Type I and Type II Errors — Section 8: Frequentist Inference

Every hypothesis test can be wrong in two distinct ways, and the framework names both:

A Type I error rejects $H_0$ when it's actually true — a false alarm. Its rate is $\alpha$ , the significance level you chose.

A Type II error fails to reject $H_0$ when $H_1$ is actually true — a missed detection. Its rate is $\beta$ .

Power = $1 - \beta$ , the probability of correctly rejecting a false $H_0$ . Higher power means you'll catch real effects more often.

There's a fundamental trade-off: lowering $\alpha$ (fewer false alarms) raises $\beta$ (more misses), and vice versa. The only ways to reduce both at once are to collect more data or improve the signal-to-noise of your measurement.

In trading, low Type II error often matters more than low Type I. Missing a real alpha signal is usually costlier than a few false alarms — especially when each "test" is cheap to validate further.

Every hypothesis test can be wrong in two distinct ways, and the framework names both:

A Type I error rejects $H_0$ when it's actually true — a false alarm. Its rate is $\alpha$ , the significance level you chose.

A Type II error fails to reject $H_0$ when $H_1$ is actually true — a missed detection. Its rate is $\beta$ .

Power = $1 - \beta$ , the probability of correctly rejecting a false $H_0$ . Higher power means you'll catch real effects more often.

In trading, low Type II error often matters more than low Type I. Missing a real alpha signal is usually costlier than a few false alarms — especially when each "test" is cheap to validate further.