PRSPEARMAN procedure

Calculates probabilities for Spearman's rank correlation statistic, PC Windows only (D.B. Baird).


No options


Parameters

N = scalars
Sizes of the first groups of observations

CORRELATION = scalars
Values of the signed rank statistic

CLPROBABILITY = scalars
Cumulative lower probability of CORRELATION

CUPROBABILITY = scalars
Cumulative upper probability of CORRELATION

PROBABILITY = scalars
Probability density of CORRELATION

UPROBABILITIES = variates
Probability densities of CORRELATION...1

UCORRELATION = variates
Values of CORRELATION at corresponding elements of UPROBABILITIES


Description

PRSPEARMAN calculates various probabilities for Spearman's rank correlation coefficient (see procedure SPEARMAN). These can be used to give a nonparametric assessment of whether paired samples are correlated.

correlation = ∑i=1...N ((Ri-(N+1)/2) × (Si-(N+1)/2)) / (N × (N2-1) / 12

where Ri and Si are the ranks of Xi and Yi respectively.

   The number of sample pairs of observations is specified by the N parameter, and the CORRELATION parameter specifies the value of the rank correlation for which the probabilities are required. The CLPROBABILITY and CUPROBABILITY parameters can specify scalars to save the cumulative lower and upper probabilities,

Pr.(s ≤ CORRELATION)

and

Pr.(s > CORRELATION)

respectively. PROBABILITY can save the probability density at CORRELATION,

Pr.(s == CORRELATION),

UPROBABILITIES can save a variate containing the densities for CORRELATION...1, and UCORRELATION can save the values of CORRELATION for the elements in UPROBABILITIES.


Options: none.

Parameters: N, CORRELATION, CLPROBABILITY, CUPROBABILITY, PROBABILITY, UPROBABILITIES, UCORRELATION.


Method

The procedure uses PASS to call an external program which calculate the coefficents of the generating function for the Spearman rank correlation coefficient under the null hypothesis using recurrence functions (see van de Weil et al. 1999). The central limit theorem is used when N exceeds 20, and a Normal approximation of the CDF is returned.


Action with RESTRICT

Restrictions are not applicable to any of the parameters.


Reference

van de Wiel, M.A. Di Bucchianico, A. & van de Laan, P. (1999). Symbolic computation and exact distributions of nonparametric test statistics. The Statistician, 48, 507-516.