Bonferroni correction
The Bonferroni or Bonferroni correction (after Carlo Emilio Bonferroni ) is a method of mathematical statistics, with the help of the alpha error accumulation is neutralized with multiple paired comparisons.
It says that if one is testing n independent hypotheses on a dataset, the statistical significance to be used separately for each hypothesis, 1 / n of significance is that only a hypothesis would result in the test.
Example
Consider an experiment that is sought after in the gene expression differences between healthy cells and cancer cells. It 10,000 genes were tested. If one uses the usual significance level (p < 0.05), one obtains 587 significantly different genes. Due to error by multiple testing very many of these genes in reality but not be different. The Bonferroni correction is instead a significance level of p < 0.05 / 10000, ie p < 0.000005. This value is obtained six significant genes. This eliminates a lot of false-positive results. The remaining results are thus more reliable, but also many real different genes at the same time are excluded. The Bonferroni correction is therefore more conservative than, for example, the correction of the false discovery rate ( FDR) according to Benjamini - Hochberg.
Background
If we examine a hypothesis Family with pairwise comparisons and checks each associated individual hypothesis at the significance level, then exists between the risk of the individual tests and the multiple global exposure ( as indicated ) the following inequality:
This relationship follows from the Bonferroni inequality ( Boolean inequality) and states that the multiple total risk is limited to the top. If you choose the significance level for each individual test, then the multiple global risk can not be greater than.
So to comply with the multiple overall risk, you may have to adjust in each individual test, the significance level. The Bonferroni method is a very rough approximation, and very conservative. Therefore, more accurate methods have been developed that control the error less conservative and the level of significance of the multiple testing procedure further exploit (see alpha error accumulation).
Bonferroni in signal processing
It is a voxel map with many statistical values before, in which some independent, others are interdependent. To find out special characteristics of this distribution, the Bonferroni correction can be applied. This is true only for independent testing and is too strict for only partially dependent tests. Therefore, it is the discovery of a significance limit (P value or level of significance ) in such a statistical map whose values are only partially dependent or independent, is often mixed with the Gaussian field method. For a voxel while the lower p- value of the two correction methods is given and thus determines the barrier.