RACES OF HERRING, SOUTHEASTERN ALASKA 
125 
The method used in testing the homogeneity of the means of all of the samples is 
merely an extension of the method of comparison of two means to the comparison of 
several means. This method is called the “Analysis of variance” by Fisher (1930, 
p. 196). Wollaston (1933) in an article in the Journal du Conseil, with a foreword by 
R. A. Fisher, expounds the use of this method and its applicability to herring race 
problems. Quoting from Wollaston: 
There are two fundamentally different ways of approaching observational scientific data. The 
first is to lay out the data as graphically as possible and see what they suggest; the second, to formu- 
late, without examining the data in detail, hypotheses which the data may be expected to prove or 
disprove, and then to test the agreement of the data with the hypotheses. The first result remains 
but a suggestion, and the actuality of the suggested phenomena cannot be stated in terms of proba- 
bility. The second allows definite statement of probability that the hypotheses are true or not true. 
The great majority of fishery workers, including Dr. Schnakenbeck in his work criticized in this 
paper, have adopted the first way. His conclusions may be right, but his method of approach, 
which I will call the a posteriori method, includes no test whatever as to the probability of his being 
right. 
******* 
Sound statistical tests of probability can only be applied to data treated in the second way. It 
is even better to formulate hypotheses to be tested by the data before these are collected than to do 
so before they are worked up. The research can then be given the exactness of pure experimental 
science, giving equally definite positive or negative results. 
******* 
The main object of this paper is to introduce into fishery research some of the most important 
methods developed by R. A. Fisher, of Rothamsted Laboratory. These are offered as alternative 
and far preferable to empirical methods which take no account of the variability which occurs be- 
tween samples drawn from a larger population. For the purpose in question I have used the data 
collected by Dr. Schnakenbeck from the North Sea, and I propose to show that Dr. Fisher’s methods 
are perfectly adequate to deal with such data and to extract all the information from them which 
they are capable of giving. As I have not had access to subsidiary data, collected by other workers 
and used by Dr. Schnakenbeck in his report, it cannot be said definitely whether these would have 
modified my conclusions and brought them more nearly into line with Schnakenbeck ’s. It is hoped 
that all available data bearing on the herring race question will eventually be combined in a com- 
plete statistical analysis on the lines laid down here. This must be considered merely as an introduc- 
tion to such analysis. 
******* 
Though the mathematical theory on which the present paper is founded is somewhat advanced, 
the methods introduced herein are very simple in application. The first part deals almost exclu- 
sively with Fisher’s methods for finding the best-fitting Curve of Error to fit to highly grouped 
data. Readers who have not to deal with such data may prefer to omit this part. The second 
part (from p. 23 on) deals with Fisher’s method of the Analysis of Variance, which is of almost 
universal application in testing the significance of variations in any phenomenon under different 
conditions. There is no other method so ideally fitted for this kind of test. This second part 
will be therefore found worth reading by anyone who is engaged in fishery research and who is 
not familiar with Fisher’s work. Every step in the application of the method to the present prob- 
lem is shown in detail, and described as far as possible in nonmathematical language. 
******* 
We have then an ideal set of conditions for the application of Fisher’s Analysis of Variance, 4 
which is a powerful weapon for distinguishing between real differences between samples and those 
which are probably due to variation “within samples.” 
« The term “Analysis of Variance” is somewhat misleading. It is the total sum of squares which is analyzed. If, however, 
each estimate of variance is considered as weighted by its degrees of freedom, the term Analysis of Variance is quite correct, as will 
be seen later. 
103465°— 35 2 
