# Bonferroni Test – Definition

### Bonferroni Test Definition

A Bonferroni Test is defined as a comparison tests often used in statistics that involve several statistics. Bonferroni correction and Bonferroni adjustment are other terms that have the same meanings and use as Bonferroni Test.

When multiple tests are run using the hypothesis, there is a tendency for an error to occur in the results and the result might be posed as statistically significant by the experimenter. The Bonferroni test permits that comparison of different variables in order to prevent inaccurate data from appearing as statistically significant. This test prevent data from falsely appearing as statistically significant by lowering the alpha value. multiple comparison statements to be made.

### A Little More on What is a Bonferroni Test

The Bonferroni test was named after its developer an Italian Mathematician, Carlo Emilio Bonferroni. Aside from this test, there are other comparison tests that were developed, examples are Scheffe’s Test and the Tukey-Kramer method test. The Bonferroni Test method allows confidence intervals to be constructed in statistical analysis, in a way that the significant parameters can be maintained. Carlo Emilio Bonferroni, who developed the Bonferroni test lived between 1892 and 1960. Despite the usefulness of the Bonferroni test, it was criticised for being overly conservative and unable to do specific significant findings.

### Academic Research on Bonferroni test

A stagewise rejective multiple test procedure based on a modified Bonferroni test, Hommel, G. (1988). Biometrika, 75(2), 383-386.

A simple sequentially rejective multiple test procedure, Holm, S. (1979). Scandinavian journal of statistics, 65-70.

An improved Bonferroni procedure for multiple tests of significance, Simes, R. J. (1986). Biometrika, 73(3), 751-754.

An improved sequentially rejective Bonferroni test procedure, Holland, B. S., & Copenhaver, M. D. (1987). Biometrics, 417-423.

A sharper Bonferroni procedure for multiple tests of significance, Hochberg, Y. (1988). Biometrika, 75(4), 800-802.

A sequentially rejective test procedure based on a modified Bonferroni inequality, Rom, D. M. (1990). Biometrika, 77(3), 663-665.

Multiple significance tests: the Bonferroni method, Bland, J. M., & Altman, D. G. (1995). Bmj, 310(6973), 170.

Improved Bonferroni-type multiple testing procedures., Holland, B. S., & Copenhaver, M. D. (1988). Psychological Bulletin, 104(1), 145.

On the power of some binomial modifications of the Bonferroni multiple test., Teriokhin, A. T., & Guégan, J. F. (2007). Zhurnal obshchei biologii, 68(5), 332-340.

What’s wrong with Bonferroni adjustments, Perneger, T. V. (1998). Bmj, 316(7139), 1236-1238.

A modified Bonferroni method for discrete data, Tarone, R. E. (1990). Biometrics, 515-522.