Ridit and exponential type scores for estimating the kappa statistic
Keywords:Cohen’s kappa, exponential scores, ordinal, ridit type scores, weights.
Cohen's kappa coefficient is a commonly used method for estimating interrater agreement for nominal and/or ordinal data; thus agreement is adjusted for that expected by chance. The weighted kappa statistic is used as an agreement index for ordinal data. The weights quantify the degree of discrepancy between the two categories. The choice of this particular set of weights affects the value of kappa. The common scores are Cicchetti-Allison and Fleiss-Cohen weights. In this article, we discuss the use of ridit type and exponential scores to compute kappa statistics in general.
Agresti, A. (1988). A model for agreement between ratings
on an ordinal scale. Biometrics, 44(2):539–548.
Bagheban, A.A. & Zayeri, F. (2010). A generalization of
the uniform association model for assessing rater agreement
in ordinal scales. Journal of Applied Statistics, 37(8): 1265–
, DOI: 10.108002664760903012666/.
Bross, I.D.J. (1958). How to us eridit analysis. Biometrics,
Cicchetti, D. & Allison, T. (1971). A new procedure
for assessing reliability of scoring eeg sleep recordings.
American Journal EEG Technology, 11:101–109.
Cohen, J. (1960). A coefficient of agreement for nominal
scales. Educational and Psychological Measurement,
Cohen, J. (1968). Weighted Kappa: Nominal scale agreement
with provision for scaled disagreement or partial credit.
Psychological Bulletin, 70(4): 213 -220.
Fleiss, J.L. & Cohen, J. (1973). The equivalence of weighted kappa
and the intraclass correlation coefficient as measure of reliability.
Educational and Psychological Measurement, 33: 613–619.
Fleiss, J.L., Cohen, J. & Everitt, B.S. (1969). Large sample
standard errors of kappa and weighted kappa. Psychological
Iki, K., Tahata, K. & Tomizawa, S. (2009). Ridit score type
quasi-symmetry and decomposition of symmetry for square
contingency tables with ordered categories. Austrian Journal
of Statistics, 38(3): 183–192.
Landis, J.R. & Koch, G.G. (1977). The measurement
of observed agreement for categorical data. Biometrics,
Saberi, Z. & Ganjali, M.A.(2013). A conditional Bayesian
approach for testing independence in two-way contingency
tables. Kuwait Journal of Science,40(2):103- 113.
Shoukri, M.M. (2004). Measures of Interobserver
Agreement. Chapman & Hall/CRC, Florida.
Tanner, M.A. & Young M.A. (1985). Modeling agreement
among raters. Journal of the American Statistical Association,
Warrens, M. J. (2012). Cohen’s quadratically weighted
kappa is higher than linearly weighted kappa for tridiagonal
agreement tables. Statistical Methodology, 9:440 -444, DOI:
Warrens, M. J. (2013). Weighted kappas for 3×3
tables. Journal of Probability and Statistics, DOI:
Yang, J. (2007). Measure of agreement for categorical
data. Ph.D. thesis, The Pennsylvania State University, The
Graduate School, Department of Statistics, USA.