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Related Experiment Videos

Hubert's multi-rater kappa revisited.

Antonio Martín Andrés1, María Álvarez Hernández2

  • 1Bioestadística, Facultad de Medicina, Universidad de Granada, Granada, Spain.

The British Journal of Mathematical and Statistical Psychology
|May 7, 2019
PubMed
Summary
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This study addresses measuring agreement among multiple raters using kappa-type coefficients. It introduces Hubert

Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • Measuring inter-rater reliability is crucial for consistent data collection across multiple observers.
  • Existing kappa-type coefficients have limitations, particularly when more than two raters are involved.
  • The interpretation of 'agreement' varies, leading to different coefficient definitions.

Purpose of the Study:

  • To provide a unified framework for kappa-type coefficients applicable to R > 2 raters.
  • To introduce Hubert's (nominal) and Schuster and Smith's (ordinal) kappa coefficients based on a strict agreement definition.
  • To derive formulae for the large-sample variances of these estimators for robust statistical inference.

Main Methods:

  • Utilized Hubert's interpretation of agreement: all raters must agree on a subject's category.
Keywords:
Cohen's kappaConger's kappaHubert's kappaSchuster and Smith's kappanominal agreementordinal agreement

Related Experiment Videos

  • Derived kappa coefficients for nominal (Hubert's kappa) and ordinal (Schuster and Smith's kappa) data.
  • Developed formulae for the large-sample variances of the estimated kappa coefficients.
  • Main Results:

    • Presented Hubert's and Schuster and Smith's kappa coefficients as extensions for multiple raters.
    • Provided variance formulae enabling statistical inference and comparison of different agreement measures.
    • Demonstrated that Schuster and Smith's ordinal kappa aligns with intraclass and concordance correlation coefficients under quadratic weighting.

    Conclusions:

    • Hubert's and Schuster and Smith's kappa coefficients offer robust measures of inter-rater agreement for R > 2 observers.
    • The derived variance formulae facilitate hypothesis testing and confidence interval construction for these coefficients.
    • The alignment of Schuster and Smith's kappa with correlation coefficients in the ordinal case provides a valuable link between different reliability metrics.