Family-wise error rate
Topic of High-dimensional analysis, part of Statistical learning · Also in Analysis of variance
Family-wise error rate
| Type | Topic |
| Taught in | High-dimensional analysis · Analysis of variance |
| Part | Statistical learning · Statistical inference |
| Questions using it | 2 |
The probability of at least one false rejection among a family of tests. Bonferroni’s correction and Tukey’s intervals control it. It is stricter than the false discovery rate, and with thousands of tests it leaves almost no power.
In High-dimensional analysis
The family-wise error rate is controlled at a level such as 0.05. The Bonferroni method exists, and it is often far too stringent when the number of tests is in the thousands. No particular value of a null p-value, including a very small one, is specially expected: under a continuous null the p-value is uniform.
In Analysis of variance
From Analysis of variance
The studentised range is the law of the largest minus the smallest of k independent standard normals, divided by an independent \sqrt{V/m} with V\sim\chi^2_m. Bounding the largest difference among the group means bounds all of them at once. A pair whose interval excludes zero is declared different at familywise level \alpha.
Used in
- Taught in High-dimensional analysis · Analysis of variance
- Also used in Analysis of variance · Analysis of variance examples
- Questions that use it (2) — A Tukey interval for two varieties · Five treatments, ten pairs
- All 9 questions on High-dimensional analysis
See also
Bonferroni correction · Multiple testing · False discovery rate · Benjamini–Hochberg · Tukey intervals · Rank bound · Family-wise control implies false-discovery control · Benjamini–Hochberg controls the false discovery rate · Why classical methods fail when p > n