78 



Fishery Bulletin 100(1) 



280 300 320 340 



Effective sample size 



280 300 320 340 



Effective sample size 



280 300 320 340 



Effective sample size 



19 6 19 8 20 20 2 20 4 



196 198 200 202 20 4 



19 8 20 20,2 



Mean lengtfi (cm) 



Figure 1 



Simulated estimates of the distribution of the effective sample 

 size, m^,^, and of the mean length, R, when the total number of 

 fish measured is reduced for the 1995 winter survey in the Bar- 

 ents Sea. The top panel is when a maximum of/.' = 100 fish are 

 selected per subsample for a total of /»? = 30,403 fish m each run; 

 the middle panel, k = 30, m = 11,123; and the bottom panel, k = 

 10, m = 3911. The estimate of the population mean based on the 

 entire sample (m=47,286) is 19.96 and its 95"^^ confidence inter- 

 val is (18.29, 21.63). 



was approximately one fish per tow and it seems to 

 be typical that the effective sample size for estimating 

 length distributions is relatively small for trawl surveys. 

 For example, the effective sample size for trawl surveys 

 of haddock on Georges Bank was on average less than 

 0.5 fish per tow (Pennington and Volstad. 1994) and for 

 shrimp in a small area off West Greenland, about 3 

 shrimp per tow (Folmer and Pennington, 2000). 



The reason that the effective sample sizes were small, 

 and, therefore, the estimates of the length distributions 

 were rather imprecise, given the number of fish that 

 were measured, is that the lengths of fish in a haul 

 tend to be more similar than those in the entire popula- 

 tion. An additional factor is that the density of fish in 

 a sui-vey region is usually quite variable. To see this, 

 consider the equation for the expected value of var(i?). 

 If every fish is measured during a survey, then subject 

 to some assumptions, the expected variance of R when 

 n stations are sampled is given approximately by (Pen- 

 nington and Volstad, 1994) 



var(7?) = 



a:li + iM -i + (t: 



I M )p\ 



M 



where M = the expected mean catch per tow; 

 a'r,, = the tow-to-tow variance of catch; 

 M{= nM ) = the expected total number offish caught; 

 a'~ = the population variance of length; and 

 p = the coefficient of intrahaul correlation (see 

 Cochran, 1977, p. 209) for length. 



