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Fishery Bulletin 108(2) 
to the random aggregations observed on Georges Bank. 
All shell-height measurements could be linked with 
each individual sea scallop in experiment 2 because 
the right valve of 172 individual sea scallop shells was 
numbered uniquely. The identification numbers were 
large and written under the valve with dark indelible 
ink and clearly visible with video equipment when the 
sea scallops were turned over so that the labels faced 
the camera. The numbered sea scallops were assigned 
randomly to fifteen groups. All members of the same 
group were stored together in a bag with a unique label 
for group identification. 
In each experimental replicate, a group of shell 
valves was placed randomly on the bottom of the tank. 
Two video images were made for each group. The first 
image (with the valve turned towards the sediment 
and identification numbers hidden) was used by four 
technicians to independently measure shell heights. 
The second image was taken with identification num- 
bers visible after divers turned the shells over and 
replaced them in their original positions. After video 
images were recorded, the shell valves were measured 
with measuring boards by two technicians who could 
not see the identification numbers and once by a third 
technician with calipers. 
A stock assessment model that incorporates 
errors from shell-height measurements 
Following NEFSC 2 ’ 3 procedures, we used results from 
experiment 2 and a modified version of the CASA (catch- 
at-size-analysis, Sullivan et al., 1990) stock assessment 
model (Appendix 1) to investigate potential effects of 
shell-height measurement errors on model-based bio- 
mass and fishing mortality estimates for two sea scallop 
stocks. Assessment model results in this article should 
not be used by managers because model runs were 
tailored to investigate potential effects of shell-height 
measurement errors and because some types of data 
were omitted. 
As described in Appendix 1, the CASA model that 
is routinely used for sea scallop stock assessments ac- 
commodates both bias and imprecision in shell-height 
measurements. CASA models were run for sea scal- 
lops in the Mid-Atlantic Bight during 1982-2006. In 
contrast to NEFSC 2 , measurement error parameters 
were obtained from experiments and not estimated in 
the CASA model itself. The data used in modeling in- 
cluded commercial landings in metric tons (t), survey 
trend data (numbers per unit of sampling effort) from 
the camera video and dredge surveys, and shell-height 
composition data from the commercial fishery, video, 
and dredge surveys. Survey selectivity patterns were 
not estimated because the video and dredge surveys 
have flat selectivity patterns (catch sea scallops equally 
well) at shell height >40 mm, and goodness-of-fit calcu- 
lations were restricted to this size range (Appendices 
B7-B8 in NEFSC 3 ). Measurement errors in commercial 
shell-height data were assumed to be the same as those 
in the dredge survey for lack of better information and 
because procedures for measuring sea scallops on land 
in port samples and at-sea in fishery observer samples 
are similar to procedures followed in surveys. 
As described in Appendix 1, bias and precision of 
shell-height measurements are represented in the CASA 
model by an error matrix ( E ) that gives the probability 
that a sea scallop in each true shell-height bin is as- 
signed to a range of observed shell-height bins (a range 
that accommodates measurement errors). As described 
by Methot (1989, 1990) for age data, the error matrix 
E can be set up to deal with a wide range of situations 
for bias and variance (e.g., both can vary among shell- 
height bins or over time). 
For the calculation of E for sea scallops in this analy- 
sis, shell-height measurement error distributions were 
assumed to be normally distributed with means and 
standard deviations from experiment 2. The normal 
distributions for measurement errors were truncated 
three standard deviations above and below the mean. 
In calculating distributions of measurement errors, true 
shell heights were assumed with or without bias to be 
uniformly distributed within each true 5-mm SH bin 
so that, for example, the frequency of sea scallops with 
true shell heights of 70, 71, 72, 73, and 74 mm (in the 
70-74.9 mm SH bin with midpoint 72.5) was the same. 
Distributions for measurement errors were normalized 
to sum to one before use in the CASA model. 
Results 
Height and width measurements from the same tiles 
in experiment 1 were not significantly different by a 
paired t-test (£=-0.23, P=0.30, 91 df). Therefore, height 
and width measurements from 91 tiles in experiment 1 
were combined to form a single set of video data (a total 
of 182 measurements) (Table 1). 
The RMSE statistic for video tile-size composition 
and measurement errors in experiment 1 (Table 1) was 
3.5 mm (%RMSE = 7%, Table 1). Bias (-2.2 mm) and 
imprecision (standard deviation 2.7 mm) of video tile 
measurements were similar. In comparison to the true 
size of the tiles (48.5 mm), the smallest measurement 
was 38 mm, and the largest measurement was 50 mm. 
The video size-composition data and measurement er- 
rors were left skewed (g 1 =-0.28) and flatter (g 2 =-0.53) 
than expected for a normal distribution. There were 
gaps in the distribution of the video tile measurements 
(Fig. 3) due to the resolution of the video images used 
in digitizing (each pixef=3x3 mm). 
Measurement error increased with DFO for the video 
tile measurements (Fig. 3). Bias was positive for DFO 
<400 mm and negative at larger DFO levels. 
RMSE for shell-height composition data in experi- 
ment 2 was 33 mm (%RMSE 30%) for video and 34 mm 
(%RMSE = 31%) for measuring board data (Table 2). 
Mean shell height was 106 mm for video and 109 mm 
for measuring boards, compared to 110 mm for calipers. 
Minimum shell height was 34 mm for video, 38 mm for 
measuring boards, and 39 mm for calipers. Maximum 
