Spearman {SuppDists} R Documentation

## Spearman's rho

### Description

Density, distribution function, quantile function, random generator and summary function for Spearman's rho.

### Usage

```dSpearman(x, r, log=FALSE)
pSpearman(q, r,  lower.tail=TRUE, log.p=FALSE)
qSpearman(p, r,  lower.tail=TRUE, log.p=FALSE)
rSpearman(n, r)
sSpearman(r)
```

### Arguments

 `x,q` vector of non-negative quantities `p` vector of probabilities `n` number of values to generate. If n is a vector, length(n) values will be generated `r` (r >= 3) vector of number of observations `log, log.p` logical vector; if TRUE, probabilities p are given as log(p) `lower.tail` logical vector; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

### Details

Spearman's rho is the rank correlation coefficient between r pairs of items. It ranges from -1 to 1. Denote by d, the sum of squares of the differences between the matched ranks, then x is given by:

1-6 d /(r(r^2-1))

This is, in fact, the product-moment correlation coefficient of rank differences. See Kendall (1975), Chapter 2. It is identical to Friedman's chi-squared for two treatments scaled to the -1, 1 range – if X is the Friedman statistic, then rho = X/(r-1) -1.

Exact calculations are made for r <= 100

These exact calculations are made using the algorithm of Kendall and Smith (1939).

The incomplete beta, with continuity correction, is used for calculations outside this range.

### Value

The output values conform to the output from other such functions in R. `dSpearman()` gives the density, `pSpearman()` the distribution function and `qSpearman()` its inverse. `rSpearman()` generates random numbers. `sSpearman()` produces a list containing parameters corresponding to the arguments – mean, median, mode, variance, sd, third cental moment, fourth central moment, Pearson's skewness, skewness, and kurtosis.

### Author(s)

Bob Wheeler bwheelerg@gmail.com

### References

Kendall, M. (1975). Rank Correlation Methods. Griffin, London.

Kendall, M. and Smith, B.B. (1939). The problem of m rankings. Ann. Math. Stat. 10. 275-287.

### Examples

```
pSpearman(.95, 10)
pSpearman(c(-0.55,0,0.55), 10) ## approximately 5% 50% and 95%
sSpearman(10)
plot(function(x)dSpearman(x, 10),-.9,.9)

```

[Package SuppDists version 1.1-9.4 Index]