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A FORTRAN program for computing the exact variance of weighted kappa.

Paul W Mielke¹, Kenneth J Berry, Janis E Johnston

¹Department of Statistics, Colorado State University, Fort Collins, CO 80523-1877, USA. mielke@lamar.colostate.edu

Perceptual and Motor Skills

|December 31, 2005

Summary

This study presents an algorithm and FORTRAN program for calculating the exact variance of weighted kappa. The VARKAP program offers comprehensive statistical outputs for this agreement measure.

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Area of Science:

Statistics
Biostatistics
Psychometrics

Background:

Weighted kappa is a crucial metric for inter-rater reliability.
Accurate variance estimation is essential for hypothesis testing and confidence interval construction.
Existing methods for weighted kappa variance may lack precision or accessibility.

Purpose of the Study:

To develop and present an algorithm for the exact variance of weighted kappa.
To provide a user-friendly FORTRAN program (VARKAP) for implementing this algorithm.
To offer a complete statistical output for weighted kappa analysis.

Main Methods:

Development of a novel algorithm for exact weighted kappa variance calculation.
Implementation of the algorithm in a FORTRAN program named VARKAP.

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Validation of the algorithm and program through theoretical and empirical means (implied).

Main Results:

The VARKAP program computes the weighted kappa test statistic.
It accurately determines the exact variance of weighted kappa.
Provides Z scores and precise one-sided and two-sided N(0,1) probability values.

Conclusions:

The provided algorithm and VARKAP program offer a robust solution for calculating the exact variance of weighted kappa.
This tool facilitates more accurate statistical inference in reliability studies.
Researchers gain access to precise measures of agreement and their statistical significance.