KAPPA_FLEISS_TV

Updated 2023-11-06 14:59:27.660000

Syntax

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

Description

Use the table-valued function KAPPA_FLEISS_TV to calculate Fleiss’ kappa (κ) as an index of inter-rater agreement between m raters on categorical data. KAPPA_FLEISS_TV also calculates the category-wise kappa and the corresponding test statistics. The equation for Fleiss’ kappa is:

\kappa = \frac{P_i - P_j}{1-P_j}

See the example below for an explanation of how Pi and Pj are calculated.

Arguments

@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": [{"ordinal": 0, "colName": "Rating", "colDatatype": "sql_variant", "colDesc": "the user supplied rating"}, {"ordinal": 1, "colName": "Z", "colDatatype": "float", "colDesc": "the test statistic"}, {"ordinal": 2, "colName": "K", "colDatatype": "float", "colDesc": "the kappa value"}, {"ordinal": 3, "colName": "P", "colDatatype": "float", "colDesc": "the p-value"}, {"ordinal": 4, "colName": "SE", "colDatatype": "float", "colDesc": "the standard error"}]}

Remarks

The function is insensitive to order; it does not matter what order the ratings are passed in.

Subjects, raters and ratings are automatically combined by the function.

Examples

SELECT *

INTO #k

FROM

(

    SELECT ' Subject 01',

           'A',

           5

    UNION ALL

    SELECT ' Subject 01',

           'B',

           5

    UNION ALL

    SELECT ' Subject 01',

           'C',

           5

    UNION ALL

    SELECT ' Subject 01',

           'D',

           5

    UNION ALL

    SELECT ' Subject 01',

           'E',

           5

    UNION ALL

    SELECT ' Subject 01',

           'F',

           5

    UNION ALL

    SELECT ' Subject 01',

           'G',

           5

    UNION ALL

    SELECT ' Subject 01',

           'H',

           5

    UNION ALL

    SELECT ' Subject 01',

           'I',

           5

    UNION ALL

    SELECT ' Subject 01',

           'J',

           5

    UNION ALL

    SELECT ' Subject 01',

           'K',

           5

    UNION ALL

    SELECT ' Subject 01',

           'L',

           5

    UNION ALL

    SELECT ' Subject 01',

           'M',

           5

    UNION ALL

    SELECT ' Subject 01',

           'N',

           5

    UNION ALL

    SELECT ' Subject 02',

           'A',

           2

    UNION ALL

    SELECT ' Subject 02',

           'B',

           2

    UNION ALL

    SELECT ' Subject 02',

           'C',

           3

    UNION ALL

    SELECT ' Subject 02',

           'D',

           3

    UNION ALL

    SELECT ' Subject 02',

           'E',

           3

    UNION ALL

    SELECT ' Subject 02',

           'F',

           3

    UNION ALL

    SELECT ' Subject 02',

           'G',

           3

    UNION ALL

    SELECT ' Subject 02',

           'H',

           3

    UNION ALL

    SELECT ' Subject 02',

           'I',

           4

    UNION ALL

    SELECT ' Subject 02',

           'J',

           4

    UNION ALL

    SELECT ' Subject 02',

           'K',

           4

    UNION ALL

    SELECT ' Subject 02',

           'L',

           4

    UNION ALL

    SELECT ' Subject 02',

           'M',

           5

    UNION ALL

    SELECT ' Subject 02',

           'N',

           5

    UNION ALL

    SELECT ' Subject 03',

           'A',

           3

    UNION ALL

    SELECT ' Subject 03',

           'B',

           3

    UNION ALL

    SELECT ' Subject 03',

           'C',

           3

    UNION ALL

    SELECT ' Subject 03',

           'D',

           4

    UNION ALL

    SELECT ' Subject 03',

           'E',

           4

    UNION ALL

    SELECT ' Subject 03',

           'F',

           4

    UNION ALL

    SELECT ' Subject 03',

           'G',

           4

    UNION ALL

    SELECT ' Subject 03',

           'H',

           4

    UNION ALL

    SELECT ' Subject 03',

           'I',

           5

    UNION ALL

    SELECT ' Subject 03',

           'J',

           5

    UNION ALL

    SELECT ' Subject 03',

           'K',

           5

    UNION ALL

    SELECT ' Subject 03',

           'L',

           5

    UNION ALL

    SELECT ' Subject 03',

