p-values. Consider a family of tests of H : = 0 (or 0), with

p-values. Consider a family of tests of H : θ = θ0 (or θ ≤ θ0), with level-α rejection regions Sα, such that

(a) Pθ0 {X ∈ Sα} for all 0 <α< 1, and

(b) Sα ⊂ Sα
for α<α

. If the tests Sα are unbiased, the distribution of ˆα under any alternative θ satisfies Pθ{αˆ ≤ α} ≥ Pθ0 {αˆ ≤ α} = α

so that it is shifted toward the origin.

Section 4.2