Performs a Bhapkar V test.
NI — Vector of length NGROUP containing the number of responses for each of the NGROUP groups. (Input)
Y — Vector of
length NI(1) +
NI(2) + … + NI(NGROUP) containing the
responses for each of the NGROUP
groups. (Input)
Y must be sorted by
group with the NI(1) observations for
group 1 coming first.
V — Bhapkar V statistic. (Output)
PROB — Asymptotic
probability of exceeding V under the null
hypothesis that the populations are equal. (Output)
Asymptotically, V follows a chi-squared distribution with NGROUP − 1 degrees of
freedom.
NGROUP — Number
of groups. (Input)
Default: NGROUP = size (NI,1).
Generic: CALL BHAKV (NI, Y, V, PROB [,…])
Specific: The specific interface names are S_BHAKV and D_BHAKV.
Single: CALL BHAKV (NGROUP, NI, Y, V, PROB)
Double: The double precision name is DBHAKV.
Routine BHAKV
tests the hypothesis that several samples are from the same population using the
Bhapkar V statistic. Let the number of samples be denoted by K =
NGROUP.
To compute the Bhapkar V statistic, one first computes, for each group
i, the statistic ti = the number of
K-tuples that can be formed with one observation from each sample such
that the element from population i is the smallest. The sample variance
of the ratio of ti to the total number of
such k-tuples is then computed. The Bhapkar V statistic is then a
constant c multiplied by this variance, where
c =
n(2m − 1), m =
NGROUP,
and n is the sum of the sample sizes (after missing values are
eliminated).
Workspace may be explicitly provided, if desired, by use of B2AKV/DB2AKV. The reference is
CALL B2AKV (NGROUP, NI, Y, V, PROB, IWK, WK, YWK)
The additional arguments are as follows:
IWK — Integer work vector of length NI(1) + … + NI(NGROUP) + NGROUP
WK — Work vector of length NGROUP
YWK — Work vector of length NI(1) + … + NI(NGROUP). If Y is not needed, Y and YWK can share the same storage locations.
We want to test the null hypothesis that three samples of size 3, 2, and 4, respectively, are from the same population using the Bhapkar V statistic.
USE BHAKV_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER NGROUP
PARAMETER (NGROUP=3)
!
INTEGER NI(NGROUP), NOUT
REAL PROB, V, Y(9)
!
DATA NI/3, 2, 4/
DATA Y/1, 3, 2, -1, 5, 4, 7, 2, 9/
! Perform Bhapkar V test
CALL BHAKV (NI, Y, V, PROB)
! Print results
CALL UMACH (2, NOUT)
WRITE (NOUT,99998) V
WRITE (NOUT,99999) PROB
!
99998 FORMAT (' V = ', F12.5)
99999 FORMAT (' Prob = ', F12.5)
!
END
V =
1.89429
Prob = 0.38785
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