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Fishery Bulletin 98(4) 



rejections out of 26 tests, rather than the 18 rejections for 

 7t = 0.80. On the other hand, setting a = 0.05 would have 

 rejected H„ only 14 times. 



Discussion 



Statistical considerations 



Any /-test assumes that the observations are indepen- 

 dent and are identically distributed normal random vari- 

 ables. Assuming a normal distribution for r is reasonable, 

 because R (its antilog) has been found to be approximately 

 lognormally distributed (Botsford and Brittnacher, 1998). 

 More generally, observations on fish population sizes or 

 survival rates are often found to be approximately lognor- 



mally distributed, as if arising from a series of random 

 multiplicative events (Hennemuth, 1980). 



The requirement that the growth rate observations be 

 identically distributed as well (same underlying mean and 

 variance), is not directly verifiable, but this assumption 

 is reasonable given the short time period over which the 

 test is conducted (77=5-year period). Indeed, this was our 

 rationale for limiting the testing protocol to a 5-year time 

 horizon. Although a longer time frame would boost the 

 test's sample size and. for fixed a, increase its power, we 

 believe identity of distribution beyond a 5-year horizon 

 is an untenable assumption. Thus, the proposed protocol 

 limits the test to a 5-year time frame, achieving the neces- 

 sary power at the expense of a higher type-1 error rate. 



The issue of independence of observations is more dif- 

 ficult to assess. Winter chinook salmon adults return to 



