**5.7****
****Pearson's Chi-Square Test** (.NET, C#, CSharp, VB, Visual Basic, F#)

**NMath Stats**
provides class **PearsonsChiSquareTest**
for performing Pearson's chi-square test. Pearson's
chi-square test is the most well-known of the chi-square tests, which
are statistical procedures whose results are evaluated by reference to
the chi-square distribution. It tests the null hypothesis that the frequency
distribution of experimental outcomes are consistent with a particular
theoretical distribution. The event outcomes considered must be mutually
exclusive and have a total probability of 1.

Instances of **PearsonsChiSquareTest**
are constructed either from raw data or tables of counts. For example,
this code constructs a **PearsonsChiSquareTest**
using outcomes from a series of experiment runs, along with the expected
frequencies:

Code Example – C# chi-square test

int[] outcomes = { 59, 20, 11, 10 }; DoubleVector probs = new DoubleVector( 0.5625, 0.1875, 0.1875, 0.0625 ); PearsonsChiSquareTest test = new PearsonsChiSquareTest( outcomes, probs );

This code uses a contingency table (or cross tabulation) to store the relation between two or more categorical variables:

Code Example – C# chi-square test

var data = new int[2, 2]; data[0, 0] = 4298; data[0, 1] = 767; data[1, 0] = 7136; data[1, 1] = 643; bool yatesCorrect = true; PearsonsChiSquareTest test = new PearsonsChiSquareTest( data, yatesCorrect );

The Yates' correction for continuity may optionally be applied.

Once you've constructed and configured a **PearsonsChiSquareTest **object, you can
access the various test results using the provided properties, as described
in Section 5.1:

Code Example – C# chi-square test

Console.WriteLine( "chi-square statistic = " + test.ChiSquareStatistic ); Console.WriteLine( "numerator df = " + test.DegreesOfFreedom ); Console.WriteLine( "p-value = " + test.P ); Console.WriteLine( "reject the null hypothesis? " + test.Reject );

The output is:

chi-square statistic = 147.761248704421 numerator df = 1 p-value = 0 reject the null hypothesis? True

Again, the ToString() method returns a formatted string representation of the complete test results:

Pearson chi-square test ----------------- Sample size = 12844 Yates corrected = True Computed chi-square statistic: 147.761248704421, df = 1 P-value: 0 REJECT the null hypothesis for alpha = 0.01