FISHERY BULLETIN: VOL. 85, NO. 3 



Table 6. — Minimum rates of annual decrease 

 and minimum total decreases in spotted dol- 

 phin population size which could be detected in 

 5 years under different conditions. Changes 

 were calculated for several alpha and beta lev- 

 els, with a one-tailed test, using 1, 2, and 3 

 ships, for CV {N) determined using jackknife 

 formulae, and data in the north area pooled 

 over all strata (method B). 



and would lead to a 44% reduction in population 

 size over the 5-yr period. If two or one ship is used, 

 however, the minimum detectable rates of de- 

 crease are higher still, 13% and 19%, respec- 

 tively. When the power of the survey design is 

 considered, the same dilemma is evident (Table 

 7). Even when three ships are used, the power is 

 acceptably high only if the rate of decrease is at 

 least 10% per year. The probability of detecting a 

 5% per annum decrease at a 5% alpha level, for 

 example, is only 0.51. This means that with a 

 probability of 0.49 we would conclude that no 



Table 7. — Power, or the probability of detecting a decrease in 

 spotted dolphin population size dunng a 5-yr penod. Power was 

 calculated for surveys using 1, 2, or 3 ships, for various rates of 

 annual and total population decrease, and for testing the regres- 

 sion of population size against time at vanous significance levels 



0.20 



0.14 



0.12 



0.01 

 0.03 

 0.05 

 0.10 



0.01 

 0.03 

 0.05 

 0.10 



0.01 

 0.03 

 0.05 

 0.10 



0.05 

 0.14 

 023 

 0.41 



0.05 

 0.14 

 0.23 

 0.41 



0.05 

 0.14 

 0.23 

 0.41 



0.08 

 0.15 

 0.26 

 0.62 



0.09 

 0.22 

 0.42 

 0.87 



0.10 

 0.27 

 0.51 

 0.94 



0.14 

 0.25 

 0.40 

 0.75 



0.16 

 0.34 

 0.56 

 0.93 



0.18 

 0.40 

 0.66 

 0.97 



0.26 

 0.41 

 0.57 

 0.86 



0.29 

 0.52 

 0.73 

 0.97 



0.31 

 0.57 

 0.80 

 0.99 



decrease had taken place, when in fact it had. 

 Power is even less if only one or two ships are 

 used. 



Alternatively, we may have either to conduct 

 the surveys for more than 5 years and/or relax the 

 acceptable alpha and beta error level (Table 8). 

 With three ships and 5% error levels, 5 years is 

 sufficient to detect a 10% per annum decline, but 

 9 years are required to detect a 5% per annum 

 decline and 13 years are required to detect a 3% 

 per annum decline. For alpha and beta levels 

 equal 0.10 or 0.20 and use of three ships, a 5% 

 decrease can be detected in 7 or 5 years, respec- 

 tively. 



Table 8. — Number of years required to detect various annual de- 

 creases and total declines of spotted dolphins calculated for sev- 

 eral alpha and beta levels using 1, 2, and 3 ships. CV {N)s were 

 calculated using jackknife formulae and using data in the north 

 area pooled over all strata (method B). 



Number 

 ships 



CV(A/) 



Decrease 

 per year 



Number 



years 



required 



a = P = 0.05 

 1 



a = p = 0.10 

 1 



a = p = 0.20 

 1 



0.20 



0.14 



0.12 



0.20 



0.14 



0.12 



0.20 



0.14 



0.12 



Total 

 decrease 



444 



