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Fishery Bulletin 91(2). 1993 



when the amount of interannual variability exceeds 

 precision of the estimates. In other words, in the in- 

 evitable trade-off between Type-I and Type-II errors, 

 the smoothed test has lower Type-II error rates at the 

 expense of an increase in the Type-I error rate. From 

 the management point of view, this is a safer compro- 

 mise than the one posed by the linear test, since the 

 probability of failing to detect a significant trend is 

 smaller with the smoothed test. The increase in Type-I 

 error rates can be related to the amount of smoothing 

 done by the particular algorithm chosen. An algorithm 

 that would smooth the estimates more would be less 

 prone to this problem, but it would have less power to 

 detect trends in the estimates in certain situations. 

 Such an algorithm would also induce more correlation 

 between smoothed estimates, and the separation in 



time between them would have to be greater in order 

 not to compromise validity of the comparisons. An al- 

 ternative would be a smoothing algorithm that can 

 adaptively change the amount of smoothing done on 

 the estimates, either by cross-validation techniques or 

 by controlling the amount of smoothing through incor- 

 porating auxiliary information, such as birth and death 

 rates, in the procedure; in other words, by building a 

 model of the population dynamics. 



Acknowledgments 



I would like to thank Bill Bayliff, Steve Buckland, 

 Martin Hall, and Tim Gerrodette for their valuable 

 comments. 



