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XLeratorDB/statistics Documentation

SQL Server independent samples T test


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 groups
The 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
XLeratorDB syntax for SQL Server 2008 analytic function TTEST_INDEP
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
 


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