Bennett, Alpert and Goldstein's S

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.^[2] They proposed an index which adjusted the proportion of rater agreement based on the number of categories employed.

The formula for S is

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

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

The variance of S is

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

This statistic is also known as Guilford’s G.^[3] Guilford was the first person to use the approach extensively in the determination of inter-rater reliability.^{[citation needed]}