Application of Statistical Power Analysis to the Oregon Coho Salmon (Oncorhynchus kisutch) Problem

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Abstract
Nickelson (1986; Can. J. Fish. Aquat. Sci. 43:527-535) was unable to reject the null hypothesis (Ho) of density-independent marine survival rate for Oregon coho salmon (Oncorhynchus kisutch) when wild, private hatchery, and public hatchery stocks were analyzed separately. Thus, even though there appears to have been no consistent increase in adult abundance in recent years in spite of large increases in smolt abundance, Nickelson''s anlaysis does not support the alternative hypothesis (HA) of density-dependent marine survival. Some fishery managers are using Nickelson''s results to support proposals to increase smolt production further. I calculated statistical power for these cases, i.e. the probability that the null hypothesis of density-independence could have been rejected, even if marine survival were truly density-dependent. Power was below 0.19 for all cases, which meant that Nickelson (1986) had at least an 81% chance of making a Type II error (incorrectly accepting Ho), if Ho was actually false. Therefore, Oregon fishery managers should be cautious about making decisions on increased smolt production based on current data; they run a high risk of mistakenly assuming density-independent marine survival. More generally, managers should not take action based on a failure to reject a null hypothesis unless power is high.