public void ConstructorTest2()
{
double[] observed = { 6, 6, 16, 15, 4, 3 };
double[] expected = { 6.24, 5.76, 16.12, 14.88, 3.64, 3.36 };
int degreesOfFreedom = 2;
var chi = new ChiSquareTest(expected, observed, degreesOfFreedom);
Assert.AreEqual(0.0952, chi.Statistic, 0.001);
Assert.AreEqual(2, chi.DegreesOfFreedom);
Assert.AreEqual(false, chi.Significant);
}
public void ConstructorTest()
{
double[] observed = { 639, 241 };
double[] expected = { 660, 220 };
int degreesOfFreedom = 1;
var chi = new ChiSquareTest(expected, observed, degreesOfFreedom);
Assert.AreEqual(2.668, chi.Statistic, 0.015);
Assert.AreEqual(1, chi.DegreesOfFreedom);
Assert.AreEqual(0.1020, chi.PValue, 1e-4);
}
public void ConstructorTest3()
{
// Example based on Wikipedia's article for χ²-Squared Test
// http://en.wikipedia.org/wiki/Pearson's_chi-squared_test
// Suppose we would like to test the hypothesis that a random sample of
// 100 people has been drawn from a population in which men and women are
// equal in frequency.
// Under this hypothesis, the observed number of men and women would be
// compared to the theoretical frequencies of 50 men and 50 women. So,
// after drawing our sample, we found out that there were 44 men and 56
// women in the sample:
// man woman
double[] observed = { 44, 56 };
double[] expected = { 50, 50 };
// If the null hypothesis is true (i.e., men and women are chosen with
// equal probability), the test statistic will be drawn from a chi-squared
// distribution with one degree of freedom. If the male frequency is known,
// then the female frequency is determined.
//
int degreesOfFreedom = 1;
// So now we have:
//
var chi = new ChiSquareTest(expected, observed, degreesOfFreedom);
// The chi-squared distribution for 1 degree of freedom shows that the
// probability of observing this difference (or a more extreme difference
// than this) if men and women are equally numerous in the population is
// approximately 0.23.
double pvalue = chi.PValue; // 0.23
// This probability is higher than conventional criteria for statistical
// significance (0.001 or 0.05), so normally we would not reject the null
// hypothesis that the number of men in the population is the same as the
// number of women.
bool significant = chi.Significant; // false
Assert.AreEqual(0.23013934044341644, pvalue);
Assert.IsFalse(significant);
}
public void ConstructorTest_WithZero_NoNaN()
{
double[] observed = { 639, 0 };
double[] expected = { 660, 0 };
int degreesOfFreedom = 1;
var chi = new ChiSquareTest(expected, observed, degreesOfFreedom);
Assert.AreEqual(0.66818181818181821, chi.Statistic, 0.015);
Assert.AreEqual(1, chi.DegreesOfFreedom);
Assert.AreEqual(0.41368622699316782, chi.PValue, 1e-4);
}
public void ConstructorTest5()
{
Accord.Math.Tools.SetupGenerator(0);
double[] unif = UniformContinuousDistribution.Standard.Generate(1000);
double[] norm = NormalDistribution.Standard.Generate(1000);
var u = UniformContinuousDistribution.Standard;
var n = NormalDistribution.Standard;
{
var chi = new ChiSquareTest(unif, u);
Assert.AreEqual(3.2399999999999958, chi.Statistic, 1e-6);
Assert.AreEqual(7, chi.DegreesOfFreedom);
Assert.AreEqual(0.86194834721001945, chi.PValue, 1e-6);
Assert.IsFalse(chi.Significant);
}
{
var chi = new ChiSquareTest(unif, n);
Assert.AreEqual(1547.9120000000009, chi.Statistic, 1e-6);
