Bangdiwala's B

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.[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]

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]

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