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:

Wherer is the sum of the ranks of the ratings for all raters for each subjectµ2 is the second central momentnr is the number of ratersns 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 ratergj is the number of unique ratings within a rater

Arguments

@CorrectTies

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

@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"
        }
    ]
}

@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"}]}