Bangdiwala's B statistic was created by
Shrikant Bangdiwala
Shrikant is a male Indian given name.
People with the name
*Shrikant Bhasi (born 1968), Indian businessman
*Shrikant Jadhav (born 1960), Indian cricketer
*Shrikant Jichkar (1954–2004), Indian politician
*Shrikant Joshi (born 1958), Indian busin ...
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, 307–308][Bangdiwala 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
Cohen's kappa coefficient ('κ', lowercase Greek kappa) is a statistic that is used to measure inter-rater reliability (and also intra-rater reliability) for qualitative (categorical) items. It is generally thought to be a more robust measure than ...
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):71-76][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][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 ][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
In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the limiting distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing appr ...
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
In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research, business int ...
.
The value of B varies in value between 0 (no agreement) and +1 (perfect agreement).
In large samples B has a
normal distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
f(x) = \frac ...
whose variance has a complicated expression.
[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) 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 ] 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 ]
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.
See also
*
Cohen's kappa
Cohen's kappa coefficient ('κ', lowercase Greek kappa) is a statistic that is used to measure inter-rater reliability (and also intra-rater reliability) for qualitative (categorical) items. It is generally thought to be a more robust measure than ...
*
Fleiss' kappa
Fleiss' kappa (named after Joseph L. Fleiss) is a statistical measure for assessing the reliability of agreement between a fixed number of raters when assigning categorical ratings to a number of items or classifying items. This contrasts with o ...
*
Scott's Pi
References
{{statistics
Comparison of assessments
Categorical variable interactions