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Fishery Bulletin 108(2) 
In previous analyses, correction factors were applied 
to the raw video shell-height measurements to account 
for distance from the origin (DFO), which is the dis- 
tance of a specimen from the “origin” (center) of the 
sampling frame (Stokesbury et ah, 2004). Subsequent 
work during routine stock assessments (unpublished) 
indicated that adjustments were unnecessary because 
the distributions of measurement errors were simpler 
and easier to describe statistically, and data were easier 
to model without adjustments. Moreover, adjusted data 
were sometimes less accurate than the unadjusted data. 
Additional research may result in more accurate adjust- 
ments or transformations of body-size data. However, 
unadjusted video data from the “large” camera on the 
sampling frame are used in current stock assessments 
and in this analysis. 
NEFSC sea scallop surveys are conducted with a 
2.44-m New Bedford sea scallop dredge with a 38-mm 
liner. The catch is sorted, counted, and measured on the 
deck of the research vessel. In most cases, the entire 
catch is counted and measured, but a few large catches 
were subsampled. During the early 1980s through 2003, 
sea scallops in the catch were measured to the nearest 
5-mm shell-height interval with a standard NEFSC sea 
scallop measuring board. 
Experiments 
Two experiments were conducted during 20 and 23 Feb- 
ruary 2003 when the SMAST video pyramid was placed 
in a 341,000-L tank filled with seawater in the SMAST 
laboratory. NEFSC sea scallop measuring boards and 
SMAST video equipment in the experiments were con- 
figured and used in a realistic manner that was similar 
to use during actual surveys at sea. Accurate measure- 
ments used as true shell heights in this analysis were 
made to the nearest mm by using scientific calipers 
under laboratory conditions with adequate lighting. 
We used the experimental data to evaluate statisti- 
cal characteristics of shell-height composition data and 
shell-height measurement errors. 
Accuracy, bias, and precision of measurements were 
quantified by comparing data obtained from the mea- 
suring board and video camera with data from the 
caliper. Accuracy is the closeness to the true underlying 
value and is measured by mean square error (MSE). For 
shell-height composition data, 
MSE = (h-H) 2 , (2) 
where h = the mean of the measurements; and 
H = the mean of the true values for the sample 
(Cochran, 1977). 
For measurement errors in our analysis, 
n 
MSE = — — , (3) 
n 
where e- - h—H j = the error for the j th observation (where 
hj is the measurement and is the 
true value). 
Bias and variance both contribute to MSE. In fact, 
MSE = s 2 + b 2 , where s 2 is the variance and b is bias 
(Cochran, 1977). In our study, b-h-H where h is the 
mean of shell-height measurements and H is the mean 
of the true shell heights in the sample. Bias is the same 
for shell-height composition data and measurement er- 
rors as shown below: 
n 
^ ](h j -H j )/n = h-H . (4) 
7=1 
Variance (s 2 ) was computed from shell-height composi- 
tion data or measurement errors by using the standard 
formula. Variance of shell-height composition data and 
measurement errors will generally be different because 
true shell heights usually differ among specimens in a 
sample. 
It is convenient to express accuracy, bias, and preci- 
sion in terms of the square root of the MSE (RMSE), 
bias (b), and standard deviation (s) because all three 
are absolute measures with the same units (mm for sea 
scallop shell-height data). Percent RMSE (RMSE /h true ), 
percent bias ( blh true ), and the CV (s/h) are useful for 
making comparisons on a relative basis. 
The third and fourth moment statistics, g l and g 2 
were used to measure skewness (asymmetry) and kur- 
tosis (peakedness) of shell-height composition data and 
measurement errors, in relation to what would be ex- 
pected from a normal distribution (Sokal and Rohlf, 
1995). Skewness and kurtosis statistics for shell-height 
composition data and measurement errors from the 
same sample differ if there is variability in size among 
specimens. For normally distributed random variables 
with no skewness, g r - 0. Negative g 1 values indicate 
skewness to the left (a distribution with a long left 
tail and more small values than expected in a normal 
distribution). Positive g 1 values indicate skewness to 
the right (long right tail with more large values than 
expected). Similarly, positive g 2 values indicate dis- 
tributions more peaked than expected for a normal 
distribution, and negative g 2 values indicate distribu- 
tions that are less peaked (flatter) than expected. The 
two statistics convey information about the shape of 
any distribution in relation to a normal distribution, 
but care is required in interpreting g 1 and g 2 , particu- 
larly for data that are far from normally distributed. 
The skewness and kurtosis statistics were easier to 
interpret for measurement errors than for shell-height 
measurements because the latter were not normally 
distributed. 
We used a test for normally distributed statistics 
(Sokal and Rohlf, 1995) to evaluate the statistical sig- 
nificance of skewness and kurtosis for distributions of 
measurement errors that might be otherwise assumed 
normally distributed. Statistical tests were carried out 
