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XLeratorDB/statistics Documentation

SQL Server Fleiss's Kappa function


KAPPA_FLEISS_TV

Updated: 24 May 2013


Use the table-valued function KAPPA_FLEISS_TV to calculate Fleiss’ kappa (Κ) as an index of inter-rater agreement between m raters on categorical data. KAPPA_FLEISS_TV also calculates the category-wise kappa and the corresponding test statistics. The equation for Fleiss’ kappa is

XLeratorDB formula for Kappa Fleiss function for SQL Server
See the example below for an explanation of how Pi and Pj are calculated.
Syntax
SELECT * FROM [wctStatistics].[wct].[KAPPA_FLEISS_TV](
   <@InputData_RangeQuery, nvarchar(max),>)
Arguments
@InputData_RangeQuery
a T-SQL statement, as a string, that specifies the subject, rater, and rating values.
Return Type
RETURNS TABLE (
      [Rating] [sql_variant] NULL,
      [Z] [float] NULL,
      [K] [float] NULL,
      [P] [float] NULL,
      [SE] [float] NULL
)

Column
Column Description
Z
the test statistic
K
the kappa value
P
the p-value
SE
the standard error
Remarks
·         The function is insensitive to order; it does not matter what order the ratings are passed in.
·         Subjects, raters, ratings are automatically combined by the function.

 

