CAXADIAX FISTIKRIEH KXPEDITIOX, 19r',-l.j 133 



is attached to the investigation of those year-classes which are best represented, and 

 for which we have the most accurate average figures, care being taken, however, 

 throughout to make sure that these good year-classes do not differ essentially with 

 regard to growth from the inferior ones. We thus avoid the necessity of making 

 lengtliy calculation for the inferior year-classes, and obtain at the same time some 

 idea as to how far the growth of the good year-classes is representative of the sample 

 (or samples, or water). 



In the case of two equally strong year-classes the older will generally be employed, 

 as, in the case of the younger fish, a greater allowance will have to be made for the 

 effects of the dissociation previously mentioned. And in comparing young fish, there- 

 fore, the rule as to taking fish of equal age will have to be more strictly observed. 



In making these comparisons, the average values (^4) only, have in some cases 

 been used. In cases requiring closer analysis, however, the standard errors (e) have 



8 

 been calculated from the standard deviation (8) according to the formula e=\/n, where 

 n is the number of variates. In testing the difference between two averages, the stan- 

 dard error (d) of this difference calculated according to the formula d:=^e'^ + e\, 

 where e^ and e.^ are the respective standard errors of the two' averages. The standard 

 error of the difference compared with the difference itself (D) will then serve to indi- 

 cate what value should be attached to the difference; if the difference be great in pro- 

 portion to its error then it will in all probability be significant, i.e., not due to fluc- 

 tuations of sampling, and vice versa. 



This calculation of the standard errors in the averages lias been carried out for 

 the growth dimensions t^ — t^; for t^ — ^k, the method employed was, save in such cases 

 where averages only were compared, as follows: When the analysis of and examination 

 of the averages for the remaining dimensions indicates similarity between a number 

 of samples, then one of these is selected, and the standard deviation for the dimen- 

 sions t^ — tj„ calculated for that sample. Presuming then that the standard deviations 

 for the other samples will be more or less equal to these, the standard errors for all 

 samples may be calculated from the standard deviations for the one. I have tested 

 this method, and convinced myself that the presumption is correct, and the consequent 

 simplification of the calculations thus justifiable. 



In all mathematical comparisons, the calculated increment oi gro\\i:.h (0 

 has been employed, and not the calculated length (I), the former is, as far as I can see, 

 easier to deal with than the length ; for reasons of economy also it was found neces- 

 sary to restrict the work to the consideration of one of these dirnensions. In the fol- 

 lowing comparisons of the results, on the other hand, the calculated lengths have been 

 used, as being more immediately legible (the length of a herring can be seen, whereas 

 one can only form an idea as to its growth or increment). 



1. Samples from Neivfoundland. — The age investigations led to the results that 

 all samples of grown fish from the coast of Newfoundland, with a single exception, 

 were characterized by the marked superiority of the lOO-t year-class. The single 

 exception (sample from St. Georges bay, jMay 27, 1915, exhibit remarkable likeness 

 to a sample from Korth Sydney, and will therefore be taken together with this. 



Table 13 shows the averages for all increments of the year-class 1004, and the 

 standard errors of the averages for dimensions t, — t. all each single one of the nine 

 samples selected for growth measurements ; the lowest series in the table further shows 

 the total averages with corresponding standard errors, arrived at by taking all specimens 

 of the said yesr-class (in the nine samples) together as a single larger sample. 



