6 
Fishery Bulletin 1 15(1) 
Table 2 
Number of simulations in which criteria for coverage levels for individual confidence 
intervals coverage were not met for combinations of estimator type (scenario). Simula- 
tions were conducted for 4 variables of interest with varying numbers of categories ik). 
Scenario Criterion 
Variable of interest (number of categories) 
Sex 
{k=2) 
Brood year 
(/j=5) 
Stock 
0fe=10) 
Agexstock 
(/2=50) 
Pooled asymptotically normal 
Coverage <0.85 
0 
1 
5 
18 
Coverage <0.80 
0 
0 
3 
6 
Pooled parametric bootstrap 
Coverage <0.85 
0 
0 
5 
13 
Coverage <0.80 
0 
0 
3 
2 
Stratified asymptotically normal 
Coverage <0.85 
0 
1 
0 
12 
Coverage <0.80 
0 
0 
0 
3 
Stratified parametric bootstrap 
Coverage <0.85 
0 
0 
0 
8 
Coverage <0.80 
0 
0 
0 
0 
We obtained estimates of abundance and boot- 
strapped CIs for the groups of interest for every simu- 
lation iteration, using the window counts and the pri- 
mary and secondary samples, as explained previously. 
After 500 simulation iterations, we had 500 estimates 
of the total number of wild steelhead, female and male 
wild, wild by age, and wild by stock. We also had 500 
individual and joint CIs for each estimate. We saved 
the estimates and CIs for subsequent evaluation. 
The evaluation of estimator performance was based 
on bias and Cl coverage. We computed bias as the 
mean of the simulated estimates minus the true value. 
We computed the coverage of any individual Cl by tal- 
lying the number of times the true population number 
fell inside the CL For the pooled and stratified estima- 
tors, we tallied the number of cases for which the bias 
was >5%. Likewise, we tallied the number of cases for 
which the coverages for estimators were <0.85 (consid- 
ered poor) and <0.80 (considered very poor). 
Analysis of SY201 1 data 
We evaluated precision using the preferred estimator 
(determined from the simulations) that was applied to 
real data from SY2011; these data had more irregulari- 
ties than the simulated data. For this application, we 
determined the age-by-stock proportions from the data, 
not as the product of age and stock proportions. We 
measured precision as the half-width of a (l-a)100% 
Cl expressed as a percentage of the point estimate 
(Find for individual CIs or Pjoj values for joint CIs). Re- 
searchers often set a stringent goal of a Cl half-width 
<10% of the estimate. For management purposes, it is 
recommended that salmon stocks have unbiased abun- 
dance estimates with a coefficient of variation of 15% 
or less (Crawford and Rumsey^). For a 90% asymptotic 
Cl (which indicates a critical value of the t distribution 
at 1.645), it follows that 
|W - W| < 1.645se < 1.645(0. 15)W < 0.25W (12) 
or 
|W-W|/W<0.25 (13) 
(i.e., half of the width of the Cl interval should be <25% 
of the estimate). We compare the Pjnd and Pjoi values for 
all CIs with 0.10 and 0.25. To determine whether Pjnd 
was related to the number of fish sampled or estimated 
size of the target group, we fitted power curves, using 
the results from all cases. 
Results 
Simulations 
Performance of the pooled and stratified estimators 
was similar when the variable of interest had few 
categories, but the stratified estimators did better as 
complexity increased (Table 2). Detailed simulation 
results are provided in Suppl. Tables 3 and 4. All es- 
timators produced acceptable accuracy and Cl cover- 
age when numbers of wild fish were estimated by sex. 
Similarly, all estimators provided acceptable accuracy 
^ Crawford, B. A., and S. M. Rumsey. 2011. Guidance for 
monitoring recovery of Pacific Northwest salmon and steel- 
head listed under the federal Endangered Species Act, 117 
p. Northwest Region, National Marine Fisheries Service, 
NOAA. [Available at website.) 
