Bonferroni correction

Examples of Bonferroni correction in the following topics:

• Pairwise Comparisons (Correlated Observations)

  • The standard practice for pairwise comparisons with correlated observations is to compare each pair of means using the method outlined in the section "Difference Between Two Means (Correlated Pairs)" with the addition of the Bonferroni correction described in the section "Specific Comparisons. " For example, suppose you were going to do all pairwise comparisons among four means and hold the familywise error rate at 0.05.
  • Using the Bonferroni correction for three comparisons, the p value has to be below 0.05/3 = 0.0167 for an effect to be significant at the 0.05 level.

• Elements of a Designed Study

  • The most conservative, but free of independency and distribution assumptions method, is known as the Bonferroni correction ${\alpha }_ {\text{per comparison}}=\frac { \bar { \alpha } }{ n }$.
  • Another procedure is the Holm–Bonferroni method, which uniformly delivers more power than the simple Bonferroni correction by testing only the most extreme $p$-value ($i=1$) against the strictest criterion, and the others ($i>1$) against progressively less strict criteria.
  • Multiple testing correction refers to re-calculating probabilities obtained from a statistical test which was repeated multiple times.
  • This is called the Bonferroni correction and is one of the most commonly used approaches for multiple comparisons.
  • These methods provide "strong" control against Type I error, in all conditions including a partially correct null hypothesis.

• Multiple comparisons and controlling Type 1 Error rate

  • The Bonferroni correction suggests that a more stringent significance level is more appropriate for these tests: α* = α/K, where K is the number of comparisons being considered (formally or informally).
  • Complete the three possible pairwise comparisons using the Bonferroni correction and report any differences.

• Exercises

  • The dependent variable is "Number correct. " Make sure to label both axes.
  • Test differences among the four levels of B using the Bonferroni correction.

• Exercises

  • Are these corrected scores significantly different from 65 at the .05 level?
  • Make sure to control for the familywise error rate (at 0.05) by using the Bonferroni correction.
  • True/false: If you are making 4 comparisons between means, then based on the Bonferroni correction, you should use an alpha level of .01 for each test.

• Specific Comparisons (Independent Groups)

  • This inequality is called the Bonferroni inequality.
  • The Bonferroni inequality can be used to control the family wise error rate as follows: Id you want the family wise error rate to be alpha, you use alpha/c as the per-comparisson error rate.
  • This correction, called the Bonferroni correction, will generally result in a familywise error rate less than α.

• Glossary

• Stepwise Regression

  • The key line in the sand is at what can be thought of as the Bonferroni point: namely how significant the best spurious variable should be based on chance alone.

• Optional Collaborative Classrom Exercise

  • Is the table correct?
  • If it is not correct, what is wrong?
  • True or False: Three percent of the people surveyed commute 3 miles.If the statement is not correct, what should it be?
  • If the table is incorrect, make the corrections.

• Example Calculations

  • Bond correct more than 0.50 of the time?
  • Bond is correct, and compute the probability of being correct that many or more times given that the null hypothesis is true.
  • The probability of being correct on 11 or more trials is 0.105 and the probability of being correct on 12 or more trials is 0.038.
  • Bond is correct 0.75 of the time.
  • Bond's true ability to be correct on 0.75 of the trials, the probability he will be correct on 12 or more trials is 0.63.