Spearman rank correlation coefficient. More...

#include <yat/statistics/Spearman.h>

Public Member Functions
	Spearman (void)
	Constructor.

virtual	~Spearman (void)
	Destructor.

void	add (double x, double y)
	add pair of data

size_t	n (void) const
	Number of data points. More...

double	p_left (bool exact=false) const
	Lower one-sided p-value. More...

double	p_right (bool exact=false) const
	Upper one-sided p-value. More...

double	p_value (bool exact=false) const
	Two-sided p-value. More...

void	reset (void)
	reset to empty

double	score (void) const
	spearman rank correlation coefficient More...

Detailed Description

Spearman rank correlation coefficient.

Class for Spearman rank correlation coefficient which can be understood as Pearson correlation of ranks.

Since: New in yat 0.9

Member Function Documentation

size_t theplu::yat::statistics::Spearman::n ( void ) const

Number of data points.

Returns: Number of pairs of data added to object.

double theplu::yat::statistics::Spearman::p_left ( bool exact = false ) const

Lower one-sided p-value.

Calculates, $P(R \le r)$ , the probability to get a score less (or equal) than score() given that there is no association between two variables.

See Also: p_right()

double theplu::yat::statistics::Spearman::p_right ( bool exact = false ) const

Upper one-sided p-value.

Calculates, $P(R \ge r)$ , the probability to get a score greater (or equal) than score() given that there is no association between two variables.

In exact mode the score is calculated for each permutation and compared to the actual score. In each permutation one variable, say x, is kept fix while the other (y) is shuffled in determionsitic fashion. Number of permutations grows quickly as number of data points grows and with no ties there are N! permutations and the exact method gets very expensive.

In approximative mode P-value is calculated using pearson_p_value().

double theplu::yat::statistics::Spearman::p_value ( bool exact = false ) const

Two-sided p-value.

Calculates, $P(|R| \ge |r|)$ , the probability to get a score more extreme (or equal) than score() given that there is no association between two variables. If score(), r, is greater than zero, this equals 2 * p_right(). Otherwise it equals 2 * p_left().

double theplu::yat::statistics::Spearman::score ( void ) const

spearman rank correlation coefficient

The Spearman rank correlation coeeficient is defined as $\frac{12\sum (R_i-\frac{n+1}{2})(S_i-\frac{n+1}{2})}{n(n^2-1)}$ where $ R_i $ and $ S_i $ are ranks of X and Y, respectively. In case of ties, the rank is defined as the average rank of the ties.

The documentation for this class was generated from the following file:

yat/statistics/Spearman.h

Public Member Functions

Detailed Description

Member Function Documentation