nSHfcKY BULLETIN: VUL. 84, NU. Z 



and si = Z (y lk - ^/(m, - 1); W = I W^n; 



/! - Z W,IW;f 2 = 





W,- 



w 



(7) 



We will consider an operationally feasible plan in 

 which sample trips at a port during a month are 

 poststratified into categories and clusters are sub- 

 sampled from each category; where one or more 

 categories are missed due to inadequate field staff 

 and/or management problems, clusters should be 

 selected from other boat trips containing the missed 

 categories. 



Assuming that the cluster weight of the unequal 

 cluster size varies over trips, i.e., w^ = Z Z w ijlc / 



J k 



Z m„ estimates of mean and total are 

 j 3 



n n 



£ Z wA Z wA 



(8) 



Z Wilwt Z Wi 



where R t = -=?- ; viY^) and viY^) can be obtained 

 similar to Equations (4) and (5). 



(11) 



j <k W* v ^' 



and 



v(Y 3R ) ± v(Y 3 ) + 2 Z Z cov(fy, f,). (13) 



Both v(^) and v(F 3 ^) are of standard forms and can 

 be obtained as in Equation (4). Similarly, v(Y 3 ) and 

 v(Y SR ) can be obtained. The covariance terms in 

 Equations (12) and (13) are ignored when the sub- 

 samples from different categories are from different 

 boat trips and are, therefore, independent. In rock- 

 fish sampling this was found true, because the sam- 

 pler failed in almost all cases to subsample from 

 more than one category. In general, for all fish 

 where sampling from more than one category per 

 boat trip is feasible, e.g., with few species-size- 

 qualities, Equation (13) should be used. 



Assume that the clusters vary in size over trips. 

 For any sort (say j ) 



Y k- 



Z w 13 r 13 iL w i3 



W J = R J W J (14) 



Estimation Based on 

 Categories as Domains of Study 



This method is almost as precise as proportional 

 stratified sampling if within each port-month 

 stratum (a) a minimum of four landings or boat trips 

 (n 3 > 4) is selected for each category and (b) the 

 landing weights are available by categories after the 

 season to serve as weights at the estimation stage. 

 The minimum number in (a) is mainly based on 

 limitations of field staff and budget restrictions. The 

 ratio estimates of mean catch per cluster, total 

 catch, and their errors, assuming clusters of equal 

 size and using categories as domains of study are 

 given by 



Y 3R = Z W^y/Z Wfi Y 3R = Z Yj (9) 



where y 3 = Z W^lJ. W l} (10) 



and 



y, 



= Z wdtdl. WJw. 



ir"iy-r xy^i) 



where iL = !*; A = Z iL-WyZ Wu. 

 y w ..' J y lJ i lJ 



(15) 



(16) 



If yij is small compared to N 3 and if the same sub- 

 sampling strategy is applied to each of the sample 

 landings, we have, ignoring contribution due to 

 second-stage sampling units, 



Vjffij) = 



n j( n j ~ 1) 



W 



(R^ - R 3 ) 2 . (17) 



Another estimator v 2 (R 3 ) is the jackknife 



v&lj) =  - Z (R i3 - - R 3 f (18) 



thi 



412 



