假设您有一个随机样本 X1,…,Xn 来自涉及参数的分布 θ 假设参数空间中的值 Θ。您将参数空间划分为Θ=Θ0∪Θ1，而您想检验假设
H0:θ∈Θ0,
H1:θ∈Θ1,
这是所谓的零和替代分别假设，。
让 X 表示随机向量所有可能值的样本空间 X=(X1,…,Xn)。您建立测试程序的目标是对样本空间进行分区X分为两部分：关键区域 C，包含的值 X 为此，您将拒绝原假设 H0 （因此，请接受替代方法 H1），以及接受区域 A，包含的值 X 为此，您不会拒绝原假设 H0 （因此，拒绝其他选择 H1）。
Formally, a test procedure can be described as a measurable function φ:X→{0,1}, with the obvious interpretation in terms of the decisions made in favor of each of the hypotheses. The critical region is C=φ−1({1}), and the acceptance region is A=φ−1({0}).
For each test procedure φ, we define its power function πφ:Θ→[0,1] by
πφ(θ)=Pr(φ(X)=1∣θ)=Pr(X∈C∣θ).
In words, πφ(θ) gives you the probability of rejecting H0 when the parameter value is θ.
The decision to reject H0 when θ∈Θ0是错误的。因此，对于给定的问题，您可能只想考虑那些测试过程φ 为此 πφ(θ)≤α，每个 θ∈Θ0，其中 α有一定的意义（0<α<1）。请注意，重要程度是一类测试程序的属性。我们可以将这个类准确地描述为
Tα={φ∈{0,1}X:πφ(θ)≤α,for everyθ∈Θ0}.
For each individual test procedure φ, the maximum probability αφ=supθ∈Θ0πφ(θ) of wrongly rejecting H0 is called the size of the test procedure φ.
It follows directly from these definitions that, once we have established a significance level α, and therefore determined the class Tα of acceptable test procedures, each test procedure φ within this class will have size αφ≤α, and conversely. Concisely, φ∈Tα if and only if αφ≤α.