626 



Fishery Bulletin 90(3|. 1992 



all eight stocks similarly by eliminating the 1983 

 estimate. 



For each series, we calculated regressions using as 

 many data points as existed for each species for that 



number of years. In some cases, this resulted in as few 

 as three data points contributing to the regression. 

 Because we omitted data from 1983, the 10-year series 

 contained at most nine data points. Because some years 

 were omitted or were missing abundance indices, not 

 all year-series comprised strictly consecutive x-values 

 (year values). 



We reexpressed the slope estimate of trend (b) in 

 terms of a change parameter r, where 



r = b/Ai 



and Ai (estimated abundance in first year of series) is 

 calculated from the estimated slope and intercept for 

 each year-series. For these linear regressions, the 

 parameter r expresses the annual rate of change as a 

 fraction of the estimated initial abundance (Gerrodette 

 1987). Linear regressions were calculated only for 

 series with at least three data points. 



Power 



We estimated power of statistical conclusions about the 

 significance of each slope by assuming a two-sided 

 alternative hypothesis and using the non-central t (net) 

 distribution. In all cases, we assumed error levels a = 

 P = 0.10. We used a two-sided hypothesis test to be con- 

 sistent with earlier estimates of 5-year trends in abun- 

 dance (Buckland and Anganuzzi 1988, Anganuzzi and 

 Buckland 1989, Anganuzzi et al. 1991). 



To calculate power using the net distribution, we 

 utilized a series of programs (available upon request) 

 designed to return power estimates as a function of 

 three input variables: 



K.df = normal t statistic given a level of a 

 and degrees of freedom, 



IDF = degrees of freedom, and 



6 = b/Sb. 



Degrees of freedom were n-2 where n is the number 

 of years for which abundance estimates existed in a 

 series. Values for b and s^ were calculated from the 

 weighted linear regressions. 



6 is the offset of the alternative distribution (the net) 

 standardized by the standard error of the offset. In all 

 cases, we assumed as the alternative distribution the 

 observed trend for a series. 6 is thus the distance, ex- 

 pressed as standard deviation units, between the mean 

 of the null distribution (taken here to be zero slope) and 

 the mean of the alternative distribution (the slope 

 estimated from regression of the data). 



