ANOVA Part IV: Bonferroni Correction | Statistics Tutorial #28 | MarinStatsLectures

ANOVA & Bonferroni Correction for Multiple Comparisons: What is Bonferroni’s Correction and When Do We Use It? 👉🏼 ANOVA with R Tutorial: (https://goo.gl/kY4kyE); ANOVA Complete Video Tutorials (https://bit.ly/2zBwjgL); 👍🏼Best Statistics & R Programming Language Tutorials: ( https://goo.gl/4vDQzT )

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In this ANOVA video tutorial, we learn about Bonferroni's multiple testing correction (Bonferroni Correction) for Analysis of Variance (ANOVA). When comparing multiple groups, if the null hypothesis is rejected (with a small p-value), the conclusion is that there is evidence that at least one of the means differs from the rest, but there is no indication of which differ from others. To decide which we believe differ, we can conduct "multiple comparisons" of all pairwise sets of means.

While working through an example with multiple comparisons, we will see that because we are making multiple comparisons at once, the chance of making a type I error (false positive) increases. Also called family-wise error rate (FWER), this is the probability of at least one type I error (at least one false positive) when performing multiple hypotheses tests.

Bonferroni proposed a method to correct the inflated type I error rate. Bonferroni assumes that all pairwise tests are independent. This may not be true, but as we will see in this video, independence makes calculations simpler and it is also a bit more conservative. Bonferroni’s approach is to use an adjusted alpha level. The Bonferroni correction sets the significance cut-off for each test at (α/# of tests), in order to have an overall type I error rate of approximately α (alpha).


While Bonferroni's method is not necessarily the `optimal' correction to use, it is easy to understand, and it is conservative. Other methods of correction for multiple comparisons do exist, Tukey's or Dunnett's, for example. They are all based on the same concept, so once you understand Bonferroni's correction, you will be able to understand the concepts behind the other options.

▶︎ The purpose of ANOVA: One Way Analysis of Variance (ANOVA) is used to compare the means of 3 or more independent groups.
▶︎ ANOVA test Assumptions: The ANOVA test requires assuming independent observations, independent groups, that the variance (or standard deviation) of the two groups being compared are approximately equal or that the sample size for each group is large



▶︎▶︎ Watch More

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▶︎ ANOVA: Bonferroni Multiple Comparisons Correction    • ANOVA Part IV: Bonferroni Correction ...  
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