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Related Concept Videos

Bonferroni Test01:10

Bonferroni Test

3.1K
The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
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Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
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Wilcoxon Rank-Sum Test01:21

Wilcoxon Rank-Sum Test

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The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a nonparametric test used to determine if there is a significant difference between the distributions of two independent samples. This test is designed specifically for two independent populations and has the following key requirements:
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Related Experiment Video

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The Use of Reverse Phase Protein Arrays RPPA to Explore Protein Expression Variation within Individual Renal Cell Cancers
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Reversing Bonferroni.

Gregory Francis1, Evelina Thunell2,3

  • 1Department of Psychological Sciences, Purdue University, 703 Third Street, West Lafayette, IN, 47907-2004, USA. gfrancis@purdue.edu.

Psychonomic Bulletin & Review
|January 19, 2021
PubMed
Summary
This summary is machine-generated.

Researchers often require multiple significant outcomes, but this lowers statistical power. A novel "reverse Bonferroni" method increases significance criteria to maintain power and Type I error rates, especially when analysis plans are pre-registered.

Keywords:
BonferroniError ratePowerReplication

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Area of Science:

  • Statistics
  • Empirical Research Methodology

Background:

  • Empirical studies frequently require multiple significant outcomes for conclusions.
  • This practice can lead to unintended consequences, including a lower compound Type I error rate and a significant drop in statistical power.

Purpose of the Study:

  • To address the issue of hyper-conservative error rates and low power associated with multiple significance criteria in empirical studies.
  • To propose a novel statistical method to maintain the intended compound Type I error rate while improving statistical power.

Main Methods:

  • The study proposes a 'reverse Bonferroni' approach, which involves increasing the significance criterion.
  • This method is presented as a way to manage the compound Type I error rate across multiple statistical tests.

Main Results:

  • The reverse Bonferroni approach can effectively maintain the intended compound Type I error rate.
  • This method significantly improves statistical power compared to traditional approaches.

Conclusions:

  • The reverse Bonferroni method offers a solution to the challenges posed by multiple significance criteria in empirical research.
  • The authors recommend restricting this method to pre-registered analysis plans to ensure responsible research practices and avoid questionable research practices.