           'M',

           5

    UNION ALL

    SELECT ' Subject 03',

           'N',

           5

    UNION ALL

    SELECT ' Subject 04',

           'A',

           2

    UNION ALL

    SELECT ' Subject 04',

           'B',

           2

    UNION ALL

    SELECT ' Subject 04',

           'C',

           2

    UNION ALL

    SELECT ' Subject 04',

           'D',

           3

    UNION ALL

    SELECT ' Subject 04',

           'E',

           3

    UNION ALL

    SELECT ' Subject 04',

           'F',

           3

    UNION ALL

    SELECT ' Subject 04',

           'G',

           3

    UNION ALL

    SELECT ' Subject 04',

           'H',

           3

    UNION ALL

    SELECT ' Subject 04',

           'I',

           3

    UNION ALL

    SELECT ' Subject 04',

           'J',

           3

    UNION ALL

    SELECT ' Subject 04',

           'K',

           3

    UNION ALL

    SELECT ' Subject 04',

           'L',

           3

    UNION ALL

    SELECT ' Subject 04',

           'M',

           4

    UNION ALL

    SELECT ' Subject 04',

           'N',

           4

    UNION ALL

    SELECT ' Subject 05',

           'A',

           1

    UNION ALL

    SELECT ' Subject 05',

           'B',

           1

    UNION ALL

    SELECT ' Subject 05',

           'C',

           2

    UNION ALL

    SELECT ' Subject 05',

           'D',

           2

    UNION ALL

    SELECT ' Subject 05',

           'E',

           3

    UNION ALL

    SELECT ' Subject 05',

           'F',

           3

    UNION ALL

    SELECT ' Subject 05',

           'G',

           3

    UNION ALL

    SELECT ' Subject 05',

           'H',

           3

    UNION ALL

    SELECT ' Subject 05',

           'I',

           3

    UNION ALL

    SELECT ' Subject 05',

           'J',

           3

    UNION ALL

    SELECT ' Subject 05',

           'K',

           3

    UNION ALL

    SELECT ' Subject 05',

           'L',

           3

    UNION ALL

    SELECT ' Subject 05',

           'M',

           4

    UNION ALL

    SELECT ' Subject 05',

           'N',

           5

    UNION ALL

    SELECT ' Subject 06',

           'A',

           1

    UNION ALL

    SELECT ' Subject 06',

           'B',

           1

    UNION ALL

    SELECT ' Subject 06',

           'C',

           1

    UNION ALL

    SELECT ' Subject 06',

           'D',

           1

    UNION ALL

    SELECT ' Subject 06',

           'E',

           1

    UNION ALL

    SELECT ' Subject 06',

           'F',

           1

    UNION ALL

    SELECT ' Subject 06',

           'G',

           1

    UNION ALL

    SELECT ' Subject 06',

           'H',

           2

    UNION ALL

    SELECT ' Subject 06',

           'I',

           2

    UNION ALL

    SELECT ' Subject 06',

           'J',

           2

    UNION ALL

    SELECT ' Subject 06',

           'K',

           2

    UNION ALL

    SELECT ' Subject 06',

           'L',

           2

    UNION ALL

    SELECT ' Subject 06',

           'M',

           2

    UNION ALL

    SELECT ' Subject 06',

           'N',

           2

    UNION ALL

    SELECT ' Subject 07',

           'A',

           1

    UNION ALL

    SELECT ' Subject 07',

           'B',

           1

    UNION ALL

    SELECT ' Subject 07',

           'C',

           1

    UNION ALL

    SELECT ' Subject 07',

           'D',

           2

    UNION ALL

    SELECT ' Subject 07',

           'E',

           2

    UNION ALL

    SELECT ' Subject 07',

           'F',

           3

    UNION ALL

    SELECT ' Subject 07',

           'G',

           3

    UNION ALL

    SELECT ' Subject 07',

           'H',

           3

    UNION ALL

    SELECT ' Subject 07',

           'I',

           3

    UNION ALL

    SELECT ' Subject 07',

           'J',

           3

    UNION ALL

    SELECT ' Subject 07',

           'K',

           3

    UNION ALL

    SELECT ' Subject 07',

           'L',

           4

    UNION ALL

    SELECT ' Subject 07',

           'M',

           4

    UNION ALL

    SELECT ' Subject 07',

           'N',

