COMPARISON OF YELLOWFIN TUNA OF HAWAIIAN WATERS AND THE AMERICAN WEST COAST 367 



equation does not, for any dimension, accurately 

 describe both. It is quite evident that differences 

 may be expected among different samples from the 

 same region. The problem, then, is to determine 

 whether the differences between regions are greater 

 than might reasonably be expected among different 

 samples from the same region. In comparing 

 Hawaiian and west-coast data, where the differ- 

 ences are so large that the distributions of means of 

 subclasses (size groups) are completely separate 

 between the two regions for the most part, the 

 answer is fairly obvious from the graphs of the type 

 herein presented. In table 7 have been tabidated 

 the linear-regression coefficients for each of Godsil's 

 f3 samples, for my Costa Rican sample, and for 

 the Hawaiian sample. From this tabulation it 

 may readily be seen that the Hawaiian regression 



coefficients fall, for each dimension, well below the 

 lowest value encountered among the several west- 

 coast subsamples. 



Although in the case at hand we are spared the 

 need for an efficient means of comparing variation 

 between samples within a region with differences 

 between regions where a null hypothesis is not 

 valid for samples within the region, this will not in 

 general be true. The desirability of a test for 

 application in other, less-clear situations is suffi- 

 ciently great that some examination of the problem 

 seems warranted, particularly in view of the fact 

 that Godsil (f948) has already attempted to 

 develop and employ such a test. We wish, there- 

 fore, to consider the problem of measuring the 

 differences between groups where a null hypothesis 

 is not satisfied. 



800 



TOTAL LENGTH 



Figure lO.^Relations between distance from snout to insertion of first dorsal fin and total length. Solid circles represent 

 Hawaiian data; open circles represent Costa Rican data; solid triangles represent Godsil's west-coast data. Fine 

 solid line is linear regression line fitting west-coast data, while heavy solid line is linear regression line fitting Hawaiian 

 data. Fine broken line is GodsU's curvilinear regression for west-coast data, while heavy broken line is similar 

 regression fitted to Hawaiian data. 



