Compromise Power Analyses

Both α and 1-β are computed as functions of

• the effect size,
• N, and
• an error probability ratio q = β/α.

To illustrate, q =1 would mean that the researcher prefers balanced type-1 and type-2 error risks (α=β), whereas q = 4 would imply that β = 4 · α, the latter of which implies that avoiding type-1 errors is regarded much more important than avoiding type-2 errors.

Compromise power analyses can be useful both before and after data collection. For example, an a priori power analysis might result in a sample size that exceeds the available resources. In such a situation, a researcher could specify the maximum affordable sample size and, using a compromise power analysis, compute α and (1-β) associated with, say, q = β/α = 4.

Alternatively, if a study has already been conducted but has not yet been analyzed, a researcher could ask for a reasonable decision criterion that guarantees perfectly balanced error risks (i.e. α = β), given the size of this sample and a critical effect size she is interested in.

Of course, compromise power analyses can easily result in unconventional significance levels larger than α=.05 (in case of small samples or effect sizes) or less than α=.001 (in case of large samples or effect sizes). However, we believe that the benefit of balanced type-1 and type-2 error risks often offsets the costs of violating significance level conventions.