COMPARISON OF YELLOWFIN TUNA OF HAWAIIAN WATERS AND THE AMERICAN WEST COAST 363 



400 



600 



800 



1200 



1400 



1600 



1800 



TOTAL LENGTH 



FiGTJRB 6. — Relations between head length 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 Godsil's 

 curvilinear regression for west-coast data, while heavy broken line is similar regression fitted to Hawaiian data. 



A detailed analysis of covariance is not neces- 

 sary to arrive at the conclusiou that with respect 

 to these dimensions the samples from the Hawaiian 

 Islands are different from the samples from the 

 west coast. It is quite obvious from the plots 

 of the mean values for each 10-cm. size class 

 (figs. 6 to 10) that the head length and the dis- 

 tances from snout to the fin insertions are sig- 

 nificantly shorter for Hawaiian than for west- 

 coast ycllowfin tuna at the larger sizes. If a 

 statement of probability is desired to test a null 

 hypothesis respecting difference between regions, 

 one may proceed in a manner similar to that 

 suggested above in the case of pectoral-fin lengths, 

 confuiing attention for sake of simplicity to the 

 larger sizes of tuna, say over 800 mm. in total 

 length. 



Considering fish of size classes between 800 mm. 

 and 1,600 mm. in total length, for which specimens 

 were available both from the west coast and from 

 Hawaii, the points for the mean values of each 

 10-cm. length class of Hawaiian fish fall below the 

 values expected on the basis of west-coast data in 



all cases for head length (fig. 6), snout to insertion 

 of anal (fig. 7), snout to insertion of second dorsal 

 (fig. 8), and snout to insertion of ventral (fig. 9). 

 Since there are 8 such points for each dunension, 

 and under a null hypothesis they might equally 

 well be above or below the value expected from 

 west-coast data, the probability of the observa- 

 tions on the hypothesis is (M)'=2cg for ^ach di- 

 mension, which is unlikely. For snout to inser- 

 tion of first dorsal, one point (900-mm. size class) 

 falls barely above the expected value; the prob- 

 ability of having at most one point above the 

 expected value under the null hypothesis is 



(K)H8(K)'=2-|- 



By the conventional methods of analysis of 

 covariance (Kendall 1946, p. 237 ct seq.), we may 

 also test for each of the dimensions the null 

 hypotheses (1) that the sample from the west 

 coast and the sample from Hawaii may both be 

 represented by a single linear-regression equation 



