PACIFIC HERRING 
259 
Table 16. — Variation between the means of the vertebral count of different year classes from the same 
locality 
[Asterisk shows those statistically significant] 
Locality 
McClure Bay. 
Eshamy Bay. 
Naked Island. 
Year 
classes 
compared 
Differ- 
ence 
between 
means 
Prob- 
able 
error of 
differ- 
ence 
Differ- 
ence 
divided 
by 
prob- 
able 
error of 
differ- 
ence 
(1920, 1921 
0. 19 
0.073 
2.6 
1920, 1922 
.00 
. 082 
.7 
1920, 1923 
.48 
. 103 
*4.7 
1921, 1922 
.25 
.095 
2.6 
1921, 1923 
.67 
. 113 
*5.9 
1922, 1923 
.42 
. 119 
3.5 
1920, 1921 
.09 
. 128 
.7 
1920, 1921 
. 50 
. 112 
*4.5 
Year 
Differ- 
Locality 
classes 
compared 
ence 
between 
means 
1920, 1921 
0.07 
1920, 1922 
.07 
Elrington Passage 
1920, 1923 
1921, 1922 
. 13 
. 14 
1921, 1923 
.20 
1922, 1923 
.06 
1922, 1923 
.36 
Macleod Harbor 
1922, 1924 
.25 
[ 1923, 1924 
. 11 
Differ- 
Prob- 
able 
error of 
differ- 
ence 
| ence 
divided 
by 
prob- 
able 
error of 
differ- 
ence 
0. 074 0. 9 
.075 .9 
.071 1.8 
. 084 1. 7 
. 081 2. 5 
.081 .7 
. 133 2. 7 
. 165 1. 5 
.117 .9 
This goes far toward explaining the variations to be found between samples from 
the same locality, as the mean of each sample will depend on the proportions of each 
year class present. As a rule, with samples of mature fish, one will have several year 
classes represented, so that means of successive samples will not fluctuate widely. 
However, in some cases, especially with schools of young fish, the sample may be 
composed very largely of fish of one year class. If this happens to be a year class that 
deviates widely from the average of the means of the year classes for that locality 
then the mean of the sample may differ considerably from the average for the locality. 
Thus, in comparing two samples from the same locality one could expect to find 
a difference in means as great as 0.67 plus or minus its probable error (as in Table 16) 
if each of the samples contained fish of only one age, but of a different year class in 
each case. In comparing samples of fish from the same locality composed of several 
age groups such a large difference can not be expected, as the presence in the samples 
of fish spawned in several different years will cause the samples to show less variability 
than if composed of one age group. 
Therefore, in evaluating the differences between any two localities, we must, if 
each sample is composed of one age group, have a difference of over 0.67 plus or minus 
its probable error before it approaches racial significance. This condition is seldom 
fulfilled, but, if not, we are confronted with another problem. Owing to changes in 
the proportions of each age group in different samples from the same locality there 
will be differences, aside from those due to chance, and the magnitude of these expected 
differences must be known so that they can be discounted in comparing samples from 
adjacent localities. 
The magnitude of these expected differences for any two samples taken the same 
year in the same locality is shown by Table 17. These differences are not great, the 
average for the table being only 1.7 times its probable error. In Tebenkof Bay and 
Larch Bay the differences have statistical significance, being 4.4 and 5.2 times their 
probable errors, but in both of these cases the sample that varied most from the mean 
for the locality was composed largely of very small fish (between 120 and 150 milli- 
meters), presumably largely of one age class. The effect this might have on the 
means has already been discussed. The actual difference between the means in 
Tebenkof Bay and in Larch Bay is 0.18 and 0.26, respectively. Elrington Passage 
and Unalaska have differences between samples of 0.19 and 0.25, respectively, which 
