388 



Fishery Bulletin 91(2). 1993 



strata; see Quinn et al. 1983) produces unbiased esti- 

 mators if all strata are sampled. The project-and-add 

 method uses the concept of a stratified, random sam- 

 pling technique (Cochran 1977). Therefore, Cochran's 

 rules (Cochran 1977:98) of optimal allocation for strati- 

 fied random sampling can be applied. In a given stra- 

 tum, take larger length and age samples if (1) the 

 stratum is larger, (2) the stratum is more variable 

 internally, and (3) sampling is cheaper in the stratum. 

 The first two rules are the basis of the Neyman alloca- 

 tion (Cochran 1977:99). The sampling-rate method pro- 

 posed by Quinn et al. (1983) built upon the first rule 

 and can easily incorporate other rules in the sampling 

 program. 



It is clear that the number of strata and variability 

 (vartot or loss function) of each stratum should be 

 evaluated first for designing ALK sampling. Then, the 

 total cost is allocated into various strata according to 

 Cochran's rules. Once the total cost for each stratum 

 is determined, an optimal sampling design for ALK 

 can be applied. The sampling rate method of Quinn et 

 al. (1983) can be used to collect the optimal length 

 sample size from clusters. After pooling the length 

 samples, a length-stratified subsample is collected for 

 ageing. 



Acknowledgments 



I thank D.K. Kimura for his help with derivation of 

 the covariance. Thanks to M. Sigler for his construc- 

 tive comments on an earlier draft. This paper is par- 

 tially supported by the U.S. Agency for International 

 Development, Fisheries Stock Assessment CRSP (DAN- 

 4146-G-SS-5071-00). 



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