258 
BULLETIN OF THE BUREAU OF FISHERIES 
probable errors. Shuyak Strait differs from both Shearwater Bay and Old Har- 
bor by four probable errors. All of the differences in these districts are of slight 
magnitude. 
Table 15 . — Comparisons of the means of the vertebral counts in the Cook Inlet and Kodiak- A fognak 
districts 
[Asterisk shows those statistically significant] 
Localities compared 
Differ- 
ence 
between 
means 
Prob- 
able 
error of 
differ- 
ence 
Differ- 
ence 
divided 
by 
prob- 
able 
error of 
differ- 
ence 
Localities compared 
Differ- 
ence 
between 
means 
Prob- 
able 
error of 
differ- 
ence 
Differ- 
ence 
divided 
by 
prob- 
able 
error of 
differ- 
ence 
Kachemak Bay and Dogfish Bay 
0.26 
0.060 
*4.3 
Dogfish Bay and Old Harbor 
0. 45 
0.071 
*6.3 
Kachemak Bay and Shuyak Strait... 
.04 
.038 
1.0 
Shuyak Strait and Zachar Bay . 
.13 
.053 
2.5 
Kachemak Bay and Zachar Bay 
.09 
.057 
1.6 
Shuyak Strait and Shearwater Bay. . 
.19 
.046 
*4. 1 
Kachemak Bay and Shearwater Bay. 
. 15 
. 051 
2.9 
Shuyak Strait and Old Harbor 
.23 
.055 
*4.2 
. 19 
.059 
3.2 
. 0G 
. 063 
1. 0 
Dogfish Bav and Shuyak Strait 
.22 
.055 
*4.0 
Zachar Bay and Old Harbor 
. 10 
. 069 
1.4 
.35 
.070 
*5.0 
. 04 
. 065 
. 6 
Dogfish Bay and Shearwater Bay 
.41 
.065 
*6.3 
In western Alaska (Table 7) the Shumagin Islands, Unalaska, and Golovin Bay 
have already been compared and the differences found to be large. The mean of 
the Chignik sample (Table 12) is lower than that of the Shumagin Islands, only 90 
miles distant, by 1.34 ± 0.060 or 22 probable errors — a large difference from a mathe- 
matical standpoint. 
VALIDITY OF DIFFERENCES IN VERTEBRAL COUNT 
It is necessary to bear in mind that there are sources of variability other than 
those of pure chance, since the latter may not prevail in what we have regarded as 
random sampling. The actual significant variability which thus arises within each 
population must be determined empirically, since such internal variability could not 
be regarded as significant from the standpoint of the determination of the distinct- 
ness of populations. Without an understanding of the extent of these variations, 
one may be led into the fallacy of believing that any difference that is statistically 
significant denotes a racial difference, since the whole theory of probable errors pre- 
supposes that the samples compared represent adequately their respective popula- 
tions. The variation which can be shown to actually arise within each stock furnishes 
a means of measuring the significance of differences between adjacent stocks. If the 
latter exceed the maximum internal difference, it is probably significant of isolation. 
In Table 16 is given a comparison of different age classes from the same locality. 
The data are not extensive and the numbers involved are rather small, yet both 
Naked Island and McClure Bay show significant differences between the means of 
different year classes. The maximum significant difference found was 0.67 ±0.113 or 
5.9 times the probable error between two age classes of McClure Bay. 
