Body Length and Scale Length in Pacific Pilchard — Landa 
171 
TABLE 1 
Coded Values Taken from Scatter Diagrams 
(Y = Body Length; X = Scale Length) 
YEAR-CLASS 
AND PORT 
COMBINATION 
nj* 
Y't 
Y'2 
XT 
X'2 
X'Y' 
1938 in: 
Pacific 
Northwest. . . 
10 
-29 
1015 
14 
88 
91 
San Francisco . . 
91 
-16 
4514 
79 
843 
1138 
Monterey 
76 
269 
4371 
26 
640 
938 
San Pedro 
60 
-26 
1692 
-32 
374 
549 
1939 in: 
Pacific 
Northwest. . . 
43 
138 
5472 
-33 
349 
807 
San Francisco . . 
150 
1079 
27721 
16 
2302 
5388 
Monterey 
166 
640 
15716 
-63 
1541 
2620 
San Pedro 
124 
-128 
4926 
54 
716 
1065 
1940 in: 
Pacific 
Northwest . . . 
14 
25 
1681 
22 
45 
96 
San Francisco . . 
50 
-12 
2120 
-4 
368 
430 
Monterey 
75 
487 
12303 
93 
1111 
2639 
San Pedro 
70 
-109 
3823 
-23 
535 
1091 
1941 in: 
San Francisco . . 
5 
-4 
102 
3 
37 
15 
Monterey 
26 
125 
3171 
42 
274 
726 
San Pedro 
90 
153 
2923 
90 
484 
809 
1942 in: 
Pacific 
Northwest. . . 
7 
61 
1415 
6 
84 
270 
San Francisco . . 
23 
16 
1531 
6 
192 
204 
Monterey 
68 
491 
12327 
159 
1283 
3464 
San Pedro 
51 
-6 
4486 
10 
502 
1308 
*nj = number of items in jth group, 
fY' = sum of coded body lengths. 
J X'= sum of coded scale lengths. 
1941 year-class in the Pacific North- 
west did not appear in the sample. 
For* each year-class and port combination 
a two-variable frequency table was made, plot- 
ting standard body lengths against scale 
lengths. Body lengths were grouped by 2- 
millimeter intervals, scale lengths by 6-milli- 
meter intervals. In order to code, arbitrary 
means were independently chosen for each of 
the variables in every frequency table. Owing 
to the magnification used in reading the 
scales, the scale-length values are 30 times 
larger than the actual scale lengths (Felin and 
Phillips, 1948). 
The values obtained from these frequency 
tables are given in Table 1. It is possible to 
pool these values in such a way as to obtain 
combinations other than port and year-class 
combinations. For example, to obtain infor- 
mation about the 1938 class as a unit, the 
sums of X' for the 1938 class from all ports 
are pooled in a single sum, the sums of Y' 
are similarly pooled, etc. 
TABLE 2 
Values Used in the Covariance Tests 
TEST 
Si 
S2 
S3 
S4 
N* 
Pf 
1 
53941 
1046 
646 
125 
1199 
5 
2 
6631 
26 
882 
1162 
237 
4 
3 
21828 
292 
1522 
18 
483 
4 
4 
9154 
392 
421 
2351 
209 
4 
5 
2899 
175 
30 
405 
121 
3 
6 
5542 
401 
279 
322 
149 
4 
* N = total number of observations, 
t p = number of groups. 
Pooled data obtained in this manner were 
used to get the Si, So, S3, and S4 values (see 
Table 2) as defined in Kendall (1946: 238 ff.) 
to make the tests indicated in Table 3. Tests 
were made after Kendall {op. cit.), at the .05 
level of significance and each consisted of 
testing the hypotheses (1) that the regression 
coefficients of the subclasses considered could 
have been drawn from the same populations 
and (2) that the regression of body length on 
scale length was a straight line (see footnote 
to Table 3). They were performed with coded 
data; later the data were uncoded to calculate 
the means, deviations, regression coefficients 
of body length on scale length, and body- 
length intercepts for the groups that were 
shown, by the tests, to be significantly dif- 
ferent. Test 1 indicated that the hypothesis 
(1) above should be rejected, and therefore 
it was necessary to consider each year-class 
separately. 
RESULTS 
From the results of Tests 1 to 6 (Table 3) 
and from the values found (Table 4), the 
questions posed can be answered, as far as the 
material treated is concerned, as follows: 
