FISHERY BULLETIN: VOL. 78, NO. 3 



Member Systematic sample 



12 3 4 



1 .Vll^-^lS >'21=-^2S ^31=^38 3'41--^4S 



2 ^12 = -^58 ^22= -^68 >'32=-^7S 3'42 = -^8S • 



In this case k — 4 and n = 2. The yifs are averages 

 of 1-5 tows (Table 1). The resulting estimates of 

 variance apply only to these hypothetical popula- 

 tions and particular mixture of tows per average 

 iyij). It was not possible to construct similar 

 hypothetical populations for the other depth inter- 

 vals because of missing cells. 



Values of V (yran), V {ysO, and V (j^gys) for the 

 first hypothetical populations are shown in Table 

 2. Comparison of the precision of the three sam- 

 pling methods indicates that systematic sampling 

 would be the most precise (has lowest variance) 

 scheme for 8 of the 15 species. Ties occurred for the 

 other seven species. Assuming that each species 

 represents an independent observation, the sign 

 test indicated that systematic sampling gave 



Table l. — Number of tows taken during the Queen Charlotte 

 survey by stratum, systematic sample, member, and group of 

 hypothetical populations. 



91-145 



146-181 



>181 



Table 2. — Variances of means of catch (per 1.8 km towed) from 

 the first hypothetical populations of Queen Charlotte rockfish. 

 Calculations are made under random, stratified random, and 

 systematic sampling schemes. 



better results than stratified random sampling 

 and random sampling at the 1% level of sig- 

 nificance, and that stratified random sampling 

 did not give significantly better results than 

 random sampling. 



Because of the uneven distribution of tows per 

 transect, we organized the data in another fashion 

 to determine if the relative precision of the three 

 sampling schemes is affected by organization of 

 the data. 



We next grouped the data into three depth 

 intervals: 91-145 m, 146-181 m, and >181 m. In 

 order to avoid missing cells it was necessary to 

 create hypothetical populations of only two sys- 

 tematic samples with two members. We did so as 

 follows: X is^ = the average of catch (kilograrhs) 

 per 1.8 km of species s in depth interval d of all 

 tows in transects i and i + 1. The hypothetical 

 population of systematic samples of species s from 

 depth interval d is 



Member 

 (stratum) 



1 

 2 



Systematic sample 

 1 2 



J'li ~ -^ 1 and 2, s. d ^21 ~ ^ 3 and 4, s, d 

 yi2 — X ^ and 6. s, d J'22 ~ X ^ and 8, s, d • 



In this case k = 2 and n = 2. The yifs are 

 averages of 1 to 9 tows (Table 1). The values 

 of V (^ranK V (^stK ^^d V (jgyg) are shown in 

 Tables. 



The results indicate that systematic sampling 

 produces more precise estimates of rockfish densi- 

 ties than either random or stratified random 

 sampling. However, the sign test revealed that 

 systematic sampling is not significantly better 

 than stratified random sampling and only better 

 than random sampling at the 5% level of sig- 

 nificance. Stratified random sampling was not 

 significantly better than random sampling. While 

 systematic sampling appears to be the most pre- 

 cise of the three survey design schemes, there 

 were many cases in which two or more of the 

 schemes would be equally precise. In many other 

 cases little precision would be lost if either strati- 

 fied random or random designs were chosen. 



Results of 1977 Survey 



The 1977 survey design included both stratified 

 random and systematic sampling strategies. The 

 coast was stratified into three types of areas: high 

 density sampling, low density sampling, and no 



662 



