Two ways to be wrong: false alarms vs missed signals

Question

A fraud-detection system flags transactions as "fraud" or "legitimate." Sometimes it flags a legitimate transaction; sometimes it lets a fraudulent one through.

Define type I and type II errors in this context, connect them to $\alpha$ , $\beta$ , and power, and explain the tradeoff between them.

Accepted Answer

Set the null. Let H0 = "the transaction is legitimate" (the default, no-action state) and H1 = "it's fraud." Then: - Type I error (false positive): flagging a legitimate transaction as fraud. Rejecting a true null. Its probability is \alpha, a false alarm. - Type II error (false negative): letting a fraudulent transaction pass as legitimate. Failing to reject a false null. Its probability is \beta, a missed detection. - Power = 1 - \beta: the chance of correctly catching fraud when it's really there. A memory hook: type I is convicting the innocent; type II is acquitting the guilty. The trade…

Two ways to be wrong: false alarms vs missed signals

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