theplu::yat::statistics::Fisher Class Reference

Fisher's exact test. More...

#include <yat/statistics/Fisher.h>

List of all members.

Public Member Functions

Fisher (void)

virtual ~Fisher (void)

double Chi2 (void) const

void expected (double &a, double &b, double &c, double &d) const

unsigned int & minimum_size (void)

const unsigned int & minimum_size (void) const

double p_value () const

double p_value_one_sided () const

double oddsratio (const unsigned int a, const unsigned int b, const unsigned int c, const unsigned int d)

Detailed Description

Fisher's exact test.

Fisher's Exact test is a procedure that you can use for data in a two by two contingency table:

$\begin{tabular}{|c|c|} \hline a&b \tabularnewline \hline c&d \tabularnewline \hline \end{tabular}$

Fisher's Exact Test is based on exact probabilities from a specific distribution (the hypergeometric distribution). There's really no lower bound on the amount of data that is needed for Fisher's Exact Test. You do have to have at least one data value in each row and one data value in each column. If an entire row or column is zero, then you don't really have a 2 by 2 table. But you can use Fisher's Exact Test when one of the cells in your table has a zero in it. Fisher's Exact Test is also very useful for highly imbalanced tables. If one or two of the cells in a two by two table have numbers in the thousands and one or two of the other cells has numbers less than 5, you can still use Fisher's Exact Test. For very large tables (where all four entries in the two by two table are large), your computer may take too much time to compute Fisher's Exact Test. In these situations, though, you might as well use the Chi-square test because a large sample approximation (that the Chi-square test relies on) is very reasonable. If all elements are larger than 10 a Chi-square test is reasonable to use.

Note:: The statistica assumes that each column and row sum, respectively, are fixed. Just because you have a 2x2 table, this assumtion does not necessarily match you experimental upset. See e.g. Barnard's test for alternative.

Constructor & Destructor Documentation

theplu::yat::statistics::Fisher::Fisher ( void )

Default Constructor.

virtual theplu::yat::statistics::Fisher::~Fisher ( void ) [virtual]

Destructor

Member Function Documentation

double theplu::yat::statistics::Fisher::Chi2 ( void ) const

The Chi2 score is calculated as $\sum \frac{(O_i-E_i)^2}{E_i}$ where E is expected value and O is observed value.

Returns:: Chi2 score

void theplu::yat::statistics::Fisher::expected	(	double &	a,
		double &	b,
		double &	c,
		double &	d
	)			const

Calculates the expected values under the null hypothesis. $a' = \frac{(a+c)(a+b)}{a+b+c+d}$ , $b' = \frac{(a+b)(b+d)}{a+b+c+d}$ , $c' = \frac{(a+c)(c+d)}{a+b+c+d}$ , $d' = \frac{(b+d)(c+d)}{a+b+c+d}$ ,

unsigned int& theplu::yat::statistics::Fisher::minimum_size ( void )

If all elements in table is at least minimum_size(), a Chi2 approximation is used for p-value calculation.

Returns:: reference to minimum_size

const unsigned int& theplu::yat::statistics::Fisher::minimum_size ( void ) const

If all elements in table is at least minimum_size(), a Chi2 approximation is used for p-value calculation.

Returns:: const reference to minimum_size

double theplu::yat::statistics::Fisher::p_value ( ) const

If all elements in table is at least minimum_size(), a Chi2 approximation is used.

Otherwise a two-sided p-value is calculated using the hypergeometric distribution $\sum_k P(k)$ where summation runs over k such that $|k-<a>| \ge |a-<a>|$ .

Returns:: two-sided p-value

double theplu::yat::statistics::Fisher::p_value_one_sided ( ) const

One-sided p-value is probability to get larger (or equal) oddsratio.

If all elements in table is at least minimum_size(), a Chi2 approximation is used.

Returns:: One-sided p-value

double theplu::yat::statistics::Fisher::oddsratio	(	const unsigned int	a,
		const unsigned int	b,
		const unsigned int	c,
		const unsigned int	d
	)

Function calculating odds ratio from 2x2 table

$\begin{tabular}{|c|c|} \hline a&b \tabularnewline \hline c&d \tabularnewline \hline \end{tabular}$

as $\frac{ad}{bc}$

Object will remember the values of a, b, c, and d.

Returns:: odds ratio.

Exceptions:

If

table is invalid a runtime_error is thrown. A table is invalid if a row or column sum is zero.

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

yat/statistics/Fisher.h


Public Member Functions
	Fisher (void)
virtual	~Fisher (void)
double	Chi2 (void) const
void	expected (double &a, double &b, double &c, double &d) const
unsigned int &	minimum_size (void)
const unsigned int &	minimum_size (void) const
double	p_value () const
double	p_value_one_sided () const
double	oddsratio (const unsigned int a, const unsigned int b, const unsigned int c, const unsigned int d)