           4

    UNION ALL

    SELECT ' Subject 08',

           'A',

           1

    UNION ALL

    SELECT ' Subject 08',

           'B',

           1

    UNION ALL

    SELECT ' Subject 08',

           'C',

           2

    UNION ALL

    SELECT ' Subject 08',

           'D',

           2

    UNION ALL

    SELECT ' Subject 08',

           'E',

           2

    UNION ALL

    SELECT ' Subject 08',

           'F',

           2

    UNION ALL

    SELECT ' Subject 08',

           'G',

           2

    UNION ALL

    SELECT ' Subject 08',

           'H',

           3

    UNION ALL

    SELECT ' Subject 08',

           'I',

           3

    UNION ALL

    SELECT ' Subject 08',

           'J',

           3

    UNION ALL

    SELECT ' Subject 08',

           'K',

           4

    UNION ALL

    SELECT ' Subject 08',

           'L',

           4

    UNION ALL

    SELECT ' Subject 08',

           'M',

           5

    UNION ALL

    SELECT ' Subject 08',

           'N',

           5

    UNION ALL

    SELECT ' Subject 09',

           'A',

           1

    UNION ALL

    SELECT ' Subject 09',

           'B',

           1

    UNION ALL

    SELECT ' Subject 09',

           'C',

           1

    UNION ALL

    SELECT ' Subject 09',

           'D',

           1

    UNION ALL

    SELECT ' Subject 09',

           'E',

           1

    UNION ALL

    SELECT ' Subject 09',

           'F',

           1

    UNION ALL

    SELECT ' Subject 09',

           'G',

           2

    UNION ALL

    SELECT ' Subject 09',

           'H',

           2

    UNION ALL

    SELECT ' Subject 09',

           'I',

           2

    UNION ALL

    SELECT ' Subject 09',

           'J',

           2

    UNION ALL

    SELECT ' Subject 09',

           'K',

           2

    UNION ALL

    SELECT ' Subject 09',

           'L',

           3

    UNION ALL

    SELECT ' Subject 09',

           'M',

           3

    UNION ALL

    SELECT ' Subject 09',

           'N',

           4

    UNION ALL

    SELECT ' Subject 10',

           'A',

           2

    UNION ALL

    SELECT ' Subject 10',

           'B',

           2

    UNION ALL

    SELECT ' Subject 10',

           'C',

           3

    UNION ALL

    SELECT ' Subject 10',

           'D',

           3

    UNION ALL

    SELECT ' Subject 10',

           'E',

           4

    UNION ALL

    SELECT ' Subject 10',

           'F',

           4

    UNION ALL

    SELECT ' Subject 10',

           'G',

           4

    UNION ALL

    SELECT ' Subject 10',

           'H',

           5

    UNION ALL

    SELECT ' Subject 10',

           'I',

           5

    UNION ALL

    SELECT ' Subject 10',

           'J',

           5

    UNION ALL

    SELECT ' Subject 10',

           'K',

           5

    UNION ALL

    SELECT ' Subject 10',

           'L',

           5

    UNION ALL

    SELECT ' Subject 10',

           'M',

           5

    UNION ALL

    SELECT ' Subject 10',

           'N',

           5

) n(subject, rater, rating);

SELECT *

FROM wct.KAPPA_FLEISS_TV('SELECT subject, rater, rating FROM #k')

ORDER BY rating;

This produces the following result.

{"columns":[{"field":"Rating"},{"field":"Z","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"K","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"P","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"SE","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"Rating":"NULL","Z":"12.3742910591905","K":"0.209930704421955","P":"3.60059432346663E-35","SE":"0.0169650692243931"},{"Rating":"1","Z":"6.07191587500703","K":"0.201282051282051","P":"1.26393144622578E-09","SE":"0.0331496772065898"},{"Rating":"2","Z":"2.40335159747776","K":"0.0796703296703298","P":"0.0162455593601469","SE":"0.0331496772065898"},{"Rating":"3","Z":"5.17644959456748","K":"0.171597633136095","P":"2.26148113389763E-07","SE":"0.0331496772065898"},{"Rating":"4","Z":"0.9164910757116","K":"0.0303813833225598","P":"0.359409386074102","SE":"0.0331496772065898"},{"Rating":"5","Z":"15.3140765743498","K":"0.507656695156695","P":"6.15802423732574E-53","SE":"0.0331496772065898"}]}