Bangdiwala's B

Definition

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

B = \frac{ \sum_{i=1}^k n_{ ii }^2 }{ \sum_{i=1}^k n_{ i. } n_{ .i } }

where n_{ii} are the values on the main diagonal, n_{i.} is the ith row total, and n_{.i} is the ith 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.Friendly, M. "Working with categorical data with R and the vcd and vcdExtra packages", CRAN R project website.

References

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) [http://www.stat.ncsu.edu/information/library/mimeo.archive/ISMS_1988_1859.pdf "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) [http://www.datavis.ca/courses/grcat/grc3.html#H2_62:Bangdiwala's "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. [[Maura Stokes. Stokes, M.]] (2011) [http://support.sas.com/resources/papers/proceedings11/346-2011.pdf "Up To Speed With Categorical Data Analysis"]. SAS Global Forum 2011, Paper 346-2011
12. [http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/vcd/html/00Index.html "Documentation for package ‘vcd’ version 1.2-13"] {{Webarchive. link. (2013-08-10 , ''R package: Visualizing Categorical Data'')