In statistics, the Bonferroni correction is a method used to address the problem of multiple comparisons.
The Bonferroni correction is derived by observing Boole's inequality
In probability theory, Boole's inequality, named after George Boole, (also known as the union bound) says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events.
A related correction is called the Šidák correction. The Šidák correction is derived by assuming that the individual tests are independent. Since we are assuming that they are independent, the probability that all of them are not significant is the product of the probabilities that each of them are not significant.
The Šidák correction gives a stronger bound than the Bonferroni correction but requires the additional condition of independence. Because the Šidák correction requires calculating fractional powers, it is more complicated to do and the simpler Bonferroni correction is often preferred.