SEN: SAMPLING COMMERCIAL FISH LANDINGS 



Table 7.— V(y st )IV(y) as a function of L for the linear regression and for some actual 



data. 



It turns out that the division point is approximate- 

 ly the same for young as well as old widow rockfish. 

 For length-age data (1981) based on 444 females 

 (widow rockfish) landed at Eureka, the boundaries 

 using 2 and 3 strata are 



Stratum 



Boundaries 



Intervals on 



cum y£ 



1 

 31.5-47 cm 



17.70 



46.5-55 cm 



29.01 



Optimum Allocation Plan 



Double sampling with regression is more efficient 

 than single sampling (when the first sample is 

 measured for age alone) for the same cost if 



p 2 > 



44 

 c 



1 + 



(32) 



where P is the correlation between length and age 

 of fish, c and c are respectively the costs of aging 

 and measuring a fish. Assuming that the average 

 cost of aging a rockfish (including small and large 

 fish) is 6 min and of measuring it is 1.2 min 

 (estimates based on measurements by W. Lenarz of 

 Tiburon Laboratory), we have from Equation 

 (32) 



or 



p 2 > 0.5555 



p > 0.7453. 



For the three data sets (Table 7) the values of p 2 

 are respectively 0.7004, 0.6515, and 0.5278 so that 

 Equation (32) is approximately satisfied. However, 



neither p nor — - are large enough to suggest that 



double sampling will be much more efficient than 

 single sampling. 



We will illustrate the use of double sampling for 

 stratification by analyzing 1981 length-age data at 

 Eureka to estimate the proportion of female in age 

 group 11, based on a sample of 444 fish. For the 

 three length strata, h = 1, 2, 3 with stratum bound- 

 aries based quadratic fit of length on age are 31.5-43, 

 43.5-49, 49.5-55. (Note this is different than bound- 

 aries based on length only.) Also 



417 



