are listed as S^, which provides information 

 on the variation about each regression coef- 

 ficient. Values of S h - h „ the estimated 



standard errors of the differences between 

 regression coefficients for females and males 

 are listed in table 2. I used the method out- 

 lined by Ostle (1966) (t = b Q - b /S b - b ) 



+ ° ? cT 



to test statistical differences between regres- 

 sion coefficients (b) for males and females of 

 each area. The resulting values of t are listed 

 in table 2. No significant difference was noted 

 between coefficients for males and females in 

 the St. Augustine and Mississippi River Delta 

 areas. 



The regression coefficients (b) ranged from 

 3.00 to 3.22 and from 2.82 to 2.95 for females 

 and males, respectively. It appears from these 

 data and the variances of the regression coef- 

 ficients (S b ) that the slopes of the lines for 

 the females in the three areas were dissimilar; 

 likewise the slopes of the lines for the males 

 were also dissimilar. Using analysis of co- 

 variance on the data from the three areas, 

 I determined whether the regression coeffi- 

 cients for females differed between areas and 

 whether the regression coefficients for males 

 differed between areas. Carrying out the "F" 

 test outlined by Dixon and Massey (1957), I 

 obtained F = 21.176 with degrees of freedom 

 V! = 2 and V 2 = 1,062 for females and F = 7.80 

 with degrees of freedom Vj = 2 and V2 = 905 



for males. These are significant at the 1- 

 percent level. Thus the regression coefficients 

 for females and for males differed statistically 

 among the three areas. For the convenience of 

 the reader, however, I have included the two 

 estimating equations using combined female 

 data and combined male data to provide an 

 overall description of the length-weight re- 

 lation of this species. In addition, all of the 

 data from each area and for each sex were 

 combined and a single estimating equation 

 was calculated. 



Table 3 lists the regression equations for 

 estimating tail weight (Y) from total weight 

 (X) and vice versa. The regression coefficients 

 for estimating tail weight ranged from 0.551 

 to 0.560 and those for estimating total weight 

 ranged from 1.794 to 1.905. Because of the 

 difference in the two regression coefficients 

 between areas, it was desirable to determine 

 by statistical tests whether the slopes of the 

 regression lines within each group were the 

 same. Using analysis of covariance, I computed 

 F = 7.694 with V L = 2 and V 2 = 1,972 degrees 

 of freedom for predicting total weight from 

 tail weight, and F = 9.50 with the same degrees 

 of freedom for predicting tail weight from 

 total weight. There is a real difference in 

 regression coefficients between areas forboth 

 estimating equations. However, I provide a 

 combined estimating equation for tail weight 

 and total weight. 



Table 3. — Regression equations for estimating tail weight (1 1 from total 

 weight (X) and estimating total weight (X) from tail weight (Y) of 

 royal-red shrimp (weight in decigrams) 



Area 



Sample size 



Regression equations 

 Y = a + b X 



Number of 

 shrimp 



St. Augustine, Fla. 



1,5-47 



Dry Tortugas . 



Mississippi River Delta. 



All areas combined. 



227 



204 



1,978 



Y = 1.006 + 0.553 X 

 X = 1.342 + 1.833 Y 



Y = 1.050 + 0.553 X 

 X = 1.051 + 1.905 Y 



Y = 1.012 + 0.560 X 

 X = 1.115 + 1.794 Y 



Y = 1.010 + 0.551 X 

 X = 1.353 + 1.834 Y 



Y = Tail weight. 

 X = Total .-.eight. 



