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

$S=\frac{Q{P}_a-1}{Q-1}$

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

The variance of S is

$\mathrm{Var}(S)={\left(\frac{Q}{Q-1}\right)}^2\frac{P_a(P_a-1)}{n-1}$

Notes

This statistic is also known as Guilford’s G. Guilford was the first person to use the approach extensively in the determination of inter-rater reliability.Template:Citation needed