272 BULLETIN OF THE BUREAU OF FISHERIES 
Table 6. — Comparisons of the means of the vertebral counts of each year class in Prince William Sound 
Localities compared 
Year 
class 
Difference 
between 
means 
Summation 
of 
populations 
Standard 
error of 
difference 
between 
means 
Difference 
between 
means 
divided by 
standard 
error 
McClure Bay and Naked Island - — . 
1921 
0.322 
119 
0. 1010 
3.19 
Do... 
1922 
.060 
33 
.1949 
.31 
McClure Bay and Eshamy Bay 
1921 
.232 
130 
.0990 
2.34 
Do - 
1922 
.328 
41 
.1811 
1. 81 
Naked Island and Eshamy Bay 
1921 
.090 
101 
.1233 
.73 
Do — - 
1922 
.268 
30 
.2341 
1. 14 
Naked Island and Elrington Passage 
1921 
.154 
152 
. 1183 
1.30 
Do...... 
1922 
.221 
89 
.2010 
1. 10 
Snug Harbor and Point Helen 
1926 
.020 
420 
.0959 
.21 
Snug Harbor and Port Chalmers 
1926 
.094 
444 
.0869 
1.08 
Snug Harbor and Glacier Bay 
1926 
.052 
518 
.0685 
.76 
Snug Harbor and Port Fidalgo 
1926 
.016 
404 
. 1086 
.15 
Zaikoff Bay and Port Fidalgo ... 
1926 
.032 
89 
.1649 
.19 
Zaikoff Bay and Port Chalmers. — 
1926 
.142 
129 
. 1520 
Glacier Bay and Port Chalmers 
1926 
.146 
262 
.0917 
l! 59 
Glacier Bay and Sleepy Bay „ . ... 
1926 
.061 
341 
.0782 
.78 
Do.. — 
1927 
.053 
43 
.1975 
.27 
Glacier Bay and Macleod Harbor 
1926 
.076 
767 
.0620 
1. 23 
Do — 
1927 
.465 
53 
.2311 
2.01 
Glacier Bay and Point Helen 
1926 
.032 
238 
.0969 
.33 
Macleod Harbor and Sleepy Bay 
1926 
.015 
772 
.0624 
.24 
Do 
1927 
.412 
58 
.2260 
Macleod Harbor and Elrington Passage.. 
1923 
.276 
86 
.1694 
l! 63 
Do 
1924 
.061 
212 
.0997 
.61 
Do. — — 
1926 
.024 
942 
.0502 
.48 
Sleepy Bay and Elrington Passage 
1926 
.009 
516 
.0721 
.12 
Sleepy Bay and Shelter Bay 
1926 
.073 
.0957 
.76 
Sleepy Bay and Point Helen 
1926 
.029 
243 
. 1025 
Shelter Bay and Elrington Passage 
1926 
. 082 
429 
.0922 
1 89 
Shelter Bay and Point Helen 
1926 
.102 
156 
.1068 
.96 
Port Chalmers and Point Helen _ 
1926 
.114 
164 
.1118 
1.02 
The desirability of calculating the standard error of the difference by a pooled 
estimate of the variance is explained by Fisher (1930, p. 108), who says: 
It may be noted in connexion with this method, and with later developments, which also 
involve a pooled estimate of the variance, that a difference in variance between the populations 
from which the samples are drawn will tend somewhat to enhance the value of t [difference between 
means divided by its standard error] obtained. The test, therefore, is decisive, if the value of t is 
significant, in showing that the samples could not have been drawn from the same population; 
but it might conceivably be claimed that the difference indicated lay in the variances and not in the 
means. The theoretical possibility, that a significant value of t should be produced by a difference 
between the variances only, seems to be unimportant in the application of the method to experi- 
mental data; as a supplementary test, however, the significance of the difference between the 
variances may be tested directly by the method of paragraph 41. 
These comparisons give two statistically significant differences between neighbor- 
ing localities which might be construed as indicating the independence of the stocks 
of herring of the localities between which these significant differences occur. How- 
ever, these differences can not be accepted as valid without a knowledge of the 
homogeneity of the material. To this end Table 7 is presented showing the means 
of the 12 samples of vertebral counts from herring of the 1926 year class caught at 
Macleod Harbor. These samples do not show any statistically significant differences 
between each other. 
