View source for Bennett, Alpert and Goldstein's S

{{primary sources|date=April 2013}}
{{DISPLAYTITLE:Bennett, Alpert and Goldstein's ''S''}}
'''Bennett, Alpert & Goldstein’s ''S''''' is a [[statistics|statistical]] measure of [[inter-rater agreement]]. It was created by Bennett ''et al.'' in 1954.<ref name=Bennett1954>{{cite journal | last1 = Bennett | first1 = EM | last2 = Alpert | first2 = R | last3 = Goldstein | first3 = AC | year = 1954 | title = Communications through limited response questioning | journal = Public Opinion Quarterly | volume = 18 | issue = 3| pages = 303–308 | doi=10.1086/266520}}</ref>

==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.<ref>{{cite journal | doi=10.1016/j.stamet.2011.09.001 | volume=9 | issue=3 | title=The effect of combining categories on Bennett, Alpert and Goldstein's | journal=Statistical Methodology | pages=341–352| date=May 2012 | last1=Warrens | first1=Matthijs J. | hdl=1887/18383 | hdl-access=free }}</ref> They proposed an index which adjusted the [[Proportionality (mathematics)|proportion]] of rater agreement based on the number of categories employed.

==[[Mathematical formula]]tion==

The formula for ''S'' is

: <math> S = \frac{ Q P_a - 1 } { Q - 1 } </math>

where ''Q'' is the number of categories and ''P''<sub>a</sub> is the proportion of agreement between raters.

The [[variance]] of ''S'' is

: <math>  \operatorname{Var}(S) = \left( \frac { Q } { Q - 1 } \right)^2 \frac { P_a ( P_a - 1 ) } { n - 1 } </math>

==Notes==
This statistic is also known as Guilford’s ''G''.<ref name=Holley1964>{{cite journal | last1 = Holley | first1 = JW | last2 = Guilford | first2 = JP | year = 1964 | title = A note on the G index of agreement | journal = Educ Psych Measurement | volume = 24 | issue = 4| pages = 749–753 | doi=10.1177/001316446402400402| s2cid = 143846590 }}</ref> Guilford was the first person to use the approach extensively in the determination of inter-rater reliability.{{Citation needed|date=March 2012}}

==References==
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{{DEFAULTSORT:Bennett, Alpert, and Goldstein's S}}
[[Category:Categorical variable interactions]]
[[Category:Inter-rater reliability]]