Bangdiwala's B
{{Short description|Measure of inter-rater agreement}}
Bangdiwala's B statistic was created by Shrikant Bangdiwala in 1985 and is a measure of inter-rater agreement.Bangwidala S (1985) A graphical test for observer agreement. Proc 45th Int Stats Institute Meeting, Amsterdam, 1, 307–308Bangdiwala K (1987) Using SAS software graphical procedures for the observer agreement chart. Proc SAS User's Group International Conference, 12, 1083-1088 While not as commonly used as the kappa statistic the B test has been used by various workers.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):71-76Ossa 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):688-694Jenkins 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}}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 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
where are the values on the main diagonal,
is the th row total, and
is the 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.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) 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.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}} It may be more useful than the more commonly used Cohen's kappa in some circumstances.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}}
Tutorials and examples
Worked examples of the use of Bangdiwala's B have been published.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'sStokes, 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
The statistical programming language R has a set of functions that will compute the B test,[http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/vcd/html/00Index.html "Documentation for package ‘vcd’ version 1.2-13"] {{Webarchive|url=https://web.archive.org/web/20130810183452/http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/vcd/html/00Index.html |date=2013-08-10 }}, R package: Visualizing Categorical Data and a tutorial on the use of a test using these R functions is available.Friendly, M.
[https://cran.r-project.org/web/packages/vcdExtra/vignettes/vcd-tutorial.pdf "Working with categorical data with R and the vcd and vcdExtra packages"], CRAN R project website.