LENARZ and ADAMS: SOME STATISTICAL CONSIDERATIONS OF TRAWL SURVEYS 



(2) 



V {yst ) - — }v~ ^st/" 



where V (5'st) = variance of the mean calcu- 

 lated from stratified random 

 sampling (J St), 



o,,* — 



1 



77 \2 



^^ = ht^) ,?i ,fi ^y^j ~ y.j ^ 



yj = '^ yijlk,and 

 1=1 



S' (Jsvs) 



sys' 



1 2 (y. - yy 



(6) 



where S^ (3' sys) - estimate of V (>'sys), 



>', = S yJk, and 

 1=1 



v(ysys) = T s iy,-y) 



r,\2 



k 



(3) 



i-i 



where V (^-gys) 



yt. = 



variance of the mean calcu- 

 lated from systematic sam- 

 pling (^sys) , 



S yijin. 



7=1 



If k systematic samples are taken from a popula- 

 tion that is sufficiently large to ignore the finite 

 population correction factor then the variance 

 estimates become: 



S' (Xan) = S'ln (4) 



where S^ (jran) = estimate of V (>'ran)> 



sL = 2 s {y,j-y)' link-1), 



1=1 ;=1 



k n 



y= 2 2 yulkn, 

 j=i j=i 



s' (yst) - si. In 



where S^ (ysO = estimate of V (yst), 



(5) 



n k 



"st 



;^(^^ A ll ^^^>"^.P' 





Results of Pilot Survey 



In the case of the Queen Charlotte survey, two 

 random starting points were chosen and then tows 

 were made along four transects for each of the two 

 systematic samples. The transects within a sys- 

 tematic sample were approximately 16.1 km 

 (10 mi) apart and bottom topography dictated 

 some deviations from the desired transects. Be- 

 cause preferred depths differ among species of 

 rockfish (e.g., Sebastes alutus is relatively scarce 

 in shallow waters, while S. proriger is relatively 

 scarce in deep waters), attempts were made to dis- 

 tribute sampling effort among 18.3 m (10-fathom) 

 depth intervals within the depth range of concern, 

 91.4 m (50 fathoms) and 292 m (160 fathoms). 

 Examination of the data indicated that, to obtain 

 reasonable sample sizes, observations should be 

 divided into only three depth intervals: 91-145 m 

 (79 fathoms), 146-181 m (80-99 fathoms), and 

 >181m. 



The Queen Charlotte data were organized in 

 two ways to examine the relative precision of the 

 three sample schemes. We first arranged tows at 

 depths >181 m into a hypothetical population of 

 four systematic samples for each species. While 

 the original sample design called for two system- 

 atic samples, the two random starting points 

 resulted in all transects being about 8.1 km (5 mi) 

 apart. Each systematic sample contains two mem- 

 bers. Furthermore, each hypothetical population 

 is composed of x is = the average catch (kilograms) 

 per 1.8 km (nautical mile) of species s of all tows 

 taken >181 m in transect i of the Queen Charlotte 

 survey. Under the preceding definition the hypo- 

 thetical population of systematic samples of spe- 

 cies s is 



661 



