Statistics Hypothesis testing Concept
Statistical hypothesis test
Builds on Statistic
Summary
A statistical hypothesis test is a rule that uses data to decide whether to reject a hypothesis about the law of the data. One fixes a null hypothesis and an alternative hypothesis , for example and with disjoint sets and . One computes a test statistic and rejects when is in a critical region . The region is chosen so that for each , for a significance level such as .
Remarks
Equivalently, one can compute the p-value and reject when it is at most . A test can make two types of errors: reject a true , or fail to reject a false . The level bounds the probability of the first error. The power of the test at is , the probability to reject when it is false. Not rejecting is not a proof that is true.
Reading path
To understand this page from the ground up, read these 49 pages in order. The foundations come first.
- Construction of the reals from Cauchy sequences concept
- Element definition
- Integers object
- Ordered field definition
- Proposition concept
- Random experiment concept
- Rational numbers object
- Real numbers object
- Set definition
- Ring of integers statement
- Disjunction definition
- Implication definition
- Predicate definition
- Ordered pair definition
- Union definition
- Sample space definition
- The rationals form a field statement
- Existential quantifier definition
- Universal quantifier definition
- Cartesian product definition
- Subset definition
- The rationals form an ordered field statement
- Uniqueness quantifier definition
- Binary relation definition
- Universal set definition
- Order on the reals definition
- Power set definition
- Complement definition
- Function definition
- Interval definition
- Preimage of a set definition
- Sigma-algebra definition
- Event definition
- Borel sigma-algebra definition
- Probability axioms concept
- Probability measure definition
- Probability distribution definition
- Probability space definition
- Conditional probability definition
- Random variable definition
- Independence of two events definition
- Law of a random variable definition
- Mutual independence of events definition
- Identically distributed random variables definition
- Independent sigma-algebras definition
- Independence of random variables definition
- Independent and identically distributed random variables definition
- Statistic definition
- Statistical hypothesis test concept
Where this leads
32 pages build on this one.
- Neyman–Pearson lemma
- P-value
- Chi-squared test
- Student's t-test
- Type I and type II errors
- Log-rank test
- Sequential analysis
- F-test
- Wald–Wolfowitz optimality of the sequential probability ratio test
- Sequential probability ratio test
- Lindley's paradox
- Score test
- Multivariate analysis of variance
- Mann–Whitney U test
- Wilcoxon signed-rank test
- Cramér–von Mises criterion
- Behrens–Fisher problem
- Kruskal–Wallis test
- Sign test
- Anderson–Darling test
- Family-wise error rate
- Dickey–Fuller test
- Uniformly most powerful test
- Power of a test
- Likelihood-ratio test
- Kolmogorov–Smirnov test
- Wald test
- False discovery rate and the Benjamini–Hochberg procedure
- Neyman construction
- Permutation test
- Fisher's exact test
- Bonferroni correction
Further reading
- Web https://en.wikipedia.org/wiki/Statistical_hypothesis_test, Definition of terms
- Web https://en.wikipedia.org/wiki/Statistical_hypothesis_test, Performing a frequentist hypothesis test in practice
About this page
| Tag | 087P03NEND |
|---|---|
| URI | m2://087P03NEND |
| Aliases | hypothesis-test, hypothesis-testing, significance-test, null-hypothesis |
| Kind | concept |
| Writing | W1 stated |
| MSC | 62F03 |
| Uses | Statistic |
| Same as |
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What this page needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Used by
- Neyman–Pearson lemma
- P-value
- Chi-squared test
- Student's t-test
- Type I and type II errors
- Log-rank test
- Sequential analysis
- F-test
- Sequential probability ratio test
- Score test
- Multivariate analysis of variance
- Mann–Whitney U test
- Wilcoxon signed-rank test
- Cramér–von Mises criterion
- Behrens–Fisher problem
- Kruskal–Wallis test
- Sign test
- Anderson–Darling test
- Family-wise error rate
- Dickey–Fuller test
- Uniformly most powerful test
- Power of a test
- Likelihood-ratio test
- Kolmogorov–Smirnov test
- Wald test
- False discovery rate and the Benjamini–Hochberg procedure
- Neyman construction
- Permutation test
- Fisher's exact test
Special cases
- Chi-squared test
- Student's t-test
- Dickey–Fuller test
- Permutation test
- Wilcoxon signed-rank test
- F-test
- Mann–Whitney U test
- Wald test
- Kruskal–Wallis test
- Cramér–von Mises criterion
- Fisher's exact test
- Anderson–Darling test
- Sign test
- Sequential probability ratio test
- Score test
- Likelihood-ratio test
- Kolmogorov–Smirnov test