# C# Hypothesis Testing

NMath Stats from CenterSpace Software is a .NET class library that provides functions for statistical computation and biostatistics, including descriptive statistics, probability distributions, combinatorial functions, multiple linear regression, analysis of variance, and multivariate statistics.

NMath Stats also includes basic hypothesis tests, such as z test, t-test, and F-test, with calculation of p-values, critical values, and confidence intervals. This functionality can be used from any .NET language including VB.NET and F#.

The NMath Stats library is part of CenterSpace Software's NMath Suite of numerical libraries, which provides building blocks for mathematical, financial, engineering, and scientific applications on the .NET platform. Features include matrix and vector classes, linear algebra, random number generators, numerical integration methods, interpolation, statistics, biostatistics, multiple linear regression, analysis of variance (ANOVA), optimization, and object-oriented interfaces to public domain computing packages such as the BLAS (Basic Linear Algebra Subprograms) and LAPACK (Linear Algebra PACKage). All NMath routines are callable from any .NET language, including C#, Visual Basic.NET, and F#.

### Hypothesis Testing Documentation

Complete documentation for all NMath libraries is available online. For more general information on linear regression, see the chapter on hypothesis testing in the NMath Stats User's Guide.

API documentation for the hypothesis testing classes is available in the NMath Stats Reference Guide, with pertainent classes outlined in the table below.

Class
Distribution
Compares a single sample mean to an expected mean from a normal distribution with known standard deviation.
Compares a single sample mean to an expected mean from a normal distribution with an unknown standard deviation.
Tests the null hypothesis that the population mean of the paired differences of two samples is zero.
Tests whether two samples from a normal distribution could have the same mean when the standard deviations are unknown but assumed to be equal.
Tests the null hypothesis that the two population means corresponding to two random samples are equal. The two samples are assumed to be independent of each other. A pooled estimate of the variance is not used.
Tests whether the variances of two populations are equal.
Performs a Kolmogorov-Smirnov test of the distribution of one sample.
Performs a two-sample Kolmogorov-Smirnov test to compare the distributions of values in two data sets.
Performs a Anderson-Darling test of the distribution of one sample.
Tests whether the frequency distribution of experimental outcomes are consistant with a particular theoretical distribution.
Tests the null hypothesis that the sample comes from a normally distributed population.

### Hypothesis Testing Code Examples

All NMath libraries include extensive code examples in both C# and Visual Basic.NET. Studying these examples is one of the best ways to learn how to use NMath libraries. For more information on hypothesis testing, see:

• HypothesisTestExample [C#]  [VB.NET]
Example showing how to use the hypothesis test classes to test statistical hypotheses.

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