116 



Abstract — For most fisheries applica- 

 tions, the shape of a length-frequency 

 distribution is much more important 

 than its mean length or variance. 

 This makes it difficult to evaluate 

 at which point a sample size is ade- 

 quate. By estimating the coefficient of 

 variation of the counts in each length 

 class and taking a weighted mean 

 of these, a measure of precision was 

 obtained that takes the precision in 

 all length classes into account. The 

 precision estimates were closely asso- 

 ciated with the ratio of the sample 

 size to the number of size classes in 

 each sample. As a rule-of-thumb, a 

 minimum sample size of 10 times 

 the number of length classes in the 

 sample is suggested because the preci- 

 sion deteriorates rapidly for smaller 

 sample sizes. In absence of such a 

 rule-of-thumb, samplers have previ- 

 ously under-estimated the required 

 sample size for samples with large 

 fish, while over-sampling small fish 

 of the same species. 



Precision estimates and suggested sample sizes 

 for length-frequency data 



Hans D. Gerritsen (contact author)^ 

 David McGrath^ 



Email address (lor H. D. Gerritsen): hans.gerritsen@marine.ie 



' Fisheries Science Service, Marine Institute 

 RInville, Oranmore 

 County Galway, Ireland 



^ Commercial Fisheries Research Group 

 Galway-Mayo Institute of Technology 

 Dublin Road 

 Galway, Ireland, 



Manuscript submitted 17 May 2006 

 to the Scientific Editor's Office. 



Manuscript approved for publication 

 22 June 2006 by the Scientific Editor. 



Fish. Bull. 106:116-120(2007). 



Length measurements are fundamen- 

 tal to many aspects of fisheries sci- 

 ence. However, there is little formal 

 guidance on the appropriate size of 

 a length sample. Such guidance is of 

 particular relevance when the number 

 of fish available exceeds the number 

 that can be measured at a reasonable 

 cost, and a subsample needs to taken. 

 Clearly, the required precision of a 

 length sample depends on the purpose 

 of sampling. In order to identify modes 

 of individual year classes for a length- 

 based assessment, the precision of the 

 sample needs to be quite high. Sample 

 sizes of more than 1000 are neces- 

 sary to identify more than half the 

 modes in a typical length distribution 

 (Erzini, 1990). A sample size of at 

 least 100 adult fish was recommended 

 for age-based stock assessment pur- 

 poses (Anderson and Neumann, 1996), 

 although the authors did not mention 

 how they arrived at this number. 



Regardless of the type of assess- 

 ment that is used, the shape of the 

 length-frequency distribution is of 

 interest, rather than simple sum- 

 mary statistics such as the mean 

 or the variance. For this reason, it 

 has proved difficult to quantify what 

 constitutes a representative or ad- 

 equately precise length distribution. 

 Some studies have attempted to find 

 minimum or optimum sample sizes 

 by comparing samples to an expected 

 distribution (e.g., Muller'; Gomez- 

 Buckley et al.2; Vokoun et al., 2001). 

 However, the true distribution is 

 usually unknown, and dissimilarity 



from the expected distribution does 

 not necessarily indicate an imprecise 

 sample. In addition, these methods 

 provide only indirect measures of pre- 

 cision that are difficult to evaluate 

 objectively. 



Thompson (1987) used the precision 

 of a sample explicitly to establish an 

 appropriate sample size. Thompson 

 proved that a sample size of 510 is 

 sufficient to be 95% confident that all 

 estimated proportions in a multinomi- 

 al distribution are no more than 5% 

 from the true proportion. However, 

 Thompson based this figure (n=51) on 

 a worst-case scenario, which, in the 

 present case, is a length-frequency 

 distribution that is evenly apportioned 

 over three size classes. Because this 

 is not the typical shape of a length- 

 frequency distribution used in fisher- 

 ies science, Thompson's measure of 

 precision is too conservative for the 

 vast majority of cases. 



For most fisheries applications, it 

 would be more useful to define the 



' Muller, H. 1996. Minimum sample 

 sizes for length distributions of the catch 

 estimated by an empirical approach. 

 ICES CM 1996/J12, 18 p. 



•^ Gomez-Buckley, M., L. Conquest, S. 

 Zitzer, and B. Miller. 1999. Use of 

 statistical bootstrapping for sample size 

 determination to estimate length-fre- 

 quency distributions for pacific albacore 

 tuna (Thuniuis alalunga). Final report 

 to National Marine Fisheries Services, 

 FRI UW 9902, 7 p. Website: http://www. 

 fish.washington.edu/research/publica- 

 tions/pdfs/9902.pdf (accessed 31 March 

 2006). 



