172 
PACIFIC SCIENCE, Vol. VII, April, 1953 
TABLE 3 
Covariance Tests for the Regression of Body Length on Scale Length 
F. RATIO* 
TEST 
DATA COMPARED 
HYPOTHESES 
STATISTIC* 
(.05 1. of S.) 
1 
1938, 1939, 1940, 1941, 
For all the data, the relationship can be expressed by 
and 1942 year-classes, 
ages 1-5, data pooled 
a straight line. 
.19 
2.93 
from all ports. 
No difference between the regression coefficients of 
each year-class. 
5.76 
2.37 
2 
1938 class in: 
For all the data, the relationship can be expressed by 
Pacific Northwest 
San Francisco 
a straight line. 
.84 
3.67 
Monterey 
No difference between the regression coefficients of 
San Pedro 
the 1938 class in each port. 
.30 
2.60 
3 
1939 class in: 
For all the data, the relationship can be expressed by 
Pacific Northwest 
San Francisco 
a straight line. 
.15 
3.67 
Monterey 
No difference between the regression coefficients of 
San Pedro 
the 1939 class in each port. 
2.12 
2.60 
4 
1940 class in: 
For all the data, the relationship can be expressed by 
Pacific Northwest 
San Francisco 
a straight line. 
.09 
3.67 
Monterey 
No difference between the regression coefficients of 
San Pedro 
the 1940 class in each port. 
2.87 
2.60 
5 
1941 class in: 
For all the data, the relationship can be expressed by 
San Francisco 
a straight line. 
.16 
5.66 
Monterey 
No difference between the regression coefficients of 
San Pedro 
the 1941 class in each port. 
3.47 
3.07 
6 
1942 class in: 
For all the data, the relationship can be expressed by 
Pacific Northwest 
San Francisco 
a straight line. 
.23 
3.67 
Monterey 
No difference between the regression coefficients of 
San Pedro 
the 1942 class in each port. 
3.40 
2.60 
* Statistic to test if the relationship can be expressed by a straight line: 
s, 2p-2 ^ J . N-2p 
. to be compared with F. ratio: 
N — 2p S2H“S3+S4 2p — 2 
Statistic to test if there is difference between the regression coefficients of the subclasses involved: 
S2 N-2p . p-1 
♦ to be compared with F. ratio: 
p-1 Si N-2p 
(1) The coefficient of regression of body 
length on scale length and the body 
intercept are significantly different for 
the 1938, 1939, 1940, 1941, and 1942 
classes (Test 1). 
(2) There is no significant difference among 
the regression constants for the whole 
1938 class regardless of area of capture 
(Test 2). The same is true for the 1939 
class (Test 3). The regression constants 
for the 1940 class are significantly dif- 
ferent for fish sampled in the Pacific 
Northwest, San Francisco, Monterey, 
and San Pedro (Test 4). This also is 
true of the 1941 class (Test 5) and the 
1942 class (Test 6 ). 
(3) The relationship between body length 
and scale length for 1- to 5-ring fish 
of the year-classes involved does not 
