly complex if multiple sets of 
assumptions about measurement errors are required 
to interpret one survey time series. Resources required 
to quantify measurement errors after each adjustment 
to survey procedures or equipment may be better spent 
on more accurately characterizing the measurement 
errors for survey gear that remains the same for longer 
periods of time. 
Bootstrap results also showed that an algebraic ap- 
proach to removing errors from the data by using the 
inverse error matrix E _1 gave negative proportions for 
both video and measuring board data in at least some 
size groups (Appendix 2). The sampling distribution for 
algebraically adjusted shell-height data may be difficult 
to characterize. These results indicate that it may be 
difficult to remove measurement errors directly from 
body-size data and we hypothesize that approaches like 
the one used in the CASA model will generally perform 
better. Bootstrap results showed that estimates of pre- 
dicted shell-height composition data with measurement 
errors as carried out in the CASA model were robust 
to uncertainties in the measurement-error matrix E 
(Appendix 2). Models can be designed to be robust to 
measurement errors. For example, the last size bin in 
the CASA model is a plus-group that absorbs data for 
large scallops that may have been strongly affected 
by measurement errors. Other data in the model may 
have also contributed to the robustness of biomass and 
