FISHERY BULLETIN; VOL. 76. NO. 3 



by the coefficient of variation increased as the 

 transect interval increased and sample size de- 

 creased (Figure 3). The cost of a survey was assum- 

 ed to be proportional to the distance covered along 

 the transects plus 360 mi to and from port. Relative 

 efficiency was 10-' times the reciprocal of the pro- 

 duct of the coefficient of variation (C.V.) and rela- 

 tive cost, i.e., precision divided by cost. Efficiency 

 generally decreased as the transect interval in- 

 creased, but peak efficiency was obtained at a 

 transect interval of 3 mi. By interpolation, it can 

 be seen that a population estimate may range 10 

 and 2U7c (2 x C.V.) from the true population size 

 when surveys are run with transect intervals of 

 8.5 and 16 mi. respectively. 



Systematic sampling gave a consistently lower 

 coefficient of variation, or greater precision than 

 random sampling (Figure 4). The variability be- 

 tween model populations, indicated by the 

 confidence limits on the mean coefficient of varia- 

 tion, was greater for the random sampling error 

 (F,,^i^, ^5.44,P<0.05 12)for8ofthe 12 sample 

 sizes. Also represented in Figure 4 are the ex- 

 pected coefficients of variation for random sampl- 

 ing calculated from the model population 

 parameters (o-^ and yu.) by the following equation 

 with a finite population correction: 



C.V. = \k- (^^) 

 [i^ n \ N / 



where a- - the average variance of the number of 

 schools per transect in the 15 model 

 populations =1,154,636 

 At = the mean number of schools per tran- 

 sect = 835.3 

 n = the number of transects in the survey 

 N = total number of transects in the survey 

 area = 180. 



0.5C 



0.20 



STRATIFIED 

 SYSTEMATIC 



1 I M [— 



2 34 5 7 

 90 45 26 



60 36 



10 12 

 18 15 



20 

 9 



25 



30 

 6 



— I 1 — TronseCt 



40 Interval-miles 

 5 Number of Transects 



Figure 4. — Comparison of the results of the simulations of 

 random, systematic, and stratified systematic surveys. For ran- 

 dom surveys, the curve represents the expected coefficients of 

 variation calculated from the parametric variance of the model 

 populations (see text). 



For 1 1 of the 12 sample sizes, the expected value 

 was within 95''^ confidence limits of the mean ob- 

 served coefficient of variation. This close agree- 

 ment supports the validity of the method used to 

 obtain the coefficients of variation in the simula- 

 tions. There was apparently no significant differ- 

 ence between the coefficients of variation of the 

 systematic and stratified systematic surveys 

 (Figure 4). This was confirmed by analysis of var- 

 iance (Table 1,P>0.25 that there was no added 

 variance due to survey design). However, there 

 were significant interaction effects between sur- 

 vey design and model population (P<0.01 that 

 there was no added variance from this source) and 

 between survey design and the number of trans- 

 ects (P<0.05). 



An attempt was made to elucidate the interac- 

 tions involving survey design by performing 

 analyses of variance on subsets of the data. It was 

 found that for large sample sizes (transect interval 

 ^15 mi, or number of transects ^12) unstratified 



Table l. — Analysis of variance of the coefficients of variation from simulated systematic and 

 stratified systematic surveys of model northern anchovy populations. This is a mixed model 

 analysis of variance (Sokal and Rohlf 1969): survey design and number of transects are fixed 

 treatment effects and model population is a random effect. 



Source of variation 



SS 



df 



MS 



Significance level 



Ivlain effects; 



Sun/ey design 



Number of transects 



Ivlodel population 

 interactions; 



Design-number of transects 



Design-population 



Number of transects-population 

 Error 

 Total 



682 



