following test determines the likelihood of a violation for at least one of these two ecologically critical AFDC quantiles as follows: No threshold violations At least one threshold violation We then compute the probability of hypothesis testing errors for independent AFDC K quantiles: Type II errors are conditional upon the type I errors selected for each AFDC quantile hypothesis test, and vice versa, since a value of one uniquely determines the other. Future work may consider the impact of cross-correlations among individual hypothesis test results when determining the overall field significance (Douglas 2000). et al., Informing dam operation decisions with hypothesis test results In this section, we introduce our Bayesian decision-tree framework, which accounts for both type I and II errors associated with hypothesis tests regarding the exceedance of percent deviation thresholds when evaluating potential hydropower and ecological consequence of reservoir operation decisions. We also contrast this approach with common deterministic and probabilistic decision-making methods. 3.1 Approaches for incorporating Type I and II errors in decisions In our or observed, power analysis, we determine the power 1 - corresponding post-hoc, to a given estimated effect size , and sample sizes and We show the importance of α, m n. carefully choosing among numerous methods for incorporating hypothesis test results into decisions. First, we apply null hypothesis significance testing (NHST), a common practice for
following test determines the likelihood of a violation for at least one of these two ecologically critical AFDC quantiles as follows: No threshold violations At least one threshold violation We then compute the probability of hypothesis testing errors for K independent AFDC quantiles: Type II errors are conditional upon the type I errors selected for each AFDC quantile hypothesis test, and vice versa, since a value of one uniquely determines the other. Future work may consider the impact of cross-correlations among individual hypothesis test results when determining the overall field significance (Douglas et al., 2000). Informing dam operation decisions with hypothesis test results In this section, we introduce our Bayesian decision-tree framework, which accounts for both type I and II errors associated with hypothesis tests regarding the exceedance of percent deviation thresholds when evaluating potential hydropower and ecological consequence of reservoir operation decisions. We also contrast this approach with common deterministic and probabilistic decision-making methods. 3.1 Approaches for incorporating Type I and II errors in decisions In our post-hoc, or observed, power analysis, we determine the power 1 - corresponding to a given α, estimated effect size , and sample sizes m and n. We show the importance of carefully choosing among numerous methods for incorporating hypothesis test results into decisions. First, we apply null hypothesis significance testing (NHST), a common practice for
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