Gerritsen and McGrath: Precision estimates and suggested sample sizes for length-frequency data 



119 



Blue whiting 



Norway pout 



Poor cod 



1 — I — I — I — \ — \ — r 



5 10 20 30 



r==0 00; P=0,88 



1 I \ I I I T 1 — I — I — I — I — I — r 



5 10 20 30 5 10 20 



r==0.06; P=0.03 



Number of length classes 



> 



o 



Blue whiting 



Norway pout 



1 — I — I — I — I — I — r 



30 5 10 20 30 



Poor cod 



r-=0 29. P<0 001 



15 20 25 30 35 14 



"1 — I — r 



18 



22 26 10 12 14 16 1 



Mean length (cm) 



Figure 2 



The sample sizes of subsamples taken on the survey were correlated with the number of length classes in 

 the samples of haddock iMelanogrammus aeglefinus) and poor cod iTrisopterus minutus), but not signifi- 

 cantly so for blue whiting {Micromesistius poutassou) and Norway pout iTrisopterus esmarkii) (top row). 

 There was considerable variation in the mean weighted coefficient of variation (MWCV), which correlated 

 with the mean length offish in the samples (bottom row). The solid lines represent linear regressions and 

 the dashed lines indicate the sample sizes and MWCV that would have resulted from a sampling scheme 

 where the sample size was chosen to be 10 times the number of length classes in the distribution. The 

 coefficients of determination, r-, are given together with their P-values. 



classes in the sample, the choice of the interval of the 

 length classes will determine the precision. Although 

 increasing the size of length intervals will reduce the 

 MWCV, this action will result in a loss of information 

 which is undesirable. The cost of sampling, the detail 

 required, and the purpose of the data collection need 

 to be considered before the required precision level can 

 be determined for applications other than the present 

 example. 



Without formal guidance on the appropriate sample 

 size, the sample sizes chosen were, at best, weakly 

 correlated with the number of size classes in the sam- 

 ples. It appears that the samplers under-estimated 

 the required sample size for samples with large fish, 

 whereas samples of smaller fish of the same species 

 were over-sampled. This tendency to under-estimate the 

 sample size may be related to the fact that the volume 

 of a sample increases with the cube of its mean length; 

 therefore a sample size of large fish may appear to be 

 larger than the same number of small fish. In addition, 

 samples with large fish tend to be spread out over a 



larger number of size classes, thus requiring higher 

 sample numbers. 



In practice, it will be difficult for a sampler to esti- 

 mate both the number of size classes and the number 

 of fish in a sample. Therefore, the Marine Institute in 

 Ireland is developing a software application that al- 

 lows samplers to examine the length frequencies of the 

 samples directly after they have been measured. The 

 software estimates the weight of the suggested sample 

 size for each distribution. Because size distributions 

 tend to be similar on consecutive hauls, the sampler can 

 gain an insight into the required weight of an appropri- 

 ate sample for each species and size category. 



The information contained in a length-frequency dis- 

 tribution is largely a function of sample size. The pres- 

 ent method allows the amount of information contained 

 in a length-frequency distribtuion to be quantified in 

 terms of precision, allowing samplers to make informed 

 decisions on the sample size that is required to obtain 

 an adequate estimate of the length-frequency distribu- 

 tion of a particular catch. 



