Jagielo et al : Demersal groundfish densities in trawlable and untrawlable habitats off Washington 



565 



where V(D,) describes the uncertainty in the abundance 

 estimator. If the bias is much less than this uncertainty, 

 then its impact will be minimal. Therefore, we arbitrarily 



set 



Bias- = (A- mo,), 



(3) 



and substituting A A^ for bias from Equation 1 into Equa- 

 tion 3 gives 



A^2^2 = (A2)V(Dp. 



Solving for A gives 



A = — 5£)(D,). 



A. 



(4) 



(5) 



where SD{ D, ) = the standard deviation of the trawl survey 

 density estimator in the trawlable habitat. 



Thus, the effect size threshold used for detecting differ- 

 ences in mean density in the power analysis is a product 

 of the arbitrary decision for the bias in the abundance 

 estimator to be equal to its standard error. 



For the statistical power analysis, we expressed A (the 

 difference in densities between habitats) as the standard- 

 ized effect size index (c/^) for a two-sample f-test (Cohen, 

 1988); dividing (Eq. 5) lay an estimate of the population 

 standard deviation, which yields 



— SD(D,)/s^ 



A, 



