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XLeratorDB/statistics Documentation

SQL Server chi-squared statistic


CHISQ2

Updated: 6 August 2010

Use CHISQ2 to calculate the chi-square (χ2) statistic. This function calculates the chi-square statistic by finding the difference between each observed and theoretical frequency for each possible outcome, squaring them, dividing each by the theoretical frequency, and taking the sum of the results. A second important part of determining the test statistic is to define the degrees of freedom of the test: this is essentially the number of squares errors involving the observed frequencies adjusted for the effect of using some of those observations to define the expected frequencies.
 
CHISQ2 requires the expected results as input to the function.
 
The value of the chi-square statistic is:

 
Where
                r              is the number of rows
                c              is the number of columns
                O             is the Observed result
                E              is the Expected result
Syntax
SELECT [wctStatistics].[wct].[CHISQ2] (
  <@Actual_range_TableName, nvarchar(4000),>
 ,<@AR_ColumnNames, nvarchar(4000),>
 ,<@AR_GroupedColumnName, nvarchar(4000),>
 ,<@AR_GroupedColumnValue, sql_variant,>
 ,<@Expected_range_TableName, nvarchar(4000),>
 ,<@ER_ColumnNames, nvarchar(4000),>
 ,<@ER_GroupedColumnName, nvarchar(4000),>
 ,<@ER_GroupedColumnValue, sql_variant,>)
Arguments
@Actual_range_TableName
the name, as text, of the table or view that contains the observed, or actual, results to be used in the calculation.
@AR_ColumnNames
the names, as text, of the columns in the de-normalized table or view specified by @Actual_range_TableName that contains the observed, or actual, results to be used in the calculation.
@AR_GroupedColumnName
the name, as text, of the column in the table or view specified by @Actual_range_TableName which will be used for grouping the observed, or actual, results.
@AR_GroupedColumnValue
the column value to do the grouping on.
@Expected_range_TableName
the name, as text, of the table or view that contains the expected results to be used in the calculation.
@ER_ColumnNames
the names, as text, of the columns in the de-normalized table or view specified by @Expected_range_TableName that contains the expected results to be used in the calculation.
@ER_GroupedColumnName
the name, as text, of the column in the table or view specified by @Expected_range_TableName which will be used for grouping the observed, or actual, results.
@ER_GroupedColumnValue
the column value to do the grouping on.
Return Types
float
Remarks
·         Use CHISQ2 for de-normalized tables. Use the CHISQN2 function for normalized tables.
·         CHISQ2 requires expected values as input. If you want the expected values calculated automatically, use the CHISQ function.
·         For queries that are more complex, consider using the CHISQ2_q function.
·         No GROUP BY is required for this function even though it produces aggregated results.
Examples
In this hypothetical situation, we want to determine if there is an association between population density and the preference for a sport from among baseball, football, and basketball. We will use the CHISQ2 function to calculate the chi-squares statistic.
CREATE TABLE #O(
      [Sport] [varchar] (20)        NOT NULL,
      [Rural] [float]               NOT NULL,
      [Suburban] [float]            NOT NULL,
      [Urban] [float]               NOT NULL
)
INSERT INTO #O VALUES ('Basketball',28,35,54)
INSERT INTO #O VALUES ('Baseball',60,43,35)
INSERT INTO #O VALUES ('Football',52,48,28)
 
CREATE TABLE #E(
      [Sport] [varchar] (20)        NOT NULL,
      [Rural] [float]               NOT NULL,
      [Suburban] [float]            NOT NULL,
      [Urban] [float]               NOT NULL
)
 
INSERT INTO #E VALUES ('Basketball',42.77,38.49,35.74)
INSERT INTO #E VALUES ('Baseball',50.44,45.4,42.16)
INSERT INTO #E VALUES ('Football',46.79,42.11,39.1)
 
SELECT wct.CHISQ2(
 '#O'
,'Rural, Suburban, Urban'
,''
,NULL
,'#E'
,'Rural, Suburban, Urban'
,''
,NULL)
 
This produces the following result
 
----------------------
22.4562079299414
           

(1 row(s) affected)



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