NTIES

Computes tie statistics for a sample of observations.

Required Arguments

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.

Optional Arguments

NOBS — The number of observations. (Input)
Default: NOBS = size (X,1).

FORTRAN 90 Interface

Generic: CALL NTIES (X, FUZZ, TIES [, …])

Specific: The specific interface names are S_NTIES and D_NTIES.

FORTRAN 77 Interface

Single: CALL NTIES (NOBS, X, FUZZ, TIES)

Double: The double precision name is DNTIES.

Description

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

Example

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

Output

 

TIES

1 2 3 4

4.00 2.50 84.00 6.00