wiki/statistical-hypothesis-testing/neyman-pearson-theory/

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wiki/statistical-hypothesis-testing/neyman-pearson-theory/

The Neyman-Pearson hypothesis testing tests two hypothesis, hypothesis $H$, and an alternative hypothesis $H_A$.
Neyman-Pearson Lemma The Neyman-Pearson Lemma is an very intuitive lemma to understand how to choose a hypothesis. The lecture notes from PennState is a very good read on this topic1.
An example For simplicity, we assume that there exists a test statistic $T$ and $T$ can be used to measure how likely the hypothesis $H$ is true, e.g., the hypothesis $H$ is false, corresponds to $T$ being small.
The reference from Shafer2007 assumes a random variable $T$ to be large if the hypothesis $H$ is false[^Shafer2007]. One example is the ratio of likelihood2,

https://datumorphism.leima.is/wiki/statistical-hypothesis-testing/neyman-pearson-theory/