FISHERY BULLETIN: VOL. 84, NO. 2 



= 1.2 min, Cj = 



w 1 = 



Si = 



3.8 min, c 2 = 3.8 min, and c 3 = 8 min 



0.0653, w 2 = 0.5451, and w 3 = 0.3896 



0.1825, s 2 = 0.4966, s 3 = 0.1503, 



and s = 0.4343 



where w lf w 2 , and w 3 are the proportions of fish in 

 the sample, c is the cost of measuring a fish and 

 c 1( c 2 , c 3 are respectively the costs of aging them in 

 the three length groups. From Cochran (1977, p. 

 331) we have 



(Pst) = 



J_ 

 C* 



I w h s h y/c h + (S 2 - Z w h sl) m \f& 



(33) 



= 0.8915/C* 



where p st is the estimated proportion and C* = 

 E(c) = £"(c n + Z. c h n h ) with nj = 14, n 2 = 120, 



n 3 = 48 and ri = 444. The efficiency of double 

 sampling with respect to single sampling is given 



by 



Vsr,(p)IVmm(Pst) = 1 - 21 



where v srs (p) = 0.1885/-^-, i.e., double sampling 



is 27% more efficient than single sampling. How- 

 ever, as noted by Ricker (1975) the increase in ac- 

 curacy achieved by combining a length sample with 

 a smaller age sample may not be great unless fish 

 used for age determination is taken from the same 

 stock, during the same season and using gear having 

 the same selective properties as the length-fre- 

 quency samples. This point will generally be met if 

 fish are subsampled systematically for age from fish 

 arranged in increasing (or decreasing) order of 

 length from a port-month stratum. Our studies have 

 shown that the best length-age fit does not change 

 significantly if age determination is made on every 

 other fish arranged in ascending order of length. 

 It is difficult to obtain reliable estimates of the 

 numbers at age for the extremely small or larger 

 sizes because lengths cannot be used for estimating 

 age. There is need for search for other auxiliary 

 variables (other than length) associated with age and 

 for increase in sampling rate at the tails. In double 

 sampling where lengths are obtained in the first 

 phase, a number of small clusters may be used 

 separated in space and time to provide a large 

 number of fish at the tails for estimating numbers 

 at age. The extent of bias in estimation of numbers 



at age through length-age key approach may be 

 tested by Monte Carlo simulation. 



COLLECTION OF REPRESENTATIVE 

 DATA-MEASUREMENT ERRORS 



Owing to uncertainty of arrival times and vary- 

 ing unloading procedures, no objective method is 

 available to ensure random sampling of the trips. 

 When the vessels return to port, they are usually 

 available for sampling except when they are tran- 

 shipped immediately due to inclement weather, lack 

 of processing facilities, uncooperative buyers, or 

 unscheduled deliveries at short notice. It is, how- 

 ever, not unreasonable to regard a set of sample 

 landings during a week at a port as random and 

 representative of the totality of all landings at the 

 port for the month. 



Although rockfish are landed by categories, which 

 are mostly determined by market agreement based 

 on size, composition, and condition of the catch, the 

 number of categories per delivery cannot be pre- 

 determined. This number would vary from delivery 

 to delivery and from dealer to dealer. Also, there 

 are no guarantees that a complete boat sample, 

 covering clusters from each category, can be taken 

 on any sampling day and some of the categories are 

 actually missed in sampling. Some of the possible 

 reasons for missing the categories are 1) when 

 landing weight would not occur during regular 

 hours, one of the sorts may have already been 

 shipped before the sample could arrive at the spot; 

 2) often one of the sorts may be quite small and there 

 may be a buyer at the dock waiting for the fish to 

 be taken away; 3) while the sampler is working on 

 a sort, the other sort(s) will have either been pro- 

 cessed or shipped away; and 4) the sampler may 



418 



