544 
Fishery Bulletin 96(3), 1998 
asymmetric to the left with respect to a fishing power 
difference ratio of 1.0. 
Discussion 
It is a well-established ideal to choose among esti- 
mators on the basis of their relative errors. These 
examples demonstrate that the approach can be func- 
tional in practice as well as in the abstract when 
deciding whether or not to apply an FPC. It is im- 
portant to distinguish between the broader notion of 
a decision rule based on the MSE and the specifics 
given here as illustrations. These examples show that 
regions of increased and reduced MSE can be esti- 
mated. They demonstrate common features of the 
regions as well as ways the regions can vary. They 
show that the MSE strategy is functional but also 
underscore problems that can arise from inappropri- 
ate choices of estimators or simulation mechanisms. 
In all three cases a region of increased estimation 
error was successfully identified and each included 
the value 1.0, which represents identical fishing 
power. However, the breadth of the noncorrection 
region differed depending on sample and population 
variance. The three noncorrection regions also dif- 
fered in their symmetry about the value 1.0, which 
was due to an interaction between the mechanism 
for imposing the fishing power difference on the simu- 
lated data and the sensitivity of the arithmetic mean 
to rare extreme observations. 
CPUE variance broadened the noncorrection re- 
gion. The flathead sole simulations demonstrated the 
effect of the sample variance, with the smaller sample 
size producing the broader region (Fig. 3, plots A and 
B). The pollock example produced a very broad re- 
gion of increased error because the population vari- 
ance was quite high (Table 1; Fig. 3C). These ex- 
amples confirm the truism of the MSE: the greater 
the variance, the less important the systematic er- 
ror due to a fishing power difference. The role of vari- 
ance was clearly shown in the two flathead sole simu- 
lations where the FPC observed in the original sur- 
vey fell within the noncorrection region for the higher 
variance case, and outside the noncorrection region 
for the lower variance case (Fig. 3, plots A and B). 
Asymmetry in the noncorrection regions was a 
function of the simulation mechanism. However, the 
problem serves to reinforce the idea that high vari- 
ance tends to reduce the relative importance of bias 
or systematic error and reduces the benefit of cor- 
recting it. Fishing power was assumed to be a simple 
multiplicative effect in these simulations. The vari- 
ance was altered, as well as the bias, when the fish- 
ing power difference was multiplied against A-dis- 
A 
25,000-i 
Q 
O 
C 
20,000- 
J5 
cc 
> 
15,000- 
10,000- 
5,000 - 
uncorrected data 
corrected data 
Variance 
0.5 
1.0 
1.5 
2.0 
B 
20,000-i 
"O 
<D 
03 
D 
15,000- 
C 0 
</) 
03 
CD 
10,000- 
5,000 - 
Bias 
0.5 1.0 1.5 
True fishing power difference 
2.0 
Figure 4 
Components of the mean square error of the estimated 
mean catch per unit of effort (CPUE) of walleye pol- 
lock. “Corrected data” refers to variances and biases 
computed from data in which the fishing power differ- 
ence had been corrected. “Uncorrected data” refers to 
variances and biases computed from data in which the 
fishing power difference had not been corrected. To il- 
lustrate general trends these results were smoothed 
with a scatterplot smoother called “lowess” in the sta- 
tistical software package S-Plus (Becker et al., 1988). 
tributed data, an undesirable consequence. Because 
the arithmetic mean is sensitive, the rare, inordi- 
nately large CPUEs exert high leverage on it. This 
leverage itself was altered with a multiplicative fish- 
ing power difference. For the highly skewed pollock 
data, the change in variance was much greater than 
the change in bias (Fig. 4). When the standard ves- 
sel was less efficient, the uncorrected data produced 
a lower MSE because the fishing power difference 
reduced the leverage of the rare large tows, reduc- 
