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Obtaining a Bayesian Estimate of Coefficient Alpha Using a Posterior Normal Distribution.

John Mart V DelosReyes1, Miguel A Padilla1

  • 1Old Dominion University, Norfolk, VA, USA.

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Summary
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A novel Bayesian approach estimates coefficient alpha using a posterior normal distribution. This method demonstrates acceptable coverage probability in simulation studies, offering a reliable statistical alternative.

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Bayesiancoefficient alphaconfidence intervalscredible intervals

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Bayesian Inference

Background:

  • Coefficient alpha is a widely used measure of internal consistency reliability in psychometric research.
  • Traditional methods for estimating coefficient alpha often rely on frequentist approaches.
  • There is a need for alternative Bayesian methods to estimate coefficient alpha, providing a different inferential framework.

Purpose of the Study:

  • To propose a new Bayesian method for estimating coefficient alpha.
  • To evaluate the performance of this Bayesian method using credible intervals.
  • To compare the proposed method with existing approaches through a simulation study.

Main Methods:

  • A Bayesian estimation of coefficient alpha was developed utilizing a posterior normal distribution.
  • Percentile, normal-theory-based, and highest probability density credible intervals were employed for assessment.
  • A simulation study was conducted to investigate the coverage probability of the proposed method.

Main Results:

  • The proposed Bayesian method for estimating coefficient alpha showed acceptable coverage probability.
  • Performance was evaluated across a range of simulation conditions.
  • Credible intervals derived from the posterior normal distribution provided valid inferential ranges.

Conclusions:

  • The proposed Bayesian approach offers a viable alternative for estimating coefficient alpha.
  • The method demonstrates good performance in terms of coverage probability.
  • This Bayesian framework contributes to the advancement of psychometric reliability estimation.