FISHERY BULLETIN: VOL. 87. NO. 3, 1989 



2.0 (pi = 2.0, Pa = 3.0, D = 1.0), with a cv(d) = 

 0.15, will require n = 67 positive tows from each 

 population. With 70 positive tows from each pop- 

 ulation, approximately 95% of the sample differ- 

 ences can be expected to be between 0.70 and 

 1.30(1.0 ±2*0.15). 



The Power Method 



The standard error of the estimated mortality 

 coefficient, SE(6), was modeled as a function of 

 the number of positive tows, n, and the true 



mortality coefficient (p) using the data listed in 

 Table 5:" 



SE(6) = 0.356 H-O-469 g0.239p_ 



The probabilities of detecting a difference be- 

 tween two mortality coefficients, given that 

 there is a difference (this is referred to as the 

 power of the test), were calculated for various 

 sample sizes and listed in Table 7. The power 

 increases as the difference of mortaUty coeffi- 

 cients increases, and it is equal to the level of 



Table 7. — Probability of detecting a difference between two mortality coeffi- 

 cients, given one of the mortality coefficients (p,), tfie true difference (D = 

 P2 ^ Pi). and the number of positive tows (n). Because of symmetry about 

 D = 0, partial figures are listed. 



410 



