Munro: Correcting relative fishing power differences in trawl survey data 
543 
answered analytically rather than through a simu- 
lation, given a known probability model. Such a so- 
lution would be difficult or impossible because of the 
complicating factor of the estimated FPC. Even if a 
model-based estimation strategy were acceptable for 
estimating mean CPUE from uncorrected data, the 
appropriate probability model for the corrected data 
is not clear, especially if, as in these examples, the 
FPC estimator has an unknown distribution. 
In this example, the two sets of simulated CPUE 
(standard and nonstandard prior to imposing the 
assumed fishing power difference) are independent 
and identically distributed random variables. This 
simulation ignored the possibility for spatial corre- 
lation among observations in a real survey. Because 
each station in the standard Bering Sea survey is 20 
n mi from its nearest neighbor, I assumed that spa- 
tial correlation was negligible and did not attempt 
to build it into the simulations. This is consistent 
with current treatment of data collected on these 
surveys. A more complex procedure would be needed 
to simulate surveys with spatial correlation among 
observations. 
Results 
For flathead sole, with a sample size of 144 per ves- 
sel, a clear region of increased error, the noncor- 
rection region, appeared between approximately 0.77 
and 1.14 in plots of MSE against the fishing power 
difference (Fig. 3A). The lowest MSE occurred with 
uncorrected data when there was identical fishing 
power (the value 1.0 on the x-axis). The FPC esti- 
mated for the original data, 0.76 (Table 1), fell just 
outside this region. 
With a sample size of 50 per vessel, a clear 
noncorrection region appeared between approxi- 
mately 0.56 and 1.19 for flathead sole (Fig. 3B). The 
FPC for the original data fell within this region. The 
minimum MSE occurred with uncorrected data. This 
minimum occurred, however, when the nonstandard 
vessel had a CPUE of about 23% less than that of 
the standard vessel rather than when the vessels had 
identical efficiencies (fishing power difference ratios 
of 0.87 and 1.0, respectively). The noncorrection re- 
gion was also clearly asymmetric to the left with re- 
spect to a fishing power difference ratio of 1.0. 
For walleye pollock, with a sample size of 149 per 
vessel, the noncorrection region was not as clearly 
defined because the lower bound occurred at some 
value less than 0.50; the upper bound was approxi- 
mately 1.05 (Fig. 3C). The FPC estimated for the 
original data, 1.32 (Table 1), fell outside this region. 
The minimum MSE occurred with uncorrected data 
uncorrected data 
corrected data 
A 
flathead sole 
8- 
n- 144 
6- 
observed FPC 
4- 
2 
0.5 1.0 1.5 2.0 
B 
8 1 
LLi 
S 6 
flathead sole 
n = 50 
observed FPC 
8 4 

O 41 
2 J 
0.5 1.0 1.5 2.0 
c 
210 
walleye pollock 
n = 149 
observed FPC 
160 
. r 
1 10 J 
' : 
0.5 1.0 1.5 2.0 
True fishing power difference 
Figure 3 
Simulation results: square root of the mean square er- 
ror ( MSE ) of mean catch per unit of effort ( CPUE ) plot- 
ted against the true fishing power difference. The fish- 
ing power difference is expressed as the ratio of the 
true CPUE for the standard vessel over the true CPUE 
of the nonstandard vessel. “Corrected data” refers to 
MSEs computed from data in which the fishing power 
difference had been corrected. “Uncorrected data” re- 
fers to MSEs computed from data in which the fishing 
power difference had not been corrected. Sample size, 
n, refers to the number of stations realized for each 
vessel in each simulation. To illustrate general trends 
these results were smoothed with a scatterplot smoother 
called ‘ 
lowess” in the statistical software package 
S-Plus (Becker et ah, 1988). 
at a fishing power difference ratio near 0.67, where 
the nonstandard vessel caught 33% less than the 
standard. The noncorrection region was extremely 