Assert.AreEqual(7, chi.DegreesOfFreedom);
Assert.AreEqual(0, chi.PValue, 1e-6);
Assert.IsTrue(chi.Significant);
}
{
var chi = new ChiSquareTest(norm, u);
Assert.AreEqual(401.71999999999991, chi.Statistic, 1e-6);
Assert.AreEqual(7, chi.DegreesOfFreedom);
Assert.AreEqual(0, chi.PValue, 1e-6);
Assert.IsTrue(chi.Significant);
}
{
var chi = new ChiSquareTest(norm, n);
Assert.AreEqual(9.7439999999999696, chi.Statistic, 1e-6);
Assert.AreEqual(7, chi.DegreesOfFreedom);
Assert.AreEqual(0.20355084764042014, chi.PValue, 1e-6);
Assert.IsFalse(chi.Significant);
}
}
public void ConstructorTest4()
{
double[] sample =
{
0.621, 0.503, 0.203, 0.477, 0.710, 0.581, 0.329, 0.480, 0.554, 0.382
};
var distribution = UniformContinuousDistribution.Standard;
var chi = new ChiSquareTest(sample, distribution);
Assert.AreEqual(0, chi.Statistic, 1e-6);
Assert.AreEqual(3, chi.DegreesOfFreedom);
Assert.AreEqual(1, chi.PValue, 1e-4);
Assert.IsFalse(chi.Significant);
}
public void ConstructorTest5()
{
Accord.Math.Tools.SetupGenerator(0);
double[] unif = UniformContinuousDistribution.Standard.Generate(10000);
double[] norm = NormalDistribution.Standard.Generate(10000);
var u = UniformContinuousDistribution.Standard;
var n = NormalDistribution.Standard;
{
var chi = new ChiSquareTest(unif, u);
Assert.AreEqual(2.7011909090910131, chi.Statistic, 1e-6);
Assert.AreEqual(10, chi.DegreesOfFreedom);
Assert.AreEqual(0.98760847271849528, chi.PValue, 1e-6);
Assert.IsFalse(chi.Significant);
}
{
var chi = new ChiSquareTest(unif, n);
Assert.AreEqual(14865.499690909099, chi.Statistic, 1e-6);
Assert.AreEqual(10, chi.DegreesOfFreedom);
Assert.AreEqual(0, chi.PValue, 1e-6);
Assert.IsTrue(chi.Significant);
}
{
var chi = new ChiSquareTest(norm, u);
Assert.AreEqual(3934.3426909090917, chi.Statistic, 1e-6);
Assert.AreEqual(10, chi.DegreesOfFreedom);
Assert.AreEqual(0, chi.PValue, 1e-6);
Assert.IsTrue(chi.Significant);
}
{
var chi = new ChiSquareTest(norm, n);
Assert.AreEqual(6.2902909090909525, chi.Statistic, 1e-6);
Assert.AreEqual(10, chi.DegreesOfFreedom);
Assert.AreEqual(0.79031311920555392, chi.PValue, 1e-6);
Assert.IsFalse(chi.Significant);
}
}
public void ChiSquareTest()
{
ConfusionMatrix target = new ConfusionMatrix(6, 2, 6, 18);
double[,] expected = target.ExpectedValues;
Assert.AreEqual(3, target.ExpectedValues[0, 0]);
Assert.AreEqual(5, target.ExpectedValues[0, 1]);
Assert.AreEqual(9, target.ExpectedValues[1, 0]);
Assert.AreEqual(15, target.ExpectedValues[1, 1]);
Assert.AreEqual(6.4, target.ChiSquare, 1e-5);
ChiSquareTest test = new ChiSquareTest(target);
Assert.AreEqual(target.ChiSquare, test.Statistic);
Assert.AreEqual(1, test.DegreesOfFreedom);
Assert.IsTrue(test.Significant);
}
/// <summary>
/// Checks if two variables can be eliminated.
/// </summary>
///
public static bool CanEliminate(bool[] actual, bool[] expected, double alpha)
{
var matrix = new ConfusionMatrix(actual, expected);
double maxExpectedFrequency = matrix.ExpectedValues.Max();
IHypothesisTest test;
if (maxExpectedFrequency > 10)
test = new ChiSquareTest(matrix, yatesCorrection: false) { Size = alpha };
else if (maxExpectedFrequency >= 5)
test = new ChiSquareTest(matrix, yatesCorrection: true) { Size = alpha };
else
test = new FisherExactTest(matrix) { Size = alpha };
return !test.Significant;
}