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.

• Overview of Statement Changes and Errors

  • Despite best efforts, occasionally an error is made on the financial statement and must be corrected.
  • Please note: an error correction is the correction of an error in previously issued financial statement; it is not an accounting change.
  • Adjust the financial statements for each prior period presented, to reflect the error correction.
  • Yet when retained earning for year Z is correct, because the two previous errors cancelled each other out.
  • Explain why a previously issued financial statement would have an error and how to correct it

• Taking Corrective Action

  • Taking corrective action requires identifying the problem and implementing a potential solution.
  • Taking corrective action is one of the three essential elements of the control process.
  • One key aspect of taking corrective action is problem-solving.
  • This problem-solving process is the central consideration for effective corrective action.
  • Once the problem is identified, and a method of corrective action is determined, it needs to be implemented as quickly as possible.

• Breast Augmentation and Reduction

  • Breast augmentation denotes the breast implant and fat-graft mammoplasty procedures for correcting the defects, and for enhancing the size, form, and feel of a woman's breasts.
  • The fat-transfer approach effects the augmentation, and corrects the contour defects of the breast hemisphere with grafts of autologous adipocyte fat tissue.
  • Reduction mammoplasty (also breast reduction and reduction mammoplasty) is the plastic surgery procedure for correcting over-sized breasts.
  • In corrective practice, the surgical techniques and praxis for reduction mammoplasty also are applied to mastopexy (breast lift).
  • Moreover, the correction of gynecomastia (woman's breast) is the analogous, enlarged male-breast reduction surgery procedure, wherein there is no consideration of lactation capability.

• 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.