NOTE Lenarz: Estimation of weight-length relations from group measurements 



201 



40 60 



Sample Size 



40 60 



Sample Size 



Figure 2 



(A) Residual of average weight (kg) as a function of 

 sample size for chilipepper rockfish (Sebastes 

 goodei ) collected in samples taken from Morro Bay 

 during July and August 1991. (B) Residual multi- 

 plied by yrij as a function of sample size. 



proach with a standard statistical package. Some of 

 the difference is probably due to the overhead in- 

 volved with using the statistical package. When 

 computationally intensive methods such as 

 bootstrapping are used, time saved by using the new 

 method is significant. 



The widening confidence limits for expected 

 weights beyond the range of most observed average 

 weights indicated use of expected weights beyond 

 the observed range is extrapolation and should not 

 be done. This also applies to comparison of param- 

 eter estimates from different sets of data. If the 

 range of observed average weights differ much 

 among the data sets, comparison of parameter esti- 

 mates is not meaningful. Estimates of the two pa- 



Table 1 



Estimates of standard errors of parameter esti- 

 mates of weight-length model for chilipepper rock- 

 fish iSebasted goodei) collected from Morro Bay 

 during July and August 1991. The Gauss-New- 

 ton method was used with observations weighted 

 by six factors to estimate the parameters, and the 

 new method with rij as the weighting factor. As- 

 ymptotic standard errors are shown for the Gauss- 

 Newton method and bootstrap standard errors for 

 the new method. Coefficients of variation of the pa- 

 rameter estimates are shown in parentheses. 



Standard error 



Weighting 

 factor 



Gauss-Newton method 



none 0.0028 (0.30) 



n, _ 0.0019 (0.21) 



raj/Wj 0.0020 (0.20) 



n/W, 2 0.0022 (0.20) 



1/W, 0.00.30 (0.29) 



1/W, : 



New method 



0.0032 (0.28) 



0.0046 (0.50) 



0.2159 (0.07) 

 0.1489 (0.05) 

 0.1528 (0.05) 

 0.1547 (0.05) 

 0.2129 (0.07) 

 0.2069 (0.07) 



0.2211 (0.07) 



rameters of the weight-length relation are highly 

 correlated even when individuals are weighed and 

 standard linear regression is used (Lenarz, 1974). 

 Thus, regardless of the type of data or statistical 



