For a fixed false-positive rate, the likelihood-ratio test is the most powerful; decision rules trade Type I against Type II error.
Neyman and Pearson's 1933 result. Its institutional consequence is that every screening programme, every audit threshold and every legal standard of proof is a choice about which error to prefer.
In practice
- A screening programme set to catch almost every case will refer many healthy people, and the threshold is a policy choice.
- An audit rule that flags 5% of transactions has chosen how many frauds it will miss, whether or not anyone stated it.
- Further reading
- Wikipedia
- Subject
- Science & Epistemology
- Essay
- The ways evidence misleads