# Bonferonni Inequality

The Bonferroni inequality is used to determine an upper bound on the p-value of an
experiment in which multiple hypotheses tests are performed, each hypothesis test of the Null hypothesis against
its alternative resulting in a p-value. A common mistake is to take the p-value of the combined multiple hypothesis
experiment as the smallest p-value *p _{min}*.
However, the true p-value is bounded above by the smallest p-value

*p*times

_{min}*N*, the number of multiple hypothesis tests performed.

The upper bound
*Np _{min}* is obtained by the Bonferroni inequality.
The Bonferroni upper bound
applies whether or not the various multiple hypothesis are dependent. However, if the correlations between
the multiplie hypothesis are all positive, then the Bonferroni upper bound can be way too high.