In a single hypothesis testing problem, we the : Rejecting the one null hypothesis when it is actually true. Given a threshold $\alpha$, we can find out the interval $\Gamma$ that leads to a probability of rejecting the hypothesis $p\leq\alpha$ (single-sided).

In a , type I error is ambiguous. Suppose we have $m$ hypotheses $H_1, \cdots, H_i, H_m$. If we define the type I error as committing at least one type I error, this is the FamilyWise Error Rate (FWER).

In such a problem, we look for intervals $\Gamma^\alpha_i$ that lead to $p_i\leq \alpha/m$, where $m$ is the number of hypotheses. These intervals will together make sure our jointed type I error greater than $\alpha$.

Planted: by ;

L Ma (2020). 'Bonferroni Correction', Datumorphism, 04 April. Available at: https://datumorphism.leima.is/cards/statistics/bonferroni-correction/.