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 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: CALLNTIES (X, FUZZ, TIES[, …])
Specific: The specific interface names are S_NTIES and D_NTIES.
FORTRAN 77 Interface
Single: CALLNTIES (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.
