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

Definition

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

${\displaystyle B={\frac {\sum _{i=1}^{k}n_{ii}^{2}}{\sum _{i=1}^{k}n_{i.}n_{.i}}}}$

where ${\displaystyle n_{ii}}$ are the values on the main diagonal, ${\displaystyle n_{i.}}$ is the ${\displaystyle i}$th row total, and ${\displaystyle n_{.i}}$ is the ${\displaystyle i}$th column total of the contingency table. The value of 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. For small samples a permutation test is indicated.

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

Tutorials and examples

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

See also

• Cohen's kappa
• Fleiss' kappa
• Scott's Pi

References

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. ^ 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) http://www.datavis.ca/courses/grcat/grc3.html#H2_62:Bangdiwala'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" Archived 2013-08-10 at the Wayback Machine, R package: Visualizing Categorical Data
13. Friendly, M. "Working with categorical data with R and the vcd and vcdExtra packages", CRAN R project website.

• Comparison of assessments
• Categorical variable interactions