Type I & Type II Errors
Statistics & analysis
Type I error: rejecting a true null hypothesis (false positive, controlled by α). Type II error: failing to reject a false null (false negative, controlled by statistical power).
A Type I error is a false positive: rejecting a null hypothesis that is actually true, and claiming an effect that is not there. Its probability is alpha, the significance level you set — conventionally 0.05, meaning a 5% risk of this error on any single test.
A Type II error is a false negative: failing to reject a null hypothesis that is actually false, and missing an effect that genuinely exists. Its probability is beta, and statistical power (1 minus beta) is its complement — the chance of detecting a real effect. Power of 0.80 is the usual minimum target.
The two trade off against each other. Lowering alpha to 0.01 reduces false positives but raises the risk of missing real effects unless the sample grows. Running many tests inflates the overall Type I risk, which is why post-hoc comparisons carry corrections such as Bonferroni. The clean way to reduce both errors at once is a larger, well-powered sample.
Where it's used
- Justifying the 0.05 significance level in your methodology
- Explaining why multiple comparisons need correction
Related concepts
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