260 
BULLETIN OF THE BUREAU OF FISHERIES 
approach statistical significance, and as in this case none of the samples were com- 
posed of fish of only one age class, one may conclude that in comparing samples from 
adjacent localities a difference of 0.25 plus or minus its probable error must be ex- 
pected, and that any such difference should not, without further proof, be considered 
as due to the existence of distinct populations. 
Table 17. — Maximum variations between the means of the vertebral count of any two samples taken the 
same year in the same locality 
Locality 
San Francisco Bay 
Straits of Georgia.. 
Pender Harbor 
Craig.. 
Tebenkof Bay 
Point Gardner 
Larch Bay 
Eirington Passage . 
Macleod Harbor. 
Year 
sam- 
pled 
Differ- 
ence be- 
tween 
means 
of two 
samples 
Prob- 
able 
error of 
differ- 
ence 
Differ- 
ence di- 
vided 
by 
prob- 
able 
error of 
differ- 
ence 
1923 
0. 06 
0.030 
1.7 
1915 
. 10 
.064 
1. 6 
1915 
.08 
.050 
1. 6 
1928 
.06 
.071 
.9 
1927 
.18 
.041 
1 4.4 
1927 
.03 
.041 
.7 
1927 
.26 
.050 
1 5.2 
1925 
.19 
.076 
2 2.5 
1926 
.07 
.082 
.9 
1927 
.13 
.093 
1.4 
1927 
.13 
.081 
1.6 
1928 
.12 
.094 
1.3 
Locality 
Snug Harbor... 
Eshamy Bay.— 
McClure Bay. . 
Kachemak Bay 
Shuyak Strait. . 
Unalaska 
Year 
sam- 
pled 
Differ- 
ence be- 
tween 
means 
of two 
samples 
Prob- 
able 
error of 
differ- 
ence 
Differ- 
ence di- 
vided 
by 
prob- 
able 
error of 
differ- 
ence 
1928 
.16 
.106 
1.5 
1926 
.02 
.074 
.3 
1927 
. 16 
.112 
1.4 
1926 
. 12 
.074 
1.6 
1927 
. 14 
. Ill 
1.3 
1925 
. 11 
. 104 
1. 1 
1926 
. 12 
.149 
.8 
1928 
.02 
. 128 
.2 
1928 
.25 
.087 
• 2'9 
i Statistically significant. 
J Approaching statistical significance. 
But, aside from chance, the mean of any population will vary, not only between 
samples taken the same year, but between those taken in different years, owing to 
the changes in the proportions of the age classes and to the annual addition of a new 
year class. The magnitude of these variations is shown by Table 18. The average 
differences are 1.9 times their probable errors, only slightly higher than the difference 
between samples taken the same year. The largest difference found between any 
two samples is that of 0.30 ±0.082 or 3.7 probable errors for San Francisco Bay. 
This difference, however, will not be applied to the present analysis for two reasons; 
first, because the two samples were counted by different investigators (1915 by 
Thompson, 1923 by Hubbs), and second, because the two samples were taken eight 
years apart, admitting of the possibility of this difference being caused by a long- 
time fluctuation that will not enter into our samples, none of which were taken over 
four years apart. 
Table 18. — Maximum variations between the means of the vertebral count of any two samples taken 
different years in the same locality 
[Asterisk indicates those approaching statistical significance] 
Locality 
Years . 
compared 
Differ- 
ence 
be- 
tween 
means 
of two 
samples 
Prob- 
able 
error 
of dif- 
ference 
Differ- 
ence 
divided 
by 
prob- 
able 
error 
of dif- 
ference 
Locality 
Y ears 
compared 
Differ- 
ence 
be- 
tween 
means 
of two 
samples 
Prob- 
able 
error 
of dif- 
ference 
Differ- 
ence 
divided 
by 
prob- 
able 
error 
of dif- 
ference 
San Francisco Bay 
Craig.— 
Tebenkof Bay 
Eirington Passage 
Macleod Harbor 
Naked Island 
1915, 1923 
1925, 1928 
1925. 1927 
1 1925, 1926 
U925, 19' 7 
1 19°0, 1997 
1927. 1928 
1925, 1927 
0. 30 
.16 
.22 
.16 
.27 
.18 
.26 
.01 
0.082 
.083 
.091 
.080 
.083 
.088 
.091 
.088 
*3.7 
1.9 
*2.4 
2.0 
*3.1 
2.0 
*2.9 
.1 
Kachemak Bay 
Shuyak Strait 
1926, 1927 
1925. 1926 
1925. 1927 
1925, 1928 
1926. 1927 
1926. 1928 
1927. 1928 
0. 11 
.21 
. 13 
.24 
.08 
.34 
.26 
0. 104 
. 144 
.087 
. Ill 
. 124 
.149 
.095 
0.1 
1.5 
1.5 
*2.2 
. 6 
*2.3 
*2.7 
