76 



Fisher/ Bulletin 100(1) 



and, therefore, m , 



mideff. Some statistical software 



packages for the analysis of complex survey data, such 

 as SUDAAN (Research Triangle Institute, 2001 ). generate 

 estimates of the design effect. 



Simulation tecimiques were used to examine the effect 

 that reducing the total number of fish measured during 

 a particular survey would have on the estimates of the 

 mean length and the effective sample size. Length mea- 

 surements consist of one or more subsamples from the fish 

 caught at each station. The simulated estimates of the dis- 

 tributions of m^,ij and R (given the actual fish measured 

 during the survey) were generated by randomly selecting 

 from every haul a maximum oik fish without replacement 

 from each subsample. If fewer than k fish were in a sub- 

 sample, then all were chosen. This was done 500 times for 

 k = 10, 30, and 100, and each run produced values of m^,„ 

 and R. 



To assess the precision of an estimated length distri- 

 bution, bootstrapping (Efron, 1982) was used to generate 

 95% confidence intei-vals for the proportion of fish in each 

 5-cm length bin. For each of 500 runs, n stations (the num- 

 ber of tows made during the survey) were randomly sam- 

 pled with replacement and the confidence interval for each 

 5-cm length bin was based on the resulting 500 estimates 

 of the proportion offish in that bin. Finally, bootstrapping 

 was used to examine how much the length of the QS'/r con- 

 fidence intervals would increase if a maximum of 10 fish 

 were selected from each subsample. 



Results 



Estimates of the effective sample size and associated sta- 

 tistics for survey-based estimates of the length composi- 



tion of cod in the Barents Sea are presented in Table 1. 

 The results indicate that for cod the estimated effective 

 sample size is small compared with the number of fish 

 measured. For example during the 1995 winter survey, 

 175,006 cod were caught, 47,286 were measured, and the 

 effective sample size was 313 fish or Q.T7( of the total 

 number measured (Table 1). The average effective sample 

 size for the winter surveys was 1.2 cod per tow and for 

 the summer surveys, 1.0 cod per tow. The estimated effec- 

 tive sample sizes for the Northeast Arctic haddock survey 

 data were, on average, approximately one fish per tow 

 (Table 2). 



The effective sample sizes for the survey estimates of 

 the length distribution of deepwater hake off Namibia and 

 off South Africa (Tables 3 and 4) followed the same pattern 

 as for cod and haddock in the Barents Sea. In particular, 

 the average effective sample size was 0.5 hake per tow for 

 the Namibian surveys and 1.3 hake per tow for the South 

 African surveys. 



The simulated distributions of mrr and R, which dem- 

 onstrate the effects of reducing the total number of mea- 

 sured fish on estimates of mean length, for the 1995 and 

 1999 winter surveys of cod in the Barents Sea are shown 

 in Figures 1 and 2. For example, if a maximum of 30 fish 

 were selected from each subsample at each station, then a 

 total of 11,123 fish would have been measured during the 

 1995 sui-vey compared with 47,286 fish that were actually 

 measured. For 1995, R = 19.96 and the 95^1 confidence in- 

 terval for R was (18.29, 21.63). As can be seen from Fig- 

 ure 1, all 500 simulated estimates of the mean based on 

 the reduced sample size were well within the 95"^ confi- 

 dence limits for R. When the number offish measured was 

 reduced to a maximum of 10 fish per subsample for a to- 

 tal sample of 2597 fish, the simulated estimates were also 



