Updated: 6 August 2010
Use CHITESTN to calculate the Pearson chi-square test for independence on normalized tables. CHITESTN returns the value from the chi-square (χ2) distribution for the statistic and the appropriate degrees of freedom. Calculate the chi-square statistic (χ2) directly using the CHISQN or the CHISQN_q function.
The chi-square statistic is calculated 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.
Given the test statistic and the degrees of freedom, the test value is returned by the regularized gamma function Q(a, x) where:
a is the degrees of freedom divided by 2
x is χ2 statistic divided by 2
CHITESTN automatically calculates the expected results and the degrees of freedom.
The value of the test 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].[CHITESTN] (
<@Actual_range_TableName, nvarchar(4000),>
,<@Key1Columnname, nvarchar(4000),>
,<@Key2ColumnName, nvarchar(4000),>
,<@DataColumnName, nvarchar(4000),>
,<@GroupedColumnName, nvarchar(4000),>
,<@GroupedColumnValue, sql_variant,>)
Arguments
@Actual_range_TableName
the name, as text, of the table or view that contains the actual, or observed, results to be used in the calculation.
@Key1Columnname
the name, as text, of the first column in the normalized table or view specified by @Actual_range_TableName that identifies the actual, or observed, results to be used in the calculation.
@Key2ColumnName
the name, as text, of the second column in the normalized table or view specified by @Actual_range_TableName that identifies the actual, or observed, results to be used in the calculation.
@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 results.
@GroupedColumnValue
the column value to do the grouping on.
Return Types
float
Remarks
· CHITESTN is designed for normalized tables. For de-normalized tables, use the CHITEST function.
· CHITESTN automatically calculates the expected values.
· For queries that are more complex, consider using the CHITESTN_q function.
· CHITESTN = CHIDIST(χ2, df), where df = (r-1)(c-1), r>1, c>1.
· Use the CHISQN function to calculate the test statistic.
· 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 CHITEST function to perform the chi-squared test.
CREATE TABLE #chin(
[Sport] [varchar] (20) NOT NULL,
[Locale] [varchar] (20) NOT NULL,
[Result] [float] NOT NULL
)
INSERT INTO #CHIN VALUES ('Basketball', 'Rural', 28)
INSERT INTO #CHIN VALUES ('Basketball', 'Suburban', 35)
INSERT INTO #CHIN VALUES ('Basketball', 'Urban', 54)
INSERT INTO #CHIN VALUES ('Baseball', 'Rural', 60)
INSERT INTO #CHIN VALUES ('Baseball', 'Suburban', 43)
INSERT INTO #CHIN VALUES ('Baseball', 'Urban', 35)
INSERT INTO #CHIN VALUES ('Football', 'Rural', 52)
INSERT INTO #CHIN VALUES ('Football', 'Suburban', 48)
INSERT INTO #CHIN VALUES ('Football', 'Urban', 28)
SELECT wct.CHITESTN(
'#chin'
,'Sport'
,'Locale'
,'Result'
,''
,NULL)
This produces the following result
----------------------
0.000162912223138266
(1 row(s) affected)