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Fishery Bulletin 108(2) 
size data may be imprecise, for example, when col- 
lected by scuba (St. John et al., 1990; Edgar et al., 
2004), remotely operated underwater vehicles (ROV; 
Butler et al., 2006), camera sleds (Rosenkranz and 
Byersdorfer, 2004), or in other optical surveys where 
body-size measurements are obtained without handling 
individual specimens. 
In fishery stock assessment modeling, body-size mea- 
surements are almost always assumed to be without 
error. In contrast, statistical sampling errors that arise 
from too few are often considered in modeling (Fournier 
and Archibald, 1982; Pennington et al., 2001). Measure- 
ment errors in fishery age data have received substan- 
tial attention and are often addressed in stock assess- 
ment modeling (Methot, 1989, 1990). Approaches to 
dealing with measurement error in body-size data have 
not been explored. 
Shell-height composition data for sea scallops are 
of two types: 1) distributions of shell-height measure- 
ments, which include measurement errors and true 
variability among individuals in size; and 2) distri- 
butions of shell-height measurements, which include 
measurement errors only. It is important to distinguish 
between these two types of data. In particular, shell- 
height compositions are sample specific and depend on 
the underlying distribution of true sizes. In our study 
measurement errors are the difference between the 
video or board measurements and the true shell height 
of individual specimens (i.e., after removing differences 
in true shell height among individuals). Shell-height 
composition data are important because they are in- 
terpreted in stock assessments to estimate year-class 
strength, mortality, and other biological characteris- 
tics. In our study measurement errors are important 
because they can be used to quantify the accuracy of 
the measurement process itself and because they affect 
shell-height data from all samples. 
Two types of measurement errors are considered in 
this study. The first type is bias that causes individual 
shell-height measurements and estimated sample means 
to differ, on average, from their true values (Cochran, 
1977). The second type is random errors, which cause 
variability in shell-height measurements and affect the 
precision of measurements and estimated mean values 
(Cochran, 1977). 
Figure 1 shows how hypothetical errors in sea scal- 
lop shell-height measurements tend to smooth the true 
underlying distribution of the data. Measurement errors 
tend to smooth modes in the data (which usually cor- 
respond to recruitment events) by moving individuals 
from size bins with relatively high numbers into adja- 
cent bins with lower numbers. Random measurement 
errors also tend to expand the range of observed sizes 
by decreasing the smallest observed size and increas- 
ing the largest (Fig. 1). Bias degrades body-size data 
by making measurements consistently larger or smaller 
than the true value. Methot (1989, 1990) highlighted 
these issues in the context of age data from survey and 
fishery samples. We use Methot’s modeling methods in 
our analysis for shell-height data. 
In principal, body-size measurement errors can cause 
errors in a wide range of important fishery estimates 
but biomass estimates are of particular importance. In 
the absence of bias, imprecise body-size data tend to 
cause positive bias in mean weight and biomass esti- 
mates because of the nonlinear relationship between 
size and biomass and Jensen’s inequality (Feller, 1966). 
For example, according to Jensen’s inequality, if body 
weight is a cubic function of body size, then a -10% 
error in body size will cause a 0.9 3 -l = -27% error in 
estimated body weight for one individual. In contrast, 
a +10% error in body size will cause a 1.1 3 -1 = +33% 
error in body weight. The combined effect of the two 
errors for two scallops of the same size would be a posi- 
tive bias of +6%. 
The length-based Beverton-Holt mortality estimator 
involves equilibrium and other assumptions that may 
make it inappropriate to use in some cases (Gedamke 
and Hoenig, 2006), but it clearly demonstrates the po- 
tential effects of errors in body-size measurements on 
stock assessment model mortality estimates: 
L-L 
( 1 ) 
where Z = 
= 
K = 
L = 
L c = 
the instantaneous rate of mortality from all 
sources; 
asymptotic length; 
rate parameter from the von Bertalanffy 
growth equation; 
average length of individuals in a sample 
from the fishery; and 
the “critical” length at which individuals 
are fully vulnerable to the fishery (Quinn 
and Deriso, 1999). 
With all other factors held constant, a positive bias in 
L will make the numerator in Equation 1 too small, the 
denominator too large, and the mortality estimate will 
be biased low. Conversely, a negative bias in L will bias 
the mortality estimate high. 
In this article, we characterize measurement 
errors in shell-height data for sea scallops in two 
types of surveys, using experimental data. The 
experimental results are used to evaluate effects 
on mean body weight and swept-area biomass es- 
timates, and on biomass and mortality estimates 
from a modern size-structured stock assessment 
model. The assessment model demonstrates a 
promising approach (used originally for age data) 
for accommodating measurement errors in body- 
size data. In the appendices, we use numerical and 
bootstrap techniques to evaluate robustness of the 
assessment model approach in comparison to an 
algebraic one. Our purpose is not to evaluate the 
merits of any particular survey, rather, we use sea 
scallops as an example for dealing with general 
problems arising from body-size measurement er- 
rors in survey and fishery-dependent data, and for 
suggesting possible approaches to using such data. 
