# SQL Server CHISQ.TEST function

Updated: 6 August 2010

Use CHITESTN_q to calculate the Pearson chi-square test for independence on normalized tables. CHITESTN_q 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_q 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_q] (
<@Actual_range_RangeQuery, nvarchar(4000),>)
Arguments
@Actual_range_RangeQuery
the select statement, as text, used to determine the actual, or observed, results to be used in the calculation.
Return Types
float
Remarks
·         CHITESTN_q is designed for normalized tables. For de-normalized tables, use the CHISTEST_q function.
·         CHITESTN_q automatically calculates the expected values and the degrees of freedom.
·         For simpler queries, consider using the CHITESTN function.
·         CHITESTN_q = CHIDIST(χ2, df), where df = (r-1)(c-1), r>1, c>1.
·         Use CHISQN_q 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 CHITESTN_q 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_q('SELECT * FROM #chin')
This produces the following result
----------------------
0.000162912223138266

(1 row(s) affected)