— 26 



A Review of the question as to requisite number and size of 

 representative samples in the International Herring Investigations. 



During the winter season 1913 — 14, 26 samples of large and spring herring, 

 amounting to some 7,000 fish in all, were collected and examined with regard to 

 age. The result of these investigations showed, that a certain year-class, (1904) 

 was more numerously represented than any other, while on the other hand, both 

 this and the remaining year-classes exhibited a certain variation in relative 

 numerical value from one sample to another. An attempt will be made, in the 

 following, to determine the nature of this variation, the part played by method- 

 ical errors, and the degree in which the variation may be regarded as an ex- 

 pression of biological facts. 



Average percentage. 



Any such investigation must necessarily commence with the average per- 

 centages of numerical value of the different year-classes. As the samples differ 

 considerably in point of size, the question arises as to what method of proceeding 

 may best be employed in order to obtain the greatest possible degree of exact- 

 itude in the averages. If all samples are taken as equal (by adding the per- 

 centages for each sample and dividing by number of samples ; Method I), then 

 the smaller samples will exert an undue influence upon the calculations ; if, on 

 the other hand, each sample is given a value proportionate to its size (by adding 

 the number of individuals of a certain year-class in all samples, and dividing 

 by the total number of specimens examined. Method II), then the error is 

 reversed, undue importance being attached to the largest samples. As will 

 be seen from Table I, in the case of the four year-classes subjected to investi- 

 gation, the two kinds of averages exhibit so close a degree of similarity that 

 we may, in this particular instance, waive the question of more accurate 

 methods of calculation altogether, merely taking the mean of the two sorts of 

 average as here given. 



Table I. Average percentages of four year-classes (two of inferior, 

 one of medium and one of high numerical value) 



