KENDALLW_TV

Updated 2023-11-06 16:26:26.713000

Syntax

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

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:

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.

@InputData_RangeQuery

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

Return Type

table

{"columns": [{"field": "colName", "headerName": "Name", "header": "name"}, {"field": "colDatatype", "headerName": "Type", "header": "type"}, {"field": "colDesc", "headerName": "Description", "header": "description", "minWidth": 1000}], "rows": [{"id": "f904af4d-c6d0-4220-a2af-d283797bd007", "colName": "W", "colDatatype": "float", "colDesc": "the Kendall w statistic"}, {"id": "0212bcb1-83aa-437f-baa6-b642edb59ce4", "colName": "X", "colDatatype": "float", "colDesc": "the chi-squared statistic"}, {"id": "757f79b1-3e1b-4b78-b71a-c8dbc5470b76", "colName": "DF1", "colDatatype": "float", "colDesc": "the degrees of freedom"}, {"id": "e39fad02-e152-427c-8c49-7336d2fbe4d5", "colName": "P", "colDatatype": "float", "colDesc": "the p-value"}]}

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.

{"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"}]}