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'''Bangdiwala's B''' statistic was created by Bangdiwala in 1985 and is a measure of [[inter-rater agreement]].<ref name=Bangwidala1985>Bangwidala S (1985) A graphical test for observer agreement. Proc 45th Int Stats Institute Meeting, Amsterdam, 1, 307–308</ref><ref name=Bangdiwala1987>Bangdiwala K (1987) Using SAS software graphical procedures for the observer agreement chart. Proc SAS User's Group International Conference, 12, 1083-1088</ref> While not as commonly used as the kappa statistic the B test has been used by various workers.<ref name=Grill2007>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</ref><ref name=Ossa2010>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</ref><ref name=Jenkins2011>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}}</ref><ref name=Bangdiwala2008>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</ref> While it is principally used as a graphical aid to inter observer agreement, its [[asymptotic distribution]] is known.


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The test is applicable to testing the agreement between two observers. It is defined to be
 
<math> B = \frac{ \Sigma n_{ ii }^2 }{ \Sigma n_{ i. } n_{ .i } } </math>
 
where ''n''<sub>ii</sub> are the values on the main diagonal.{{Clarify|reason=notation v.poorly explained|date=February 2012}} 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.<ref name=Bangdiwala1988>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)</ref> For small samples a permutation test is indicated.<ref name=Bangdiwala1988>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)</ref>
 
Guidance on its use and its extension to ''n'' x ''n'' tables have been provided by Munoz & Bangdiwala.<ref name=Munoz1997>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}}</ref> It may be more useful than the more commonly used Cohen's kappa in some circumstances.<ref name=Shankara2008>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}}</ref>
 
==Tutorials and examples==
 
Worked examples of the use of Bangdiwala's B have been published.<ref>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</ref><ref>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</ref>
The statistical programming language R has a set of functions that will compute the B test,<ref>[http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/vcd/html/00Index.html "Documentation for package ‘vcd’ version 1.2-13"], ''R package: Visualizing Categorical Data''</ref> and a tutorial on the use of a test using these R functions is available.<ref>Friendly, M.
[http://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.</ref>
 
==See also==
* [[Cohen's kappa]]
* [[Fleiss' kappa]]
* [[Scott's Pi]]
 
==References==
{{reflist}}
 
{{statistics}}
 
[[Category:Comparison of assessments]]
[[Category:Categorical data]]

Revision as of 15:22, 31 January 2014

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.

Definition

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

B=Σnii2Σni.n.i

where nii are the values on the main diagonal.Template:Clarify 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

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

References

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Template:Statistics

  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 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  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. ↑ 7.0 7.1 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 Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting .
  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 Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting .
  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", R package: Visualizing Categorical Data
  13. ↑ Friendly, M. "Working with categorical data with R and the vcd and vcdExtra packages", CRAN R project website.
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