Bonferroni adjustment

Bonferroni Adjustment

The Bonferroni adjustment is a statistical method used to counteract the problem of multiple comparisons. It is named after Italian mathematician Carlo Emilio Bonferroni.

Overview

The Bonferroni adjustment is a correction method that is used when multiple statistical tests are being performed simultaneously. The purpose of the adjustment is to control the familywise error rate (FWER), which is the probability of making one or more false discoveries, or Type I errors, among all the hypotheses when performing multiple pairwise tests.

Methodology

The Bonferroni adjustment is achieved by dividing the threshold probability by the number of comparisons being made. For example, if 20 hypotheses are being tested, the Bonferroni correction would test each individual hypothesis at a significance level of 0.05/20 = 0.0025.

Application

The Bonferroni adjustment is widely used in fields such as biostatistics, psychology, health sciences, and genomics, where researchers often need to control the FWER due to the large number of simultaneous hypotheses tests.

Criticism

While the Bonferroni adjustment is a popular method for controlling the FWER, it has been criticized for being too conservative, especially when the tests are not independent. This can lead to a high rate of Type II errors, or false negatives, where a true effect is missed.

See Also

• Multiple comparisons problem
• Familywise error rate
• Type I and type II errors
• Carlo Emilio Bonferroni