124 
BULLETIN OF THE BUREAU OF FISHERIES 
the 1926 and 1927 year classes from eight localities, caught in their fourth summer, 
were compared with samples of the same year classes from the same localities taken 
during their fifth summer (neglecting samples of less than 25). Between the two 
series the average difference in vertebral count was 0.042, which was obviously of 
no significance as the chances were 1 in 8 that the means were the same. * 1 2 (See table 1.) 
Having thus failed to note any correlation between age and number of vertebrae 
in our samples, the means of the 4-year-olds of each year class were compared with the 
means of the 5-year-olds for the same year classes in each of the eight localities. Of 
these eight comparisons, none showed a significant difference, 3 although one might 
be regarded as doubtful, the chances being 1 in 25 that the two means are the same. 
Table 1 . — Means of vertebral counts of 1926 and 1927 year classes from various localities compared 
at 4 and at 5 years of age 
Locality 
Year 
class 
Mean 
Differ- 
ence 
Locality 
Year 
class 
Mean 
Differ- 
ence 
Age 4 
Age 5 
Age 4 
Age 5 
Inside Cape Ommaney 
Larch Bay 
Do 
1926 
1927 
1926 
1926 
1926 
52.411 
52. 573 
52. 478 
52. 404 
52. 472 
52. 408 
52. 750 
52. 433 
52. 482 
52. 464 
0. 003 
-. 177 
.045 
-. 078 
.008 
Hoonah 
Petersburg 
Do. 
1926 
1927 
1926 
52. 364 
52. 488 
52. 147 
52. 474 
52. 408 
52. 253 
-0. 110 
.080 
-.106 
Coronation Island 
Average.. 
52. 417 
52. 459 
-.042 
To determine if sex had any effect on the number of vertebrae, the mean vertebral 
count for both sexes was determined for each of a series of 24 samples of the 1926 year 
class caught during the summer of 1930 at Larch Bay, containing 491 males and 493 
females. The mean of the 24 unweighted means for males was 52.431; for females, 
52.435. The difference between these means was of no statistical significance. In 
making this comparison, the means of the males and of the females were not weighted 
because the presence of more than one population amongst the samples would then 
cause a weighting of the data according to the number of individuals in the samples. 
EXISTENCE OF RACES PROVEN BY HETEROGENEITY OF SAMPLES FROM ALL 
LOCALITIES 
Proof of the existence of independent stocks of herring is furnished by an analysis 
of the averages of all samples of vertebral counts of herring of the 1926 year class in 
southeastern Alaska. (See table 3 for total samples of each locality.) The object of 
this analysis is to prove whether or not all of the samples could have been drawn from 
the same population. From localities where many samples are available some of the 
samples are statistically different from others. This is to be expected according to 
the laws of probability. Before comparing the samples of one locality with those 
from another, it is essential that it be known whether any differences found may be 
due merely to such expected random variation or may be ascribed to a difference 
between the populations from which the samples are drawn. Therefore, it was neces- 
sary to test the data as a whole to determine if all of the samples could have been 
drawn from one population. 
2 Quoting from Fisher (1930, p. Ill), “In cases in which each observation of one series corresponds in some respects to a particu- 
lar observation of the second series, it is always legitimate to take the differences and test them * * In this method the 
test shows whether the mean difference differs significantly from 0, which is taken successively as each mean of the first series. 
t is the mean difference divided by its standard error, which in this case was 1.54 which yields a probability of 0.12 or approximately 
1 to 8. 
2 This method of comparison is explained by Fisher (1930, p. 107), see section on “ Segregation of races.” Probability was 0.04 
or 1 to 2§. 
