Type I and type II errors

Type I error is rejecting a true null hypothesis; type II error is failing to reject a false null hypothesis. Their probabilities are commonly denoted α and β.

Null hypothesis: A statistical hypothesis specifying a default condition or no effect, tested against an alternative. Both error types are defined by whether this hypothesis is true and what decision the test makes.
Statistical hypothesis testing: A procedure for using sample data to evaluate a claim about a population or probability model. Type I and type II errors are outcomes of this broader decision procedure.
False positive rate: The proportion of truly negative cases incorrectly classified as positive. In a binary test, this conditional rate corresponds to type I error probability.
Clinical trial: A prospective study evaluating the effects and safety of an intervention in human participants. Trial designs set acceptable false-alarm risks while seeking enough power to detect meaningful effects.
Significance level: The maximum long-run probability of rejecting a true null hypothesis specified by a statistical test. It sets the tolerated probability of a type I error.
Alternative hypothesis: A statistical claim that differs from the null hypothesis and represents effects or patterns under investigation. A type II error occurs when this claim is true but the test does not reject the null.
False negative rate: The proportion of truly positive cases incorrectly classified as negative. In a binary test, this conditional rate corresponds to type II error probability.
Diagnostic testing: The use of tests to identify whether a person has a disease or condition. A positive or negative result can correspond to the two kinds of testing error.
Statistical power: The probability that a statistical test rejects the null hypothesis when a specified alternative is true. Power equals one minus the type II error probability for that alternative.
Sampling distribution: The probability distribution of a statistic across repeated samples drawn under specified conditions. Error probabilities come from how test statistics vary across repeated samples.

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