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Abstract:
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The traditional approach to teaching about the power of a hypothesis test generally starts by defining a rejection region based on the distribution of a test statistics under some null hypothesis, then finding the probability of falling into that region under some alternative hypothesis. Typically, this approach requires setting a specific significance level (say 5%) in order to find the exact boundary of that rejection region, but this goes against current efforts to de-emphasize rigid “p< 0.05”-type rules for determining statistical significance. We propose an alternate way to measure something akin to power that does not depend on a specific significance level or rejection region, but still illustrates general statistical ideas that are traditionally associated with power (like the effect of increasing sample size or detecting a larger difference).
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