SQL Server KENDALLT Function

Updated 2023-11-06 15:28:16.273000

Description

Use the scalar function KENDALLT to calculate Kendall's tau (𝜏), a non-parametric measure of association based on the number of concordances and discordances in paired observations. Concordance occurs when paired observations vary together and discordance occurs when paired observations vary differently. The equation for Kendall's tau is:

\tau_b = \frac{C-D}{\sqrt{(\binom{n}{2} - T)(\binom{n}{2} - U)}

Where

The function also calculates

\tau_a = \frac{C-D}{\binom{n}{2}}

Syntax

SELECT [westclintech].[wct].[KENDALLT](
  <@x_y_Query, nvarchar(max),>
 ,<@RV, nvarchar(4000),>)

Arguments

@x_y_Query

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

@RV

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

Return Type

float

Remarks

The function is insensitive to order.

If x is NULL or y is NULL the pair is not included in the calculations.

To return multiple values, use the table-valued function KENDALLT_TV.

Examples

SELECT *
INTO #k
FROM
(
    SELECT 2.5,
           1
    UNION ALL
    SELECT 2.5,
           1
    UNION ALL
    SELECT 2.5,
           1
    UNION ALL
    SELECT 2.5,
           1
    UNION ALL
    SELECT 5,
           2
    UNION ALL
    SELECT 6.5,
           1
    UNION ALL
    SELECT 6.5,
           1
    UNION ALL
    SELECT 10,
           2
    UNION ALL
    SELECT 10,
           1
    UNION ALL
    SELECT 10,
           1
    UNION ALL
    SELECT 10,
           1
    UNION ALL
    SELECT 10,
           1
    UNION ALL
    SELECT 14,
           1
    UNION ALL
    SELECT 14,
           1
    UNION ALL
    SELECT 14,
           2
    UNION ALL
    SELECT 16,
           2
    UNION ALL
    SELECT 17,
           2
) n(x, y);
SELECT p.stat,
       wct.KENDALLT('SELECT x,y FROM #k', p.stat) k
FROM
(
    SELECT 'tau_a'
    UNION ALL
    SELECT 'tau_b'
    UNION ALL
    SELECT 'C'
    UNION ALL
    SELECT 'D'
    UNION ALL
    SELECT 'S'
    UNION ALL
    SELECT 'T'
    UNION ALL
    SELECT 'U'
    UNION ALL
    SELECT 'za'
    UNION ALL
    SELECT 'zb'
    UNION ALL
    SELECT 'SDa'
    UNION ALL
    SELECT 'SDb'
    UNION ALL
    SELECT 'pa'
    UNION ALL
    SELECT 'pb'
    UNION ALL
    SELECT 'N'
) p(stat);
DROP TABLE #k;

This produces the following result.