TTEST_INDEP
Updated: 17 July 2012
Note: This documentation is for the SQL2008 (and later) version of this XLeratorDB function, it is not compatible with SQL Server 2005.
Click here for the SQL2005 version of the TTEST_INDEP function
Use the aggregate function TTEST_INDEP to perform a t-test on data in two samples, x and y assuming equal variance. An independent samples t-test is used when you want to compare the means of a normally distributed interval dependent variable for two independent groupsThe TTEST_INDEP can return any of the following values.
P1 - one-tailed probability
P2 - two-tailed probability
T - t-statistic
DF - degrees of freedom
N1 - number of observations (in the x group)
N2 - number of observations (in the y group)
ES - effect size
SD - pooled variance
MD - mean difference
SE - standard error
LCL - lower confidence level
UCL - upper confidence level
Syntax
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Arguments
@Label
the column variable which differentiates the two samples. You can use @Label to identify the control group and the treatment group.
@Value
the x-values and y-values to be used in the computation. @Value is an expression of type float or of a type that can be implicitly converted to float.
@Statistic
identifies the statistic to be returned.
@XLabel
Identifies which if the two values in the @Label column will be treated as x (or sample 1).
Return Types
float
Remarks
· @Statistic must be invariant within a GROUP.
· There must be exactly 2 values for @Label within a GROUP.
· @XLabel must be invariant within a GROUP.
· TTEST_INDEP is an aggregate function and follows the same conventions as all other aggregate function in SQL Server.
· For paired t-test use TTEST_PAIRED.
· For independent samples with unequal variances use TTEST_INDEPU.
· If @Value IS NULL, then it is not included in the aggregate
· Effect Size (ES) is calculated as Cohen’s d.
· LCL and UCL are calculated with alpha = .05
Examples
Here’s a small sample of test scores broken out by gender.
SELECT wct.TTEST_INDEP(x,val,'P1','F') as one_sided_p_value
FROM (VALUES
(1,'M',420),
(2,'M',647),
(3,'M',629),
(4,'M',569),
(5,'M',426),
(6,'F',554),
(7,'F',502),
(8,'F',580),
(9,'M',626),
(10,'F',412),
(11,'F',480),
(12,'M',478),
(13,'F',566),
(14,'F',491),
(15,'M',511),
(16,'F',556),
(17,'F',359),
(18,'F',451),
(19,'F',430),
(20,'M',441),
(21,'M',490),
(22,'M',578),
(23,'F',385),
(24,'M',592),
(25,'M',333)
) n(id, x, val)
This produces the following result.
one_sided_p_value
----------------------
0.143336729580001
If we wanted to calculate the t-statistic, we would just use T instead of P1
SELECT wct.TTEST_INDEP(x,val,'T','F') as t_observed
FROM (VALUES
(1,'M',420),
(2,'M',647),
(3,'M',629),
(4,'M',569),
(5,'M',426),
(6,'F',554),
(7,'F',502),
(8,'F',580),
(9,'M',626),
(10,'F',412),
(11,'F',480),
(12,'M',478),
(13,'F',566),
(14,'F',491),
(15,'M',511),
(16,'F',556),
(17,'F',359),
(18,'F',451),
(19,'F',430),
(20,'M',441),
(21,'M',490),
(22,'M',578),
(23,'F',385),
(24,'M',592),
(25,'M',333)
) n(id, x, val)
This produces the following result.
t_observed
----------------------
-1.09076167249426
Here we show all the values the can be returned by TTEST_INDEP.
SELECT t.s
,t.descr
,wct.TTEST_INDEP(x,val,t.s,'F') as Value
FROM (VALUES
(1,'M',420),
(2,'M',647),
(3,'M',629),
(4,'M',569),
(5,'M',426),
(6,'F',554),
(7,'F',502),
(8,'F',580),
(9,'M',626),
(10,'F',412),
(11,'F',480),
(12,'M',478),
(13,'F',566),
(14,'F',491),
(15,'M',511),
(16,'F',556),
(17,'F',359),
(18,'F',451),
(19,'F',430),
(20,'M',441),
(21,'M',490),
(22,'M',578),
(23,'F',385),
(24,'M',592),
(25,'M',333)
) n(id, x, val)
CROSS APPLY(VALUES
('P1','one_tailed_p_value'),
('P2','two_tailed_p_value'),
('T','t_observed'),
('ES','effect_size'),
('N1','num_observed_one'),
('N2','num_observed_two'),
('SD','pooled_variance'),
('DF','deg_freedom'),
('MD','mean_difference'),
('SE','std_error'),
('LCL','lower_ci'),
('UCL','upper_ci')
)t(s,descr)
GROUP BY t.s, t.descr
This produces the following result.
s descr Value
---- ------------------ ----------------------
P1 one_tailed_p_value 0.143336729580001
P2 two_tailed_p_value 0.286673459160002
T t_observed -1.09076167249426
ES effect_size -0.436654132144636
N1 num_observed_one 12
N2 num_observed_two 13
SD pooled_variance 7558.09698996656
DF deg_freedom 23
MD mean_difference -37.9615384615385
SE std_error 34.8027799461741
LCL lower_ci -109.956574060931
UCL upper_ci 34.0334971378542