KENDALLW

Updated 2023-11-06 16:20:40.233000

Syntax

SELECT [westclintech].[wct].[KENDALLW](
  <@InputData_RangeQuery, nvarchar(max),>
 ,<@CorrectTies, bit,>
 ,<@RV, nvarchar(4000),>)

Description

Use the scalar function KENDALLW 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

    nr is the number of raters

    ns is the number of subjects being rated

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

Where

    ti is a count of each rating within a rater

    gj is the number of unique ratings within a rater

Arguments

@RV

the value to be returned by the function. Use the following values:

{
    "columns": [
        {
            "field": "RV"
        },
        {
            "field": "Description"
        }
    ],
    "rows": [
        {
            "RV": "'W'",
            "Description": "the Kendall W statistic"
        },
        {
            "RV": "'X'",
            "Description": "the chi-squared statistic"
        },
        {
            "RV": "'DF1'",
            "Description": "the degrees of freedom"
        },
        {
            "RV": "'P'",
            "Description": "the p-value"
        }
    ]
}

@CorrectTies

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

@InputData_RangeQuery

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

Return Type

float

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.stat,
       wct.KENDALLW('SELECT s,rater,rating 
          FROM #k', 'False', p.stat) k
FROM
(
    SELECT 'W'
    UNION ALL
    SELECT 'X'
    UNION ALL
    SELECT 'df1'
    UNION ALL
    SELECT 'p'
) p(stat);
DROP TABLE #k;

This produces the following result.

{"columns":[{"field":"stat"},{"field":"k","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"stat":"W","k":"0.501921470342523"},{"stat":"X","k":"28.6095238095238"},{"stat":"df1","k":"19"},{"stat":"p","k":"0.072380354693757"}]}