Examples
SELECT *
INTO #k
FROM (
      SELECT' Subject 01','A',5 UNION ALL
      SELECT' Subject 01','B',5 UNION ALL
      SELECT' Subject 01','C',5 UNION ALL
      SELECT' Subject 01','D',5 UNION ALL
      SELECT' Subject 01','E',5 UNION ALL
      SELECT' Subject 01','F',5 UNION ALL
      SELECT' Subject 01','G',5 UNION ALL
      SELECT' Subject 01','H',5 UNION ALL
      SELECT' Subject 01','I',5 UNION ALL
      SELECT' Subject 01','J',5 UNION ALL
      SELECT' Subject 01','K',5 UNION ALL
      SELECT' Subject 01','L',5 UNION ALL
      SELECT' Subject 01','M',5 UNION ALL
      SELECT' Subject 01','N',5 UNION ALL
      SELECT' Subject 02','A',2 UNION ALL
      SELECT' Subject 02','B',2 UNION ALL
      SELECT' Subject 02','C',3 UNION ALL
      SELECT' Subject 02','D',3 UNION ALL
      SELECT' Subject 02','E',3 UNION ALL
      SELECT' Subject 02','F',3 UNION ALL
      SELECT' Subject 02','G',3 UNION ALL
      SELECT' Subject 02','H',3 UNION ALL
      SELECT' Subject 02','I',4 UNION ALL
      SELECT' Subject 02','J',4 UNION ALL
      SELECT' Subject 02','K',4 UNION ALL
      SELECT' Subject 02','L',4 UNION ALL
      SELECT' Subject 02','M',5 UNION ALL
      SELECT' Subject 02','N',5 UNION ALL
      SELECT' Subject 03','A',3 UNION ALL
      SELECT' Subject 03','B',3 UNION ALL
      SELECT' Subject 03','C',3 UNION ALL
      SELECT' Subject 03','D',4 UNION ALL
      SELECT' Subject 03','E',4 UNION ALL
      SELECT' Subject 03','F',4 UNION ALL
      SELECT' Subject 03','G',4 UNION ALL
      SELECT' Subject 03','H',4 UNION ALL
      SELECT' Subject 03','I',5 UNION ALL
      SELECT' Subject 03','J',5 UNION ALL
      SELECT' Subject 03','K',5 UNION ALL
      SELECT' Subject 03','L',5 UNION ALL
      SELECT' Subject 03','M',5 UNION ALL
      SELECT' Subject 03','N',5 UNION ALL
      SELECT' Subject 04','A',2 UNION ALL
      SELECT' Subject 04','B',2 UNION ALL
      SELECT' Subject 04','C',2 UNION ALL
      SELECT' Subject 04','D',3 UNION ALL
      SELECT' Subject 04','E',3 UNION ALL
      SELECT' Subject 04','F',3 UNION ALL
      SELECT' Subject 04','G',3 UNION ALL
      SELECT' Subject 04','H',3 UNION ALL
      SELECT' Subject 04','I',3 UNION ALL
      SELECT' Subject 04','J',3 UNION ALL
      SELECT' Subject 04','K',3 UNION ALL
      SELECT' Subject 04','L',3 UNION ALL
      SELECT' Subject 04','M',4 UNION ALL
      SELECT' Subject 04','N',4 UNION ALL
      SELECT' Subject 05','A',1 UNION ALL
      SELECT' Subject 05','B',1 UNION ALL
      SELECT' Subject 05','C',2 UNION ALL
      SELECT' Subject 05','D',2 UNION ALL
      SELECT' Subject 05','E',3 UNION ALL
      SELECT' Subject 05','F',3 UNION ALL
      SELECT' Subject 05','G',3 UNION ALL
      SELECT' Subject 05','H',3 UNION ALL
      SELECT' Subject 05','I',3 UNION ALL
      SELECT' Subject 05','J',3 UNION ALL
      SELECT' Subject 05','K',3 UNION ALL
      SELECT' Subject 05','L',3 UNION ALL
      SELECT' Subject 05','M',4 UNION ALL
      SELECT' Subject 05','N',5 UNION ALL
      SELECT' Subject 06','A',1 UNION ALL
      SELECT' Subject 06','B',1 UNION ALL
      SELECT' Subject 06','C',1 UNION ALL
      SELECT' Subject 06','D',1 UNION ALL
      SELECT' Subject 06','E',1 UNION ALL
      SELECT' Subject 06','F',1 UNION ALL
      SELECT' Subject 06','G',1 UNION ALL
      SELECT' Subject 06','H',2 UNION ALL
      SELECT' Subject 06','I',2 UNION ALL
      SELECT' Subject 06','J',2 UNION ALL
      SELECT' Subject 06','K',2 UNION ALL
      SELECT' Subject 06','L',2 UNION ALL
      SELECT' Subject 06','M',2 UNION ALL
      SELECT' Subject 06','N',2 UNION ALL
      SELECT' Subject 07','A',1 UNION ALL
      SELECT' Subject 07','B',1 UNION ALL
      SELECT' Subject 07','C',1 UNION ALL
      SELECT' Subject 07','D',2 UNION ALL
      SELECT' Subject 07','E',2 UNION ALL
      SELECT' Subject 07','F',3 UNION ALL
      SELECT' Subject 07','G',3 UNION ALL
      SELECT' Subject 07','H',3 UNION ALL
      SELECT' Subject 07','I',3 UNION ALL
      SELECT' Subject 07','J',3 UNION ALL
      SELECT' Subject 07','K',3 UNION ALL
      SELECT' Subject 07','L',4 UNION ALL
      SELECT' Subject 07','M',4 UNION ALL
      SELECT' Subject 07','N',4 UNION ALL
      SELECT' Subject 08','A',1 UNION ALL
      SELECT' Subject 08','B',1 UNION ALL
      SELECT' Subject 08','C',2 UNION ALL
      SELECT' Subject 08','D',2 UNION ALL
      SELECT' Subject 08','E',2 UNION ALL
      SELECT' Subject 08','F',2 UNION ALL
      SELECT' Subject 08','G',2 UNION ALL
      SELECT' Subject 08','H',3 UNION ALL
      SELECT' Subject 08','I',3 UNION ALL
      SELECT' Subject 08','J',3 UNION ALL
      SELECT' Subject 08','K',4 UNION ALL
      SELECT' Subject 08','L',4 UNION ALL
      SELECT' Subject 08','M',5 UNION ALL
      SELECT' Subject 08','N',5 UNION ALL
      SELECT' Subject 09','A',1 UNION ALL
      SELECT' Subject 09','B',1 UNION ALL
      SELECT' Subject 09','C',1 UNION ALL
      SELECT' Subject 09','D',1 UNION ALL
      SELECT' Subject 09','E',1 UNION ALL
      SELECT' Subject 09','F',1 UNION ALL
      SELECT' Subject 09','G',2 UNION ALL
      SELECT' Subject 09','H',2 UNION ALL
      SELECT' Subject 09','I',2 UNION ALL
      SELECT' Subject 09','J',2 UNION ALL
      SELECT' Subject 09','K',2 UNION ALL
      SELECT' Subject 09','L',3 UNION ALL
      SELECT' Subject 09','M',3 UNION ALL
      SELECT' Subject 09','N',4 UNION ALL
      SELECT' Subject 10','A',2 UNION ALL
      SELECT' Subject 10','B',2 UNION ALL
      SELECT' Subject 10','C',3 UNION ALL
      SELECT' Subject 10','D',3 UNION ALL
      SELECT' Subject 10','E',4 UNION ALL
      SELECT' Subject 10','F',4 UNION ALL
      SELECT' Subject 10','G',4 UNION ALL
      SELECT' Subject 10','H',5 UNION ALL
      SELECT' Subject 10','I',5 UNION ALL
      SELECT' Subject 10','J',5 UNION ALL
      SELECT' Subject 10','K',5 UNION ALL
      SELECT' Subject 10','L',5 UNION ALL
      SELECT' Subject 10','M',5 UNION ALL
      SELECT' Subject 10','N',5
      )n(subject, rater, rating)
 
SELECT *
FROM wct.KAPPA_FLEISS_TV('SELECT subject, rater, rating FROM #k')
ORDER BY rating
This produces the following result.



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