FisherExactTest Class

[SerializableAttribute]
public class FisherExactTest : HypothesisTest<HypergeometricDistribution>

<SerializableAttribute>
Public Class FisherExactTest
	Inherits HypothesisTest(Of HypergeometricDistribution)

// Example from https://en.wikipedia.org/wiki/Fisher%27s_exact_test

// This example comes directly from the Wikipedia page referenced above. In this example, 
// a sample of teenagers might be divided into male and female on the one hand, and those
// that are and are not currently studying for a statistics exam on the other. We hypothesize,
// for example, that the proportion of studying individuals is higher among the women than
// among the men, and we want to test whether any difference of proportions that we observe
// is significant. The data might look like this:

var matrix = new ConfusionMatrix(new int[,] 
{
    /*                    Men     Women  */
    /* Studying    */  {   1,       9    },
    /* Not-studying*/  {  11,       3    },
});

// Let's check that the row totals and column
// totals match the ones reported in Wikipedia:
int[] rowTotals = matrix.RowTotals;    // should be 10, 14
int[] colTotals = matrix.ColumnTotals; // should be 12, 12
int total = matrix.NumberOfSamples;    // should be 24

// The question we ask about these data is: knowing that 10 of these 24 teenagers are studiers,
// and that 12 of the 24 are female, and assuming the null hypothesis that men and women are 
// equally likely to study, what is the probability that these 10 studiers would be so unevenly
// distributed between the women and the men? If we were to choose 10 of the teenagers at random,
// what is the probability that 9 or more of them would be among the 12 women, and only 1 or fewer
// from among the 12 men?

var fet = new FisherExactTest(matrix, alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis);
double p = fet.PValue; // should be approximately 0.0027594561852200832
bool significant = fet.Significant; // should be true

// The same result can be verified in R using:
//  fisher.test(matrix(c(1, 9, 11, 3), 2,2))
/*
    Fisher's Exact Test for Count Data

    data: matrix(c(1, 9, 11, 3), 2, 2)
    p - value = 0.002759
    alternative hypothesis: true odds ratio is not equal to 1
    95 percent confidence interval:
                0.0006438284 0.4258840381
    sample estimates:
    odds ratio
    0.03723312*/