Vertebral Number of Nehu — Tester and Hiatt 
65 
TABLE 1 {coni' d) 
LOCALITY AND DATE 
LENGTH 
GROUP 
NUMBER OF FISH WITH 
COUNTS OF 
40 41 42 43 
44 
TOTAL 
NUMBER 
MEAN FOR 
LENGTH ENTIRE 
GROUP SAMPLE 
Kawaihae Bay, Hawaii 
1/29/49 
33 
- 
- 
12 
12 
1 
25 
42.560 
36 
- 
~ 
9 
24 
2 
35 
42.800 
39 
- 
- 
13 
18 
2 
33 
42.667 
42 
- 
- 
14 
6 
1 
21 
42.381 
45 
— 
— 
8 
10 
2 
20 
42.700 
All 
— 
— 
59 
77 
9 
145 
— 
42.655 
Kawaihae Bay, Hawaii 
3/28/49 
33 
- 
- 
12 
20 
4 
36 
42.778 
36 
- 
1 
4 
28 
3 
36 
42.917 
39 
- 
- 
4 
10 
2 
16 
42.875 
42 
— 
1 
3 
8 
3 
15 
42.867 
All 
- 
2 
29 
78 
14 
123 
— 
42.845 
samples are shown in Figure 3b, the number 
in each length category being represented as 
a percentage of the total number in the sam- 
ple. There is considerable variation between 
samples in both the length range and the 
position of the mode. Two of the samples, 
both from Honolulu Harbor, have at least 
two modes. In the first (12/27/48) the mean 
vertebral number for the smaller modal group 
(less than 39 mm.) is 42.136, and for the 
larger modal group (greater than 39 mm.), 
42.431. The difference of 0.295 has a standard 
error of 0.133 and is significant (P = 0.03). 
In the second (7/18/49) the mean of the 
smaller group (less than 45 mm.) is 42.459 
and of the larger group (greater than 45 mm.), 
42.443. In this case, the difference of 0.016 
has a standard error of 0.146 and is not signi- 
ficant. Again, differences such as these, if 
real, might be induced by differences in en- 
vironmental conditions during the period of 
early development. 
In the preceding paragraphs it has been 
shown that variation other than that due to 
chance may occur between length groups 
within samples. Accordingly, more generally 
to assess its significance and to allow for it in 
comparisons between samples, this source of 
variation was included in an analysis of 
variance of the data, considering the sampling 
to have been completely randomized. The 
analysis, limited to length groups containing 
10 or more individuals, is summarized in the 
following tabulation: 
SOURCE OF 
VARIATION 
DEGREES 
OF 
FREEDOM 
SUM OF 
SQUARES 
MEAN 
SQUARE 
F 
Localities 
6 
451.2679 
75.2113 
37.59** 
Samples 
Length 
10 
20.0099 
2.0010 
4.09** 
groups 
55 
26.8984 
0.4891 
1.39* 
Individuals 
2119 
743.3730 
0.3508 
** Highly significant; P is 0.01 or less. 
* Significant; P is 0.05 or less, but greater than 0.01. 
From a comparison of these F values with 
those tabulated for homogeneous distribu- 
tions by Snedecor (1946: 10.4), it will be 
found that significant heterogeneity occurs 
between length groups of the same sample, 
between samples of the same locality, and 
between localities. The component of vari- 
ance associated with "length groups" is 
obviously small. The conclusion for "sam- 
ples" would have remained the same if the 
sum of squares and degrees of freedom for 
"length groups" and "individuals" had been 
pooled, and the resultant mean square used 
as the error term in testing this next higher 
category. In view of this, a second analysis, 
which does not allow for variation between 
