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Related Concept Videos

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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.
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How to Calculate and Validate Inter-brain Synchronization in a fNIRS Hyperscanning Study
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How to Calculate and Validate Inter-brain Synchronization in a fNIRS Hyperscanning Study

Published on: September 8, 2021

Resampling permutation probability values for Cronbach's alpha.

Andrew J Prelog1, Kenneth J Berry, Paul W Mielke

  • 1Department of Sociology, Colorado State University, Fort Collins, CO 80523-1784, USA. Andrew.Prelog@colostate.edu

Perceptual and Motor Skills
|June 24, 2009
PubMed
Summary
This summary is machine-generated.

A new permutation method enhances Cronbach's alpha reliability testing, especially for small sample sizes. This approach provides robust resampling probability values and empirical quantile limits when standard assumptions are unmet.

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Last Updated: Jun 22, 2026

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05:33

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Published on: September 8, 2021

Area of Science:

  • Psychometrics
  • Statistical Methods

Background:

  • Cronbach's alpha is a widely used measure of internal consistency reliability.
  • Traditional use of Cronbach's alpha relies on specific statistical assumptions.
  • Violations of these assumptions, particularly with small sample sizes, can compromise reliability estimates.

Purpose of the Study:

  • To introduce a permutation procedure for calculating resampling probability and empirical quantile limits for Cronbach's alpha.
  • To discuss the assumptions underlying the conventional application of Cronbach's alpha.
  • To advocate for the utility of permutation testing in Cronbach's alpha analysis under specific conditions.

Main Methods:

  • A permutation procedure was developed to compute resampling probabilities.
  • Empirical quantile limits were derived using the permutation approach.
  • The study discusses the theoretical underpinnings and assumptions of Cronbach's alpha.

Main Results:

  • The permutation procedure provides a method for assessing Cronbach's alpha reliability.
  • Empirical quantile limits can be determined through this resampling technique.
  • The procedure is particularly effective when standard assumptions for alpha are not met.

Conclusions:

  • Permutation testing offers a valuable alternative for Cronbach's alpha when sample sizes are small.
  • This method enhances the reliability of internal consistency estimates in challenging statistical scenarios.
  • The procedure addresses limitations of conventional Cronbach's alpha analysis.