Statistics on the raw data and on the two transformed distributions 

 are given in table 2, and the relations of the means and standard devia- 

 tions of the two sets of transformed catches are shown graphically in 

 figure 3. It is at once apparent that both transformations have significant- 

 ly reduced the correlation between the standard deviation and the mean. 

 (For instance, the logarithmic transformation has reduced the correla- 

 tion coefficient of the nnean and standard deviation to -. 37, which is not 

 significant, ) The normalizing effect of the transformations is indicated 

 in figure 4, in which the raw data distributions are plotted with the distri- 

 butions of the transformed catches. Both sets of transformed data in- 

 dicate a tendency to depart from normality, but this does not appear to 

 be serious. Inasnnuch as there is little to choose between the two 

 transformations, we will use the less tedious logarithmic transformation 

 in estimating the variance of longline catches of yellowfin tuna. 



VARIATION OF THE YELLOWFIN CATCH OF A SINGLE 



SET OF LONGLINE GEAR 



Having selected a logarithmic transformation as the most 

 practical way to overcome the effect of schooling of yellowfin on the 

 variability of longline catches of that species, we now consider the 

 problem of estimating the variance of catches made by the longline gear 

 used by POFI. Estimation of the variance of the results of any sampling 

 technique is best effected by consideration of replicate samples. These 

 were not available, and as a substitute individual sets of gear were sub- 

 divided into 2 or 4 subsets, each subset consisting either of the sum of 

 the catches of alternate baskets or of every fourth basket. This scheme 

 was adopted in order to avoid bias due to the longer time that one end 

 of a series of baskets was fished. / 



The variance of a single subset was estimated by applying a 

 standard analysis of variance (Snedecor 1948) to the logarithmically 



"/ The subdivision of sets into subsets by combining alternate baskets 

 raises the question of disturbing the relation between a and the mean 

 by breaking up runs of fish that might include the ends of two adjacent 

 baskets. This does not appear serious as the double distance be- 

 tween the end hooks of adjacent baskets, as pointed out, considerably 

 reduces the probability of disturbing a run, i.e. , the runs are already 

 broken up in the field before the application of the analysis. 



