Computes tie statistics for a sample of observations.
X — Vector of
length NOBS
containing the observations. (Input)
X must be ordered
monotonically increasing with all missing values removed.
FUZZ — Value used
to determine ties. (Input)
Observations i and j
are tied if the successive differences X(k + 1) − X(k) between
observations i and j, inclusive, are all less than FUZZ. FUZZ must be
nonnegative.
TIES — Vector of
length 4 containing the tie statistics. (Output)
The tie
statistics are returned in TIES and are computed
as follows:
where tj is the number of ties in the j-th group (rank) of ties, and τ is the number of tie groups in the sample.
NOBS — The number
of observations. (Input)
Default: NOBS = size (X,1).
Generic: CALL NTIES (X, FUZZ, TIES [,…])
Specific: The specific interface names are S_NTIES and D_NTIES.
Single: CALL NTIES (NOBS, X, FUZZ, TIES)
Double: The double precision name is DNTIES.
Routine NTIES
computes tie statistics for a monotonically increasing sample of observations.
“Tie statistics” are statistics that may be used to correct a continuous
distribution theory nonparametric test for tied observations in the data.
Observations i and j are tied if the successive differences
X(k
+ 1) −
X(k),
inclusive, are all less than FUZZ.
Note that if each of the monotonically increasing observations is equal to its
predecessor plus a constant, if that constant is less than FUZZ,
then all observations are contained in one tie group. For example, if FUZZ
= 0.11, then the following observations are all in one tie group.
0.0, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00
We want to compute tie statistics for a sample of length 7.
USE NTIES_INT
USE WRRRN_INT
IMPLICIT NONE
INTEGER NOBS
REAL FUZZ
PARAMETER (FUZZ=0.001, NOBS=7)
!
REAL TIES(4), X(NOBS)
!
DATA X/1.0, 1.0001, 1.0002, 2.0, 3.0, 3.0, 4.0/
! Compute tie statistics
CALL NTIES (X, FUZZ, TIES)
! Print results
CALL WRRRN ('TIES', TIES, 1, 4, 1, 0)
!
END
TIES
1
2
3 4
4.00
2.50 84.00 6.00
PHONE: 713.784.3131 FAX:713.781.9260 |