Bonferroniin

Bonferroniin, commonly referred to as the Bonferroni correction, is a statistical adjustment used to address the problem of multiple hypothesis testing. When several hypotheses are evaluated simultaneously, the chance of obtaining at least one false positive increases. The Bonferroniin approach controls the family-wise error rate by adjusting the significance threshold.

If m tests are performed and the desired overall significance level is α, each individual test is assessed at α/m. A p-value p_i is considered significant if p_i ≤ α/m. This simple rule guarantees that the probability of one or more type I errors across all tests does not exceed α under any dependence among tests.

The method is named after Carlo Emilio Bonferroni, who proposed it in 1936. It is widely used across disciplines, including genomics, psychology, medicine, and social sciences, owing to its straightforward implementation and strong control of erroneous findings.

Despite its robustness, Bonferroniin is often conservative, particularly when many tests are involved or when tests are correlated. The stringent threshold can substantially reduce statistical power, increasing the risk of type II errors. This motivates the use of alternative procedures in some settings.

Related methods aim to improve power while controlling error rates. Holm-Bonferroni is a sequentially rejective version that tends to be less conservative, while Sidak’s correction offers a slight refinement under independence assumptions. In practice, researchers may report both unadjusted and adjusted p-values to convey the effect size and the strength of evidence after correction.