Updated: 31 Oct 2012

Use MovingDEVSQ 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 deviations is calculated for each value from the first value in the window to the last value in the window. If the column values are presented to the functions out of order, an error message will be generated.

SELECT [Example].[wct].[MovingDEVSQ](

<@Val, float,>

,<@Offset, int,>

,<@RowNum, int,>

,<@Id, tinyint,>)

GO

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

specifies the window size. *@Offset* is an expression of type **int** or of a type that can be implicitly converted to **int**.

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**.

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

· If *@Id* is NULL then *@Id* = 0.

· To calculate running sum of squares deviation over an entire dataset or partition, use the RunningDEVSQ function.

· If *@RowNum* is equal to 1, MovingDEVSQ is equal to 0.

· *@RowNum* must be in ascending order.

· To calculate a single sum of squares deviation value for an entire 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.

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 cast(x as money) as x

,cast(wct.MovingDEVSQ(x,5,ROW_NUMBER() OVER (ORDER BY x ASC),NULL) as money) 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)

ORDER BY x ASC

This produces the following result.

x DEVSQ

--------------------- ---------------------

76.5458 0.00

82.2819 16.4514

85.2968 39.5242

88.2566 75.0432

89.1731 104.5952

91.4181 146.6894

98.9415 163.7979

99.5511 172.4118

100.1934 154.4619

100.2686 122.5732

101.5546 66.6359

103.8977 15.8035

109.6867 73.4877

110.5982 109.4727

114.318 157.8386

116.3052 165.2117

118.5804 139.8529

123.3369 130.7684

126.6649 174.5738

130.3847 196.0214