Bangdiwala's B

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Bangdiwala's B statistic was created by Bangdiwala in 1985 and is a measure of inter-rater agreement.[1][2] While not as commonly used as the kappa statistic the B test has been used by various workers.[3][4][5][6] While it is principally used as a graphical aid to inter observer agreement, its asymptotic distribution is known.


The test is applicable to testing the agreement between two observers. It is defined to be

 B = \frac{ \Sigma n_{ ii }^2 }{ \Sigma n_{ i. } n_{ .i } }

where nii are the values on the main diagonal.[clarification needed] B varies in value between 0 (no agreement) and +1 (perfect agreement).

In large samples B has a normal distribution whose variance has a complicated expression.[7] For small samples a permutation test is indicated.[7]

Guidance on its use and its extension to n x n tables have been provided by Munoz & Bangdiwala.[8] It may be more useful than the more commonly used Cohen's kappa in some circumstances.[9]

Tutorials and examples[edit]

Worked examples of the use of Bangdiwala's B have been published.[10][11] The statistical programming language R has a set of functions that will compute the B test,[12] and a tutorial on the use of a test using these R functions is available.[13]

See also[edit]


  1. ^ Bangwidala S (1985) A graphical test for observer agreement. Proc 45th Int Stats Institute Meeting, Amsterdam, 1, 307–308
  2. ^ Bangdiwala K (1987) Using SAS software graphical procedures for the observer agreement chart. Proc SAS User's Group International Conference, 12, 1083-1088
  3. ^ Grill E, Mansmann U, Cieza A, Stucki G (2007) Assessing observer agreement when describing and classifying functioning with the International Classification of Functioning, Disability and Health. J Rehabil Med 39(1):71-76
  4. ^ Ossa XM, Munoz S, Amigo H, Bangdiwala SI (2010) Secular trend in age at menarche in indigenous and nonindigenous women in Chile. Am J Hum Biol 22(5):688-694
  5. ^ Jenkins V, Solis-Trapala I, Langridge C, Catt S, Talbot DC, Fallowfield LJ (2011) What oncologists believe they said and what patients believe they heard: an analysis of phase I trial discussions. J Clin Oncol 29(1):61-68 doi:10.1200/JCO.2010.30.0814
  6. ^ Bangdiwala SI, Haedo, AS, Natal, ML, Villaveces A (2008) The Agreement Chart as an Alternative to the Receiver-Operating Characteristic Curve for Diagnostic Tests. J Clin Epidemiol 61, 866–874
  7. ^ a b Bangdiwala, Shrikant I. (1988) "The Agreement Chart". Department of Biostatistics,University of North Carolina at Chapel Hill, Institute of Statistics Mimeo Series No. 1859 (Appendix)
  8. ^ Munoz SR & Bangdiwala SI (1997) Interpretation of Kappa and B statistics measures of agreement. J Applied Stats 24 (1) 105-112 doi:10.1080/02664769723918
  9. ^ Shankara V & Bangdiwala SI (2008) "Behavior of agreement measures in the presence of zero cells and biased marginal distributions". Journal of Applied Statistics, 35 (4), 445-464 doi:10.1080/02664760701835052
  10. ^ Friendly, M (1995) "Bangdiwala's Observer Agreement Chart" Webpage: Categorical Data Analysis with Graphics (Part 3: Plots for two-way frequency tables)'s
  11. ^ Stokes, M. (2011) "Up To Speed With Categorical Data Analysis". SAS Global Forum 2011, Paper 346-2011
  12. ^ "Documentation for package ‘vcd’ version 1.2-13", R package: Visualizing Categorical Data
  13. ^ Friendly, M. "Working with categorical data with R and the vcd and vcdExtra packages", CRAN R project website.