SQL Server KENDALLW_TV Function

Updated 2023-11-06 16:26:26.713000

Description

Use the table-valued function KENDALLW_TV to calculate Kendall's coefficient of concordance (w) as an index of inter-rater reliability for ordinal data. The equation for Kendall's w is:

Where

    r is the sum of the ranks of the ratings for all raters for each subject

    µ₂ is the second central moment

    n_r is the number of raters

    n_s is the number of subjects being rated

The equation for Kendall's w corrected for ties is:

Where

    t_i is a count of each rating within a rater

    g_j is the number of unique ratings within a rater

Syntax

SELECT * FROM [westclintech].[wct].[KENDALLW_TV](
  <@InputData_RangeQuery, nvarchar(max),>
 ,<@CorrectTies, bit,>)

Arguments

@InputData_RangeQuery

a T-SQL statement, as a string, that specifies the subject, rater, and rating values.

@CorrectTies

a bit value identifying whether the coefficient should be corrected for ties within raters.

Return Type

table

Remarks

The function is insensitive to order and automatically matches all the ratings for a subject.

NULL values are excluded.

Examples

SELECT n.s,
       x.rater,
       x.rating
INTO #k
FROM
(
    SELECT 1,
           3,
           3,
           2
    UNION ALL
    SELECT 2,
           3,
           6,
           1
    UNION ALL
    SELECT 3,
           3,
           4,
           4
    UNION ALL
    SELECT 4,
           4,
           6,
           4
    UNION ALL
    SELECT 5,
           5,
           2,
           3
    UNION ALL
    SELECT 6,
           5,
           4,
           2
    UNION ALL
    SELECT 7,
           2,
           2,
           1
    UNION ALL
    SELECT 8,
           3,
           4,
           6
    UNION ALL
    SELECT 9,
           5,
           3,
           1
    UNION ALL
    SELECT 10,
           2,
           3,
           1
    UNION ALL
    SELECT 11,
           2,
           2,
           1
    UNION ALL
    SELECT 12,
           6,
           3,
           2
    UNION ALL
    SELECT 13,
           1,
           3,
           3
    UNION ALL
    SELECT 14,
           5,
           3,
           3
    UNION ALL
    SELECT 15,
           2,
           2,
           1
    UNION ALL
    SELECT 16,
           2,
           2,
           1
    UNION ALL
    SELECT 17,
           1,
           1,
           3
    UNION ALL
    SELECT 18,
           2,
           3,
           3
    UNION ALL
    SELECT 19,
           4,
           3,
           2
    UNION ALL
    SELECT 20,
           3,
           4,
           2
) n(s, r1, r2, r3)
    --This CROSS APPLY UNPIVOTS the  input data into third normal form
    CROSS APPLY
(
    SELECT 'r1',
           r1
    UNION ALL
    SELECT 'r2',
           r2
    UNION ALL
    SELECT 'r3',
           r3
) x(rater, rating);
SELECT p.*
FROM wct.KENDALLW_TV('SELECT s,rater,
          rating FROM #k', 'False') k
    --This CROSS APPLY UNPIVOTS the tvf columns for formatting
    CROSS APPLY
(
    SELECT 'W',
           k.W
    UNION ALL
    SELECT 'X',
           k.X
    UNION ALL
    SELECT 'df1',
           k.df1
    UNION ALL
    SELECT 'p',
           k.p
) p(stat, value_stat);
DROP TABLE #k;

This produces the following result.