YELLOWTAIL FLOUNDER OFF NEW ENGLAND 



267 



which follows Finney (1952, p. 52). These com- 

 putations lead to 



t= 3. 281 + .04348 X 



A 



in which Y is the estimated probit and X the day 

 of the year minus 100. 



The goodness of fit was estimated by x 2 from 



X 2 =2nw(y— y) 2 - 

 X 2 = 19.76 



[Znw{x-x){y-y)) 2 



2nw(j , -i) ! 



With 16 degrees of freedom this value for x 2 

 will be exceeded by chance about once in five times. 

 We judge, therefore, that our curve (fig. 24) is a 

 satisfactory fit and our assumption that no trans- 

 formation of X was needed is justified. 



The variance of x about the 50-percent point 

 was estimated from 



V{ ' b 2 IZnw^Znw(x-x) 2 ] 



V(m)= 1.808 -yJV(m,) = 1.345 



in which m is the 50-percent point, x mean ob- 

 served x, and b the slope of the regression line. 

 The 95-percent fiducial limits are 50-percent point 

 of 



or 



x±1.9G^!V(m) 

 34.77±2.64 



If we consider that our day began at noon, then 

 we may say that the peak of spawning (in the 

 fish as landed) probably occurred on May 19 and 

 the odds are 19 to 1 that it occurred between May 

 16 and 21. 



Using similar computations (appendix table 

 F-2) for the data on length at maturity of the 

 female yellowtail, we find 



£=-0.2176 + 0.1631/ 



in which Y is the estimated probit and x is the 

 total length in centimeters. 



X 2 =13.15, #=10, P=0.2 



again indicating satisfactory fit. The standard 

 error of the 50-percent point, 



VF(m) = 0.9727 



and 95-percent fiducial limits of the 50-percent 

 point (31.98 cm.) are 30.07 and 33.89 cm. 



Table F-2. — Probit analysis of the length at maturity 

 of female yellowtail, in 194$ 



SUMMARY OF REGRESSION COMPUTATIONS 



U. S. GOVERNMENT PRINTING OFFICE : 1959 O - 476995 



