386 



Fishery Bulletin 9 1 (2). 1993 



Table 2 



Optimal sample sizes of length and age samples and min. £ 

 (£. loss function) subject to fixed total cost, C=$229.15, for 

 three different age subsampling schemes. Age-length key 

 dataset is listed in Table 1. Per-unit cost of observing a 

 length sample, c,=$0.15. Case 1 |u>,|=|l.U,l.l,H; Case 2 

 (H> i )=(10,30,30,10,l,l); and Case 3 |u>,|=| 1,1,1,1,10,601. 



Improvement of precision f'i I" vs. 

 Fixed-age subsampling 36.26 



Proportional-age 

 subsampling 4.92 



39.15 



4.23 



Fixed-age 

 subsampling 



n 



N' 

 ..£ 



Proportional-age n' 



subsampling N* 



min. £ 



103 



179 

 0.0061 



28.57 



19.12 



106 106 104 



146 141 172 



0.0091 0.2156 0.0154 



103 103 



177 183 



0.1370 0.0136 



" % = percent difference of min. ./'between length-based sam- 

 pling design and fixed or proportional-age subsampling. 



different between length-based age and proportional 

 age subsamplings in Cases 1 and 2. In Case 3, the cost 

 efficiency of length-based age subsampling increases 

 subtantially over proportional-age subsampling. 



Discussion 



To draw a general conclusion, many different sets of 

 w^'s and full matrices of W also were investigated. The 

 results from these additional analyses were similar to 

 that of Tables 2 and 3. In general, the length-based 

 age subsampling is superior to either fixed- or propor- 

 tional-age subsampling. However, precision improve- 

 ment and cost efficiency depend on the weights placed 

 on particular age-classes. Total cost will change in ac- 

 cord with the different weights and desired precision. 

 A higher total cost should be allowed for cases where 



sampling is designed to improve the precision of highly 

 variable estimates, usually young and old age-classes. 



A larger budget will increase precision of the esti- 

 mates, especially for highly variable age-classes; how- 

 ever, as Lai (1987) showed, there is a point of dimin- 

 ishing returns as the budget increases (Fig. 1). For the 

 examples used in this paper, precision improvement is 

 marginal when total cost (C) increased beyond $40 for 

 Cases 1 and 3, and beyond $120 for Case 2. Kimura 

 (1989) showed that satisfactory results from cohort 

 analysis can be obtained at low sampling levels (i.e., 

 total cost) provided that the representativeness of the 

 samples can be maintained. 



It is difficult to compare the methods of Jinn et al. 

 (1987) with those of this paper because the Bayesian 

 approach and classic sampling techniques are derived 

 from different theoretical backgrounds. Nontheless, the 

 results obtained from this paper are similar to that of 



