Fisher's exact test. More...

#include <yat/statistics/Fisher.h>

Public Member Functions
	Fisher (bool yates=false)

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_left (void) const

double	p_right (void) const

double	p_value (void) 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)

double	oddsratio (void) const

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 setup. See e.g. Barnard's test for alternative.

Constructor & Destructor Documentation

◆ Fisher()

theplu::yat::statistics::Fisher::Fisher ( bool yates = false )

Default Constructor.

Parameters

yates if true Yates's correction is used for chi-squared calculation

Since: Constructor with argument was introduced in yat 0.13

◆ ~Fisher()

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

virtual

Destructor

Member Function Documentation

◆ Chi2()

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.

If indicated in constructor, Yates's correction is used, i.e., Chi2 is calculated as $\frac{(|O_i-E_i|-0.5)^2}{E_i}$

See also: expected(double&, double&, double&, double&)

Returns: Chi2 score

◆ expected()

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

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

◆ minimum_size() [1/2]

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

◆ minimum_size() [2/2]

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

◆ oddsratio() [1/2]

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.

◆ oddsratio() [2/2]

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

Returns: oddsratio loaded via oddsratio(4)

Since: New in yat 0.8

◆ p_left()

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

Calculates probability to get oddsratio (or smaller).

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

Since: New in yat 0.11

◆ p_right()

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

Calculates probability to get oddsratio (or greater).

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

Since: New in yat 0.11

◆ p_value()

double theplu::yat::statistics::Fisher::p_value ( void ) 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 $P(k) \le P(a)$ .

Returns: two-sided p-value

◆ p_value_one_sided()

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

Deprecated:: Provided for backward compatibility with the 0.10 API. Use p_right() instead.

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

yat/statistics/Fisher.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Fisher()

◆ ~Fisher()

Member Function Documentation

◆ Chi2()

◆ expected()

◆ minimum_size() [1/2]

◆ minimum_size() [2/2]

◆ oddsratio() [1/2]

◆ oddsratio() [2/2]

◆ p_left()

◆ p_right()

◆ p_value()

◆ p_value_one_sided()