202 



Fishery Bulletin 92(1). 1994 



procedure, I recommend comparison of weight- 

 length relations among data sets by comparison of 

 expected weights of fish at sizes within the range 

 of observed average weights common to all data sets 

 of interest. 



The results of this study suggest that an additive 

 error term is more appropriate than a multiplica- 

 tive error term for modeling weight-length relations. 

 Most previous studies have assumed multiplicative 

 error, which is implied when the log-log transforma- 

 tion is used to estimate parameters of the model 

 from individually measured fish by linear regres- 

 sion. The multiplicative error assumption has not 

 been demonstrated correct even when data are 

 available from fish weighed individually. While good 

 fits to data are usually obtained under the multi- 

 plicative assumption, if the assumption is not valid, 

 statistical inferences may be erroneous. Pienaar and 

 Thomson (1969) assumed that the error term was 

 additive for their data and discussed statistical as- 

 pects of the assumption. Further examination of the 

 error term form would be interesting. 



Copies of the FORTRAN code used in this study 

 are available from the author. 



Acknowledgments 



I thank James Bence for considerable statistical 

 advice, particularly on the bootstrap procedure. 

 James Bence, Alec MacCall, and Steve Ralston con- 

 structively reviewed drafts of the note. I also thank 

 David Woodbury for his assistance during an early 

 stage of this study and Dale Roberts for his help 

 with the use of SAS. 



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