DISTRIBUTION AND GENERAL NOTES ON THE SPECIES 28? 



From these considerations it would seem that if we assume the disparity in size beUveen the sexes 

 to be at least twice as great in Patagonian hake as it is in European hake, we shall not be far wrong. 



Turning back to direct comparison of the lengths of the two stocks irrespective of sex, the figures 

 for European hake being derived from Hickling's (1933) tables XIa and Xlb as previously stated, we 

 obtain the curves of percentage length frequency shown in Fig. 21 a. This shows higher frequency ot 

 the European species in the higher length classes; but since all frequencies m these higher length 

 classes are low this difference is much better illustrated if the results are plotted on an anthlog scale, 

 as in Fig 2ib\t must also be remembered that Hickling has shown that the figures for the European 

 species were derived from a heavily overfished stock, in which the proportion of large fish had been 

 seriously depleted, so that the smaller size of the virgin Patagonian stock is even more marked than 

 can be shown from these figures. • r ^u 



Proceeding to direct comparison of mean lengths it was found that the secondary grouping ot the 

 southern data leads to an error of +0-5 cm. Further, the secondary grouping m itself reduces the 

 significance of the difference between the means, for using percentage length frequency as the basis, 

 iV becomes 100, and the value of cr, is grossly exaggerated. It is not surprising, therefore, that on 

 comparing the means of the two sets of percentage length frequencies and applymg the test rf/a,>3, 

 their difference cannot be shown to be significant. Thus : 

 European: Mi = 5i-4, ffi=i5-475> (?f = 239-476, Ni=ioo; 

 Patagonian: M2= 46-4, (72=12-535, al=i57-i26, A^2=ioo; 



J=Mi-M2=5i-4-46-4 = 5-o. 



d 5-0 

 . — = ^ — = 250. 

 Orf 1-99 



If, however, we take the true values for the southern species, calculated by the long method from 



all the individual observations, we have : 



European (M. merluccius) values as before ; 



Patagonian (M./?M6fc«):M2= 45-9. 0^=12-^2, al= 154-33. iV2 = 4704; 



J=Mi-M2=5i-4-45-9 = 5-5. 



^ __ /(4+4U /(219j476i54l3_3\ ^2-42757= 1-56, 



°^~VliVi N2' V\ 100 ^4704/ 



Oa 1-56 ^^^ 

 Here the difference is clearly significant. Moreover, if the number of individual observations upon 

 wHchtrln of Hickling's means depends were known. N, would be much larger, and the signifi- 

 rnnre of the difference even more marked as Oa diminished. i„„„tl. nf 



Even ift assume that the unknown grouping error introduced by ^^'^^'^'^f^^l^TJ^^^^^ 

 the European species from the secondarily grouped percentage frequencies was of h s^me magm^^^^^^^^ 

 and of opposite sign, from that which was found for the Patagonian data so treated, we 

 Mi=5o-9, Patagonian values as before, ^=5-° and ad=i-63, 



1=. 1^ = 3.07. 

 Oa 1-63 -* 



