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Bonferroni Test

Bonferroni Test

What Is the Bonferroni Test?

The Bonferroni test is a type of multiple comparison test utilized in statistical analysis. While performing a hypothesis test with multiple comparisons, eventually an outcome could happen that appears to demonstrate statistical significance in the dependent variable, even when there is none.

On the off chance that a particular test, for example, a linear regression, in this way yields right outcomes the vast majority of the time, running similar regression on 100 unique samples could lead to no less than one false-positive outcome sooner or later. The Bonferroni test attempts to prevent data from mistakenly appearing to be statistically critical like this by making an adjustment during comparison testing.

Understanding the Bonferroni Test

The Bonferroni test, otherwise called "Bonferroni correction" or "Bonferroni adjustment" recommends that the p-value for each test must be equivalent to its alpha separated by the number of tests performed.

The Bonferroni test is a multiple-comparison correction utilized when several dependent or independent statistical tests are being performed all the while. The explanation is that while a given alpha value might be appropriate for every individual comparison, it isn't appropriate for the set, everything being equal. To take out multiple spurious positives, the alpha value should be brought down to account for the number of comparisons being performed.

The test is named for the Italian mathematician who developed it, Carlo Emilio Bonferroni (1892-1960). Different types of multiple comparison tests incorporate Scheff\u00e9's test and the Tukey-Kramer method test. An analysis of the Bonferroni test is that it is too conservative and may fail to get a few huge discoveries.

In statistics, a null hypothesis is basically the conviction that there's no statistical difference between two data sets being compared. Hypothesis testing includes testing a statistical sample to affirm or dismiss a null hypothesis. The test is performed by taking a random sample of a population or group. While the null hypothesis is tried, the alternative hypothesis is likewise tried, by which the two outcomes are mutually exclusive.

Notwithstanding, with any testing of a null hypothesis, there's the expectation that a false-positive outcome could happen. This is officially called a Type I error, and thus, a blunder rate that mirrors the probability of a Type I mistake is assigned to the test. All in all, a certain percentage of the outcomes will probably yield a false positive.

Utilizing Bonferroni Correction

For example, a blunder rate of 5% could typically be assigned to a statistical test, implying that 5% of the time there will probably be a false positive. This 5% blunder rate is called the alpha level. In any case, when numerous comparisons are being made in an analysis, the blunder rate for every comparison can impact different outcomes, making multiple false positives.

Bonferroni planned his method of adjusting for the increased mistake rates in hypothesis testing that had multiple comparisons. Bonferroni's adjustment is calculated by stepping through the number of examinations and separating it into the alpha value. Utilizing the 5% mistake rate from our example, two tests would yield a blunder rate of 0.025 or (.05/2) while four tests would accordingly have a mistake rate of .0125 or (.05/4). Notice that the blunder rate diminishes as the sample size increments.


  • In particular, Bonferroni planned an adjustment to prevent data from mistakenly appearing to be statistically critical.
  • An important limitation of Bonferroni correction is that it might lead analysts to mix genuine true outcomes.
  • The Bonferroni test is a statistical test used to reduce the case of a false positive.