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.^[1]

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.^[2] 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

\operatorname{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.^[3] Guilford was the first person to use the approach extensively in the determination of inter-rater reliability.

References

↑ Bennett, EM; Alpert, R; Goldstein, AC (1954). "Communications through limited response questioning". Public Opinion Quarterly 18: 303–308. doi:10.1086/266520.
↑ "The effect of combining categories on Bennett, Alpert and Goldstein’s". Statistical Methodology 9: 341–352. doi:10.1016/j.stamet.2011.09.001.
↑ Holley, JW; Guilford, JP (1964). "A note on the G index of agreement". Educ Psych Measurement 24: 749–753. doi:10.1177/001316446402400402.

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