Bennett, Alpert and Goldstein's S
# Bennett, Alpert and Goldstein's S

Bennett, Alpert & Goldstein’s S is a statistical measure of inter-rater agreement. It was created by Bennett et al. in 1954.

## Rationale for use

Bennett et al. suggested adjusting inter-rater reliability to accommodate the percentage of rater agreement that might be expected by chance was a better measure than simple agreement between raters. They proposed an index which adjusted the proportion of rater agreement based on the number of categories employed.

## Mathematical formulation

The formula for S is

    $S={\frac {QP_{a}-1}{Q-1}}$

where Q is the number of categories and $P_a$ is the proportion of agreement between raters.

The variance of S is

    $\operatorname {Var} (S)=\left({\frac {Q}{Q-1}}\right)^{2}{\frac {P_{a}(P_{a}-1)}{n-1}}$
