Behavior of agreement measures in the presence of zero cells and biased marginal distributions

Viswanathan Shankar, Shrikant I. Bangdiwala

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Kappa and B assess agreement between two observers independently classifying N units into k categories. We study their behavior under zero cells in the contingency table and unbalanced asymmetric marginal distributions. Zero cells arise when a cross-classification is never endorsed by both observers; biased marginal distributions occur when some categories are preferred differently between the observers. Simulations studied the distributions of the unweighted and weighted statistics for k = 4, under fixed proportions of diagonal agreement and different patterns off-diagonal, with various sample sizes, and under various zero cell count scenarios. Marginal distributions were first uniform and homogeneous, and then unbalanced asymmetric distributions. Results for unweighted kappa and B statistics were comparable to work of Muñoz and Bangdiwala, even with zero cells. A slight increased variation was observed as the sample size decreased. Weighted statistics did show greater variation as the number of zero cells increased, with weighted kappa increasing substantially more than weighted B. Under biased marginal distributions, weighted kappa with Cicchetti weights were higher than with squared weights. Both statistics for observer agreement behaved well under zero cells. The weighted B was less variable than the weighted kappa under similar circumstances and different weights. In general, B's performance and graphical interpretation make it preferable to kappa under the studied scenarios.

Original languageEnglish (US)
Pages (from-to)445-464
Number of pages20
JournalJournal of Applied Statistics
Issue number4
StatePublished - Apr 2008
Externally publishedYes


  • Bangdiwala's B
  • Cohen's kappa
  • Observer bias
  • Zero cell

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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