dEjri. osxmr LiLlvkj ov^iuiYiii*n.v^in.u r 1011 um^iyiiiuo 



average weight of sampled clusters 

 in the ith trip. 



If W x is a constant, its estimate w will be given by 

 w = 2 X 5! w ilk IZ. 2. m vj . In practice, N and M t 



i j k J i j J 



will not be known and will be estimated by N = 



wW - - W 



= WIW; M { = -zr respectively, if W l is a 



" w 



constant = w (say). 



Ratio Estimates of Mean and Total 

 The ratio estimate of mean catch (Y) per cluster 



is 



n n 



I mm I w t 



y, 



Y P = 



(1) 



I Mi I Wi 



where y x = 1 M^-/Z My = I W^/I ^ 



California Fish and Game. The reasons for failure 

 to collect the data are discussed in the section on 

 Collection of Representative Data-Measurement Er- 

 rors. The above estimators are, however, recom- 

 mended for use in situations where the problem does 

 not exist and, in particular, for single species where 

 the categories are based on size. The estimates of 

 error are given in Equations (4) and (5). 



Estimation Ignoring Category 

 Variation Within Sampled Trips 



Assume that a cluster is selected at random from 

 all possible clusters in a sampled trip. In other 

 words, we ignore categories altogether both in sam- 

 ple selection as well as in estimation. Valid ratio 



estimates Y^ of Y and Y^ of Y are respectively 

 given by 



Y,„ = 



1 Wi 



LR 



I Wi 



Vi „ w = 



W 



(3) 



The ratio estimate of total catch Y is 



W - 



Y « - i Y °- 



(2) 



The above estimators recommended for use are not 

 workable in rockfish sampling because the sampler 

 failed in almost all cases to subsample from more 

 than one category in a sampled trip as would be seen 

 from a sample of basic data for 1982 (Table 1) 

 available for Eureka from the Department of 



Table 1 .—Distribution of landing weights (lb) from all categories 

 and from the sampled category for Eureka for 1982. 



'Shows the code number of categories which are based on species, size, 

 and quality. 



Note: In all cases, only one of the categories could be sampled from a given 

 trip. In boat 1541 there was only one category (269) of fish. 



Note these equations are essentially the same as 

 Equations (1) and (2) except that we now assume 

 that a cluster is randomly selected from all possible 

 clusters in a sampled trip where W { is the total 

 landing weight from all categories for the ith boat 



trip in the sample (W = X W { ). In practice, the 



X 



sampler would tend to subsample from a category 

 which is accessible and is preponderant. This may 

 lead to some bias in the estimate though its contribu- 

 tion to the total error will be negligible, since this 

 would occur at the second stage of sampling. 



The estimates of variance of estimated total and 

 mean are approximately given by 



HY W ) = 



JL (1 . /l)8f + MLzJ^i 



n nm 



v(Y m ) ± (^) 2 v{Y m ) 



(4) 



(5) 



where s 2 h = Z. 



K\ 2 ®i- Y m ) 2 . 



W 



n - 1 



n — 



m 



i n 



w, 



2 „2 

 s 2i 



m,- 



(6) 



411 



