the 350 baskets yield a value of . 055, considerably smaller than the 

 value of .212 obtained by averaging the two values for commercial fish- 

 ing. Very likely this difference was largely caused by failure to rigidly 

 control the conduct of each fishing operation in the instance of the 

 commercial fishing, thus increasing the variability of the catches. 

 This probably arose in part because commercial operators would have 

 no particular reason to fish in an identical manner each day, and 

 furthermore precise control would probably be more difficult when fish- 

 ing 350 units of gear than with 40-80 units of gear. Differences in gear 

 design and differences in the spatial distribution of the fish between 

 the central Pacific, where the POFI fishing was carried out, and the 

 western Pacific, where the commercial fishing was done, may also 

 have introduced additional variability. 



The demonstration that the same estimate of variability cannot 

 be applied to situations as widely different as small experimental sets 

 of fishing gear and large commercial sets indicates that our results 

 will not be vallfd elsewhere unless the general conduct of the fishing is 

 reasonably identical. The general method of determining the variabil- 

 ity does, however, appear to have wide application, even though the 

 specific numerical results obtained apply only to the fishing carried 

 out by POFI. 



SETTING FIDUCIAL LIMITS ON THE CATCHES 



The average a (.229) of the 20-basket POFI longline sets derived 

 in the previous section appears to represent the best basis for setting 

 fiducial limits on the catches of this type of gear when it is used in 

 the same manner. From this estimated cr fiducial limits can be estimat- 

 ed for any station based on 20 to 80 baskets of gearo 



If it is desired to set 95-percent confidence limits on a catch 

 based on 20 baskets of gear, the 2 cr limits (+.458) are converted to 

 ratios by using the antilogs, giving fiducial limits of 35 percent 

 (100 X 1/2.87) to 287 percent (100 x 2.87). Applied to a catch of 10 fish 

 per 100 hooks, the 95-percent confidence limits would be 3.5 to 28. 7 

 fish per 100 hooks. To estimate the fiducial limits of a set of a number 

 of baskets different from 20 it is only necessary to follow the above pro- 

 cedure after adjusting the value of 2 cr by the formula where N is the 



19 



