Bennett, Alpert, and Goldstein’s S
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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.
The formula for S is
where Q is the number of categories and Pa is the proportion of agreement between raters.
The variance of S is
- Bennett, EM; Alpert, R; Goldstein, AC (1954). "Communications through limited response questioning". Public Opinion Quarterly. 18 (3): 303–308. doi:10.1086/266520.
- Warrens, Matthijs J. (May 2012). "The effect of combining categories on Bennett, Alpert and Goldstein's". Statistical Methodology. 9 (3): 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 (4): 749–753. doi:10.1177/001316446402400402.