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]