230 



Fishery Bulletin 100(2) 



primary sampling unit in a population of season-permit 

 anglers or boat owners (i.e. party-boat owner.s or per.son- 

 al-boat owners) was an angler or a boat owner, and the 

 secondary sampling unit was a fishing day. We selected 

 anglers or boat owners by simple random sampling with- 

 out replacement from a list of anglers or boat owners, and 

 asked a sample of anglers or boat owners to record catch 

 data on all fishing days throughout the survey. Because all 

 the secondary sampling units were surveyed, we regard- 

 ed this as a single-stage cluster sampling procedure (Co- 

 chran, 1977). 



Estimation of total catch by month 



V{R,J- 



N N-n 



Mr 





(2) 



This variance estimator is obtained by dividing Equation 

 6.9 in Cochran ( 1977, p. 155 ) by the total number of fishing 

 days in the /i'th month M^,. In Equation 2, M,. is unknown; 

 hence we approximated the variance estimate by using 

 the estimator of M/, as follows (Thompson, 1992, p. 621: 



ViR,^ = —± 



N-u 



NMpiUi - 1) t" 



^iC,,-Mj,f, 



(3) 



Estimation for season-permit anglers or boat owners The 



principal notations for estimation of the total catch for 

 season-permit anglers or party-boat owners are as follows 

 (Cochran, 1977; Pollock et al., 1994): 



N = total number of sampling units (season-permit angler 

 or party-boat or personal-boat owner; known number); 

 n = sample size drawn from the population A'^; 



M). = total number of fishing days in the population in /(•th 

 month (to be estimated); 



M,;, = total number of fishing days in kth month of selected 



/th sample; 



M^_ = mean number of fishing days per sampling unit in 

 kih month (to be estimated); 



C^f. = number offish caught by ;th sample in /;th month; 



R/^ = catch rate of /?th month (to be estimated); 



Cj,"' = total catch by season-permit anglers or by party- 

 boat owners or personal-boat owners in A'th month 

 (to be estimated). 



The catch rate is the number offish caught per sampling 

 unit each day. For logbook surveys, the ratio of the mean 

 is the preferable estimator of catch rate (Jones et al.,1995; 

 Pollock etal., 1997). 



The ratio and the variance for the catch rate is estimated 

 by 



R, 



X—' " 



I,.l^-'- 



(1) 



where M^, = NMj. The variance of M^. is estimated by 

 ViM/. ) = N'ViM,. ). where M,, is the mean number of fish- 

 ing days per sampling unit in /;th month. The estimator 

 and the variance are as follows (Cochran, 1977, p. 249, 

 fromEq. 9A.2): 



V(M,) = 





Nnin-1)'^ ''■ '• 



(4) 



(5) 



The total number offish caught in A'th month is estimat- 

 ed by 



CI"' = Mi,Ri, = NM,M,, 



T.J'- TJ- N 



:7V- 





Ic.. 



(6) 



This results in an unbiased estimator. Wlien the total 

 number of fishing days M,. is unknown, the ratio estima- 

 tor coincides with the unbiased estimator. The variance is 

 evaluated by (Cochran. 1977, p. 249, from Eq. 9A.2): 



