# Spearman

##### Spearman's rho

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:

$$1-\frac{6d}{r(r^2-1)}$$

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=frac{X}{r-1)-1}{rho = X/(r-1) -1}.

Exact calculations are made for \eqn{r \le 100}{r <= 100}<="" p="">

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.$

`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.

*Rank Correlation Methods.* Griffin, London.

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

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*Documentation reproduced from package SuppDists, version 1.0-0, License: GPL vesion 2 or newer*