SEN: SAMPLING COMMERCIAL FISH LANDINGS 



where R , 



+ 72 W 



and i? 



l^y + ... + W {l _ 1)rlj + W (l+l)Ki + ... + W %i 



(19) 



i-^z*;, 



Thus i? y is obtained by omitting trip i from the 

 sample for sort j and calculating &.■ instead of R rj 

 as in Equation (16). 



Hence, for category j of a species 



or 



v(y 3 .) = w^o^ 



(20) 



where v x (Rj) and v 2 (-R/) are given by Equations (17) 

 and (18). 



For estimate of total over all sort groups for a 

 species 



y a „ = I y, 



AR 



(21) 



v(?4*) = I i;(iy + 2 1 1 cov(f v fy (22) 



A simpler formula viY^) = Z. v(Y„) can be used 



'j ' 



where subsamples from different categories are 

 from different boat trips and are, therefore, in- 

 dependent. 



It is, however, more reasonable to assume that the 

 frequency distribution of fish caught is more uniform 

 within a category so that cluster weight would be 

 approximately a constant within a category. If so, 

 the estimates of mean and total are given by 



Y 5R = I W&lL Wfi Y 5R = I Y } (23) 



J 3 3 



where y 3 = X W^fL W tJ ; 



Y 3 = 



^W^ W J 



1 W, 



(24) 



Wa 



and Wj is the simple mean weight of clusters in the 

 jth group. Where the assumption of constant cluster 

 weight within a category is not valid, the more 

 general results given in Equations (14) and (15) 

 should be used. 



Comparison of Methods: 



Ignoring Category Variation Versus 



Poststratification by Categories 



We will compare the efficiency of the estimators 

 (3), ignoring variation due to categories, with the 

 estimators (9), based on poststratification of land- 

 ings by categories at a port during a month. The 

 analyses were based on Eureka and Monterey data 

 for 1982. The coefficients of variation (c.v.) of mean 

 catch per cluster for a species based on categories 

 as domains of study (method 2) were in almost all 

 cases lower (Table 2) than ignoring category varia- 

 tion (method 1). Since method 1 results in under- 

 estimation of c.v.'s because sampling is actually 

 based on a stratified random sample instead of a 

 simple random sample, the increased precision of 

 method 2 is all the more striking. 



The c.v. of the estimated mean catch by sex-age 

 groups for a species for which the number of sam- 

 ple landings were MO (Table 3) were in all cases less 

 for method 2 than for method 1. It may, however, 

 be pointed out the c.v.'s are likely to be affected by 

 factors such as growth, maximum age, and max- 

 imum size of fish. These have not been considered 

 in this study. Thus, estimates based on categories 

 as domains of study proved more efficient than 

 ignoring categories altogether. Besides, method 2 

 has the added advantage of providing estimates by 



Table 2.— Coefficient of variation (c.v., in percent) of mean catch 

 by species at Eureka and Monterey based on the two methods 

 during 1982. 



1 Method 1, based on random categories (i.e., ignoring stratification by 

 categories). 

 2 Method 2, based on categories as domains of study. 



413 



