BiostatisticsTier 1Medical Sciences concept

Type I and Type II statistical errors - definitions

Core concept

Type I error (alpha): rejecting the null hypothesis when it is actually true -- a false positive finding (concluding an effect exists when it does not)
Type II error (beta): failing to reject the null hypothesis when it is actually false -- a false negative finding (missing a real effect)
Alpha is set by convention (usually 0.05) before the study; beta is determined by study power (1 - beta), sample size, and effect size

	H0 true	H0 false
Reject H0	Type I error (alpha)	Correct (true positive)
Fail to reject H0	Correct (true negative)	Type II error (beta)

Power = 1 - beta = probability of correctly detecting a true effect -- conventionally targeted at >=80%
Increasing sample size reduces Type II error (increases power) without changing the pre-set Type I error rate

Trap: a small, "negative" (non-significant) trial is often interpreted as proof of no effect -- more likely explanation is inadequate power (Type II error), especially if the study was small or the effect size was smaller than the study was designed to detect
Multiple comparisons inflate Type I error -- testing many outcomes/subgroups without correction (e.g. Bonferroni) increases the chance that at least one "significant" result is a false positive
Lowering alpha (e.g. to 0.01) to reduce Type I error increases the risk of Type II error for a fixed sample size -- the two error types trade off against each other, not independently adjustable

Directly determines statistical power and sample size calculation (a separate note covers power's determinants in full)
Type I error rate is exactly what a p-value threshold (e.g. p<0.05) is designed to control
A trial underpowered for its primary outcome is even more underpowered for subgroup analyses -- relevant to interpreting subgroup findings on a CI/forest plot

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