SQL Server RunningDEVSQ Function

Updated 2023-11-14 14:36:44.707000

Description

Use the scalar function RunningDEVSQ to calculate the sum of squares of deviations of column values from their sample mean in an ordered resultant table, without the need for a self-join. The sum of squares of deviations is calculated over all the values from the first value to the last value in the ordered group or partition. If the column values are presented to the functions out of order, an error message will be generated.

Syntax

SELECT [westclintech].[wct].[RunningDEVSQ](
  <@Val, float,>
 ,<@RowNum, int,>
 ,<@Id, tinyint,>)

Arguments

@Val

the value passed into the function. @Val is an expression of type float or of a type that can be implicitly converted to float.

@RowNum

the number of the row within the group for which the sum is being calculated. If @RowNum for the current row in a set is less than or equal to the previous @RowNum and @RowNum is not equal to 1, an error message will be generated. @RowNum is an expression of type int or of a type that can be implicitly converted to int.

@Id

a unique identifier for the RunningDEVSQ calculation. @Id allows you to specify multiple RunningDEVSQ calculation s within a resultant table. @Id is an expression of type tinyint or of a type that can be implicitly converted to tinyint.

Return Type

float

Remarks

If @Id is NULL then @Id = 0.

To calculate moving sum of squares deviation, use the MovingDEVSQ function.

If @RowNum is equal to 1, RunningDEVSQ is equal to 0.

@RowNum must be in ascending order.

To calculate a single sum of squares deviation for a set of data, use the DEVSQ function.

There may be cases where the order in which the data are returned to the function and the order in which the results are returned are different, generally due to parallelism. You can use OPTION(MAXDOP 1) or OPTION(MAXDOP 1,FORCE ORDER) to help eliminate this problem.

Examples

In this example, we have 20 rows of sample data from a population with a mean of 100 and a standard deviation of 15.

SELECT rn,
       x,
       wct.RunningDEVSQ(x, rn, NULL) as [DEVSQ]
FROM
(
    SELECT 1,
           85.2968
    UNION ALL
    SELECT 2,
           88.2566
    UNION ALL
    SELECT 3,
           100.1934
    UNION ALL
    SELECT 4,
           116.3052
    UNION ALL
    SELECT 5,
           109.6867
    UNION ALL
    SELECT 6,
           130.3847
    UNION ALL
    SELECT 7,
           76.5458
    UNION ALL
    SELECT 8,
           99.5511
    UNION ALL
    SELECT 9,
           101.5546
    UNION ALL
    SELECT 10,
           114.318
    UNION ALL
    SELECT 11,
           100.2686
    UNION ALL
    SELECT 12,
           110.5982
    UNION ALL
    SELECT 13,
           91.4181
    UNION ALL
    SELECT 14,
           118.5804
    UNION ALL
    SELECT 15,
           126.6649
    UNION ALL
    SELECT 16,
           103.8977
    UNION ALL
    SELECT 17,
           82.2819
    UNION ALL
    SELECT 18,
           123.3369
    UNION ALL
    SELECT 19,
           98.9415
    UNION ALL
    SELECT 20,
           89.1731
) s(rn, x);

This produces the following result.