SEN: SAMPLING COMMERCIAL FISH LANDINGS 



The variation among clusters (sf) in different land- 

 ings at Eureka and Monterey for 1978 was in almost 

 all cases greater than between clusters within the 

 same landings (Table 4); also the optimum number 

 of clusters per boat for estimating species number 

 was mostly unity. Data from other ports follow the 

 same pattern. Since a minimum of two clusters is 

 needed to provide an estimate of between cluster 

 within trip variation, a subsample of two clusters 

 per category per trip is recommended. In practice, 

 it is preferable to select a systematic sample of 

 clusters separated in time. 



VARIANCE COMPONENTS: 

 SPECIES-AGE AND LENGTH GROUPS 



A two-level nested analysis of variance for length 

 and age with unequal sample size for species based 

 on sample landings at ports during 1979 (Table 5) 

 shows that both the variation, because of length and 

 age, was generally high among sample landings 

 compared with clusters within landings. Also, varia- 

 tion between clusters was generally of the same 

 order as within clusters, and the optimum number 

 of clusters was <2. Data for other ports and years 

 (not shown in the table) mostly supported the 

 findings. 



On the whole, both the variation in species number 

 (Table 4) as well as in length and age (Table 5) was 

 consistently high among sample landings relative to 

 between clusters within landings; also, variation 

 among clusters was not significant compared with 

 variation within clusters. Hence, for precise estima- 



tion of species number, length, and age„composition 

 for a category at a port during a season, data should 

 be collected from a large number of landings and 

 from few clusters (two) from a category within a 

 sample landing. 



RELATIVE EFFICIENCY OF ESTIMATORS 

 USING POSTSTRATIFICATION 



Consider the three estimators of total catch for 

 a sort of a species at a port during a year. We will 

 use the same selection procedure with poststratifica- 

 tion by sorts but different estimation procedures. 



Y, = 



7I» 



n j i=1 



Vij 



(27) 



^ W&q Wj 



Yj 



i w* 



W: 



Y k = RjWj 



(28) 



(29) 



where Rj is given by Equation (16), y {j is the simple 

 mean of species number per cluster for sort j from 

 the ith sample, Yj is the same as Equation (24) with 

 a constant cluster weight within a sort group, and 

 Yj is a more general estimator based on the 

 assumption that cluster weight varies among trips. 

 For v(Yj) use W 2 j v 2 {R ] ) where v 2 (Rj) is the jack- 



Table 5.— Two-level nested ANOVA of length and age of 

 pie sizes by ports during 1979. MS = mean square; F 

 observed probablity level. 



species with unequal sam- 

 = F-RATIO, Statistic; P = 



415 



