358 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



the same size range from different regions, one will 

 tend to reduce the apparent difference due to the 

 failure of the regression equation employed to com- 

 pletely correct for differences in size composition of 

 the samples. 



There is probably no purely routine method of 

 analysis which may be safely employed in com- 

 paring body dimensions of timas from different 

 regions. The selection of regression equations, 

 and the application of other statistical techniques, 

 should be undertaken with proper consideration of 

 the particular data at hand, the hypotheses regard- 

 ing it that are to be tested, and the precision 

 required in each particular case. 



RELATIVE GROWTH OF HAWAIIAN 

 YELLOWFIN TUNA 



Schaefer (1948) and Schaefer and Walford 

 (1950) fitted linear regression lines to head length 

 and distances from tip of snout to insertions of the 

 first dorsal, second dorsal, anal, and ventral fins 

 plotted agamst total length for yellowfin tuna from 

 the west coast of Central America and from the 

 Atlantic coast of Africa. Godsil (1948) found more 

 extensive data on the same dimensions of yellow- 

 fin from the American west coast to be better fitted 

 by a regression line of slight curvilinearity. To the 

 Hawaiian data have been fitted Unear regressions, 

 the constants for which are given in table 2, as well 

 as curvilinear regressions of the type selected by 

 Godsil. Equations for the latter and corresponding 

 standard errors of estimate (s) about them are as 

 follows: 



Head length y= 69. 54+0. 20805i-164I9/i s= 6.02 



Snout to insertion first dorsal v= 80. 34+0. 22S6Sj-16997/j j= 7.77 



Snout to insertion second dorsal y= 17. 28+0. 4S226j+11445/t »=10. 94 



Snout to insertion ventral. y= 78. 87+0. 23340j:-16778/i s= 7.96 



Snout to insertion anal !/ = 109. 92+0. 49037i -25129/1 «= 9.32 



Over the range of sizes in our sample, the curvi- 

 linear regressions result in slightly smaller vari- 

 ances about them than the linear regressions; 

 but, as may be seen from the above equations or 

 from the graphs in the next section (figs. 6-10), 

 the differences between these curves and straight 

 lines are slight. Indeed, for snout to second dorsal 

 insei'tion the slight curvature of the regression is 

 opposite in direction to those fitting the data of 

 other dimensions and to that of Godsil for his 

 i\jnerican-west-coast fish (fig. 8). Fm-thermore, 

 the difference between the Hnear and curvilinear 

 regressions for this dimension is, for the Hawaiian 

 data, such as might arise by chance alone in 

 between 1 in 20 and 1 in 100 cases. 



The relations between body depth and total 

 length, diameter of u-is and head length, and 

 length of maxillary and head length seem to be 

 well described by linear regressions over the entire 

 size range. The statistics of these regressions are 

 tabulated in table 2. 



In each of these cases where linear regressions 

 fit the data, the y intercept of the regression line 

 differs significantly from zero. Furthermore, ex- 

 cept for depth of body on total length and length 

 of maxillary on head length, the difference is 

 sufficiently great that the expression as ratios of 

 the relation between variables would result in 

 a considerable error from this source. This 



Table 2. — Statistics of Hnear regressions of measurements of Hawaiian N. macropterus 



All logarithms are to base 10. 



jV=nuinber in sample. 



X, i/=means otx and y. 



Si', Sy', Sxy are sums of squares and products of deviations from the means i, y. 



Sx'j 

 6=^ =regression coefficient of y on x. 



»'=- —j^^^ — ""estimate of variance about regression line. 



' Only specimens 600 mm. and over ia.total length. 



