ShapiroWilkTest Class 
Namespace: Accord.Statistics.Testing
[SerializableAttribute] public class ShapiroWilkTest : HypothesisTest<ShapiroWilkDistribution>, IHypothesisTest<ShapiroWilkDistribution>, IHypothesisTest
The ShapiroWilkTest type exposes the following members.
Name  Description  

ShapiroWilkTest 
Creates a new ShapiroWilk test.

Name  Description  

CriticalValue 
Gets the critical value for the current significance level.
(Inherited from HypothesisTestTDistribution.)  
PValue 
Gets the Pvalue associated with this test.
(Inherited from HypothesisTestTDistribution.)  
Significant 
Gets whether the null hypothesis should be rejected.
(Inherited from HypothesisTestTDistribution.)  
Size 
Gets the significance level for the
test. Default value is 0.05 (5%).
(Inherited from HypothesisTestTDistribution.)  
Statistic 
Gets the test statistic.
(Inherited from HypothesisTestTDistribution.)  
StatisticDistribution 
Gets the distribution associated
with the test statistic.
(Inherited from HypothesisTestTDistribution.)  
Tail 
Gets the test type.
(Inherited from HypothesisTestTDistribution.) 
Name  Description  

Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
OnSizeChanged 
Called whenever the test significance level changes.
(Inherited from HypothesisTestTDistribution.)  
PValueToStatistic 
Converts a given pvalue to a test statistic.
(Overrides HypothesisTestTDistributionPValueToStatistic(Double).)  
StatisticToPValue 
Converts a given test statistic to a pvalue.
(Overrides HypothesisTestTDistributionStatisticToPValue(Double).)  
ToString 
Converts the numeric PValue of this test to its equivalent string representation.
(Inherited from HypothesisTestTDistribution.)  
ToString(String, IFormatProvider) 
Converts the numeric PValue of this test to its equivalent string representation.
(Inherited from HypothesisTestTDistribution.) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)  
ToT  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) 
The Shapiro–Wilk test is a test of normality in frequentist statistics. It was published in 1965 by Samuel Sanford Shapiro and Martin Wilk. The The Shapiro–Wilk test tests the null hypothesis that a sample came from a normally distributed population.
The nullhypothesis of this test is that the population is normally distributed. Thus, if the pvalue is less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not from a normally distributed population; in other words, the data are not normal. On the contrary, if the pvalue is greater than the chosen alpha level, then the null hypothesis that the data came from a normally distributed population cannot be rejected (e.g., for an alpha level of 0.05, a data set with a pvalue of 0.02 rejects the null hypothesis that the data are from a normally distributed population). However, since the test is biased by sample size, the test may be statistically significant from a normal distribution in any large samples. Thus a Q–Q plot is required for verification in addition to the test.
References:
// Let's say we would like to determine whether a set // of observations come from a normal distribution: double[] samples = { 0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43, 0.21, 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66 }; // For this