Chapter 6: Nonparametric Statistics

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



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