376 



Fishery Bulletin 89(3), 1991 



tion. If the cost of making an a-error, i.e., falsely con- 

 cluding that a stable population is increasing or de- 

 creasing, is low, a can be increased to increase power. 

 However, attention must be paid to both /3 and y-errors 

 as power increases. If y is relatively large, then power 

 should be greater than the previously suggested value 

 of 0.80. 



Additional surveys improve the power to detect 

 trends and reduce y-errors. Furthermore, if future 

 research can identify and record additional factors af- 

 fecting observed abundances, such as productivity of 

 the area surveyed (Smith et al. 1986) or ocean tem- 

 perature patterns (Reilly 1990), this may reduce the 

 variability in the model and increase power. 



Future research is planned to continue surveys and 

 search for alternative methods of analyzing these data. 

 The traditional approach to making statistical inference 

 regarding trends has been hypothesis testing with a 

 null hypothesis of no change. As seen in this paper, this 

 is a complicated approach. One must first decide what 

 levels of a, /?, and (now) y one is willing to tolerate. The 

 range of these errors is dependent on many factors, 

 including the level of change to be detected, and the 

 number of years surveyed. Once inference is made, it 

 cannot be presented to others without reference to this 

 bewildering array of decision criteria. 



Bayesian^tatistics (Iversen 1984, Press 1989) may 

 offer an alternative approach to statistical inference, 

 circumventing many of the complications discussed 

 above. Bayesian methods would allow the calculation 

 of the probability distribution of possible trends given 

 the observed data. From this distribution it would be 

 possible to directly calculate the probability that the 

 population is increasing or decreasing. Such methods 

 may be of more value than statistical test results which 

 are highly dependent on the chosen error levels. 



Acknowledgments 



Support, personnel, and flight time were provided by 

 J. Lecky, Southwest Regional Office (NMFS), the 

 Southwest Fisheries Science Center (NMFS), and the 

 California Department of Fish and Game (CDFG). We 

 thank R. Holt for assisting in planning the surveys. The 

 observers and data recorders were M. Beeson, 

 D. DeMaster, S. Diamond, T. Gallegos, A. Hudoff, 

 L. Jones, E. Konno, S. Kruse, M. Larson, J. Lecky, and 

 J. Scholl (also J.B., K.F., and D.H.). 



The aircraft were chartered from Aspen Helicopters, 

 Inc. and contracted from CDFG. The pilots were 

 B. Cheney, B. Cole, L. Heitz, K. Lankard, E. Schutze, 

 J. Turner, R. Riediger, and R. Van Benthuysen. The 

 computer data acquisition software was written by 

 J. Cubbage. We thank D. DeMaster, T. Gerrodette, 



S. Kruse, C. Lennert, B. Taylor, P. Wade, and two 

 anonymous reviewers for their careful reviews of this 

 manuscript. C. Lennert also provided valuable advice 

 regarding statistical aspects of this paper. 



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