Hypothesis testing

Personal notes on hypothesis testing in statistics.

Based on notes taken during a course [1].


null hypothesis
Hypothesis assumed to be true. Often denoted by \(H_0\).
alternative hypothesis
Hypothesis for which we are looking for evidence. Often denoted by \(H_1\) or \(H_a\).
simple hypothesis
Hypothesis which completely specifies the distribution.
composite hypothesis
Hypothesis which is not simple. I.e., aspects of the distribution are left unspecified.

Hypothesis testing either rejects or fails to reject the null hypothesis.

Types of error

Type I error
Rejecting the null hypothesis when it is true.
Type II error
Failing to reject the null hypothesis when it is false.

See also