Personal notes on hypothesis testing in statistics.
Based on notes taken during a course [1].
Hypotheses
- 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
References
[1]
Jem Corcoran. Statistical inference and hypothesis testing in data science applications. Course on Coursera.