LENARZ and ADAMS: SOME STATISTICAL CONSIDERATIONS OF TRAWL SURVEYS 



Table 3. — Variances of means of catch (per 1.8 km towed) from 

 second hypothetical populations of Queen Charlotte rockfish. 

 Calculations are made under random, stratified random, and 

 systematic sampling schemes. 



Variance 



Population 



Depth 

 interval (m) 



Stratified 

 Random random Systematic 



Se5as(es alutus 

 S. alutus 

 S. alutus 

 S. flavidus 

 S. flavidus 

 S. flavidus 

 S. pinniger 

 S. pinniger 

 S. pinniger 

 S. pa uc is pin is 

 S. paucispinis 

 S. paucispinis 

 S. brevispinis 

 S. brevispinis 

 S. brevispinis 

 S. elongatus 

 S. elongatus 

 S. elongatus 

 S. proriger 

 S. proriger 

 S. proriger 

 S. babcocki 

 S. babcocki 

 S. babcocki 

 S crameri 

 S. crameri 

 S. crameri 

 S. zacentrus 

 S. zacentrus 

 S. zacentrus 

 S diploproa 

 S. diploproa 

 S diploproa 

 S entomelas 

 S. entomelas 

 S. entomelas 

 S. reedi 

 S. reedi 

 S. reedi 

 S. aleutianus 

 S^ aleutianus 

 S. aleutianus 

 S. helvomaculatus 

 S helvomaculatus 

 S. helvomaculatus 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



91-145 



146-181 



>181 



82.313 

 2.745.670 

 1,892.520 

 8.442 

 0.259 

 0063 

 257.220 

 0.507 

 0.001 

 2.657 

 1.560 

 0.260 

 60.440 

 8.703 

 2.328 

 0.129 

 0.327 

 0.001 

 1,019.197 

 5.152 

 0.002 

 2.090 

 3.241 

 49.730 

 0.001 

 0.057 

 0.061 

 0.006 

 0.220 

 29.261 

 0.000 

 0.000 

 0.165 

 0.006 

 0.609 

 0.048 

 0.000 

 0,302 

 30.710 

 000 

 0.002 

 0.087 

 0.000 

 0.001 

 0.022 



59.446 

 3,803.277 

 1,270.058 



12.750 

 0.193 

 0.063 

 234.198 

 0.759 

 0.001 

 3.987 

 0.287 

 0.197 



19,718 



13.020 

 2.194 

 0.100 

 0.317 

 0.001 

 686814 

 5.560 

 0.002 

 1.584 

 0,339 



50,671 

 0,001 

 0051 

 0,037 

 0006 

 0.217 



30.641 

 0.000 

 000 

 0.162 

 0.006 

 0.724 

 0.048 

 000 

 0.302 



30.710 

 0.000 

 0.002 

 0.057 

 0.000 

 0.001 

 0.024 



55.285 



1,125.770 



2,502.014 



0.102 



0.160 



0.063 



228.577 



0.400 



0.001 



1.503 



0.402 



0.121 



13.783 



1 1 .262 

 3.464 

 0.102 

 0,345 

 0.001 

 657.281 

 6.494 

 0.002 

 1.169 

 0.339 



24.671 

 0.001 

 0.029 

 0.074 

 0.006 

 0.217 



30.641 

 0.000 

 0.000 

 0.162 

 0.006 

 0.378 

 0.048 

 0.000 

 0.302 



30.710 

 0.000 

 0.002 

 0.018 

 0.000 

 0.001 

 0.020 



sampling. Areas in which historical fisheries data 

 indicated high abundances of important rockfish 

 species were assigned high density sampling. In 

 these areas, transects were set at 8.1 km (5-mi) 

 intervals. The typical high density area used in 

 the study was about 81 km ( 50 mi) long. Transects 

 in other areas were set at 16.1 km (10-mi) intervals 

 unless bottom topography precluded sampling. 

 Each transect was divided into four 91 m (50- 

 fathom) depth strata between 91 and 457 m 

 (250 fathoms). Sampled depths were then chosen 

 at random within each depth stratum of a tran- 

 sect. The number of samples within a depth 

 stratum was proportional to the bottom area of 

 that stratum. 



The survey design was based on several factors. 

 The large scale stratification along the coast was 

 an attempt to make sampling proportional to 

 expected densities of important rockfish. This 

 was done with the knowledge that there often are 

 positive correlations among means and variances 

 of fish densities. Depths were randomly chosen 

 because it was known that often within an area 

 densities of many species of rockfish sometimes 

 only occur over a narrow depth interval. Thus, 

 unless depths were chosen at random, bias could 

 occur. Sampling was proportional to bottom area, 

 because bottom area is used to convert fish densi- 

 ties to abundance estimates. Systematic transects 

 were taken to ensure adequate aerial coverage for 

 one intended use of the data, because of logistics 

 and the results of the pilot survey. 



Four high density areas had sufficient sampling 

 effort to be included in the study. Eight or more 

 adjacent transects were sampled in one or more 

 depth strata in each chosen area. Area 1 was 

 between lat. 34°33' and 35°19' N, area 2: lat. 

 35°19' and 35°59' N, area 3: lat. 39°7' and 

 39°53' N, and area 4: lat. 44°59' and 45°50' N. 

 If more than one sample was taken from a depth 

 stratum of a transect, one sample was chosen at 

 random for the study. As in the case of the first 

 Queen Charlotte hypothetical populations, pop- 

 ulations of four or five systematic samples of two 

 members each were created from the data. The 

 results again indicated that systematic samples 

 were slightly more precise than either random or 

 stratified random (Table 4). The sign test indi- 

 cated that systematic sampling was more precise 

 than random at the 1% level of significance and 

 stratified random at the 107c level. Stratified 

 random sampling was not significantly less pre- 

 cise than random. 



The data were also arranged into two systematic 

 samples with four or five members each. System- 

 atic sampling was more precise than random at 

 the 1% level of significance, but was not signifi- 

 cantly more precise than stratified random (Table 

 5). Stratified random sampling was not signifi- 

 cantly less precise than random sampling. 



Discussion 



The results of this study indicate that on a scale 

 of about 80 km along the coast systematic sam- 

 pling for rockfish is slightly more precise than 

 random sampling or a stratified random scheme 

 with regularly spaced strata of equal size and 



663 



