Jacobson et al.: Measurement errors in body size of Placopecten magellanicus 
241 
Measurement 
Figure 4 
Modified Bland-Altman plots for Atlantic sea scallop ( Placopecten 
magellanicus) shell-height (SH) measurements in experiment 2. The 
y-axis shows the difference between the experimental measurement 
(measuring boards in A or video in B) and the caliper measure- 
ment. The jc-axis shows the average of the experimental and caliper 
measurement. Boxplots and 30-mm shell-height bins were used 
instead of traditional scatter plots for shell height measurements 
in experiment 2 because the large number of samples between 120 
and 150 mm SH gave the impression that variance was higher for 
those sizes. Boxplots show the interquartile range (a robust vari- 
ance measure) and are not sensitive to sample size. The width of 
the boxplots is proportional to the number of observations for the 
shell-height bin. 
surements. In contrast, Heery and Berkson 
(2009) used simulations to evaluate effects of 
systematic sampling errors (too many small 
or too many large individuals) in size-com- 
position data from commercial catches and 
three simulated stocks. The simulated data 
were used in a forward-projecting age-struc- 
tured stock assessment and in projection 
models to estimate stock size and fishing 
mortality in relation to threshold values, and 
rebuilding trajectories. Body-size data with 
too many large individuals biased stock size 
high and fishing mortality low and tended to 
support management measures that did not 
meet management goals, particularly for lon- 
ger lived and depleted stocks. Body-size data 
with too many small individuals were less 
problematic, but tended to support overly 
restrictive management actions in extreme 
cases. Heery and Berkson’s (2009) results 
indicate that systematic errors in sampling 
may be more important than errors in indi- 
vidual measurements of body size. 
Variance in calculated meat weights in- 
creased rapidly with shell height with both 
video and measuring board techniques, in 
contrast to the variance in shell heights 
(Figs. 4 and 5). This additional source of 
variability likely increases variance in bio- 
mass estimates, particularly for relatively 
large fishable sea scallops. 
In our analysis, assessment models that 
accommodated shell-height measurement er- 
rors fitted better, even though no additional 
parameters were estimated. The Mid-Atlan- 
tic Bight model that accommodated impre- 
cise (but not biased) shell-height measure- 
ment errors had a negative log likelihood 
that was 15 units smaller than the negative 
log likelihood for the no measurement er- 
ror model (Table 5). Results for the Georges 
Bank stock (not shown to conserve space) were similar. 
In contrast and based on likelihood theory, a difference 
in negative log likelihoods of just 1.92 units is sufficient 
to justify an additional parameter in a statistical model 
at the P= 0.05 level (Venzon and Moolgavkar, 1988). 
Comparing results of the “bias only” scenario to results 
from the “imprecision only” and “imprecision and bias” 
scenarios, we found that improvements in goodness of 
fit were mostly due to accommodating imprecision; bias 
was less important (Table 5). 
Experiments 
Our results highlight the value and information that 
may be gained from evaluating body size measurement 
errors experimentally. Body-size measurement error 
experiments should be conducted when survey equip- 
ment is changed, particularly if body-size measurements 
are imprecise. In some cases, frequent “mini-experi- 
ments” may be required if the accuracy of the equip- 
ment tends to drift over time or change in response to 
environmental conditions. 
Our results indicate the importance of designing mea- 
surement error experiments so that individual speci- 
mens can be identified and associated with individual 
measurements; otherwise measurement errors can not 
be estimated individually and evaluated directly. Data 
from experiment 2 were most useful because individual 
sea scallops were numbered and replicate measure- 
ments of different types could be linked and analyzed 
in detail. In addition, the full range of variability for all 
important factors (i.e., distance from the origin (DFO), 
shell height, and identity of individual technicians) 
should be included in the experimental design. 
We ignored skewness and kurtosis in measurement 
errors in calculating measurement error matrices for 
use in the CASA stock assessment model. In future 
modeling, it may be better to use the experimental dis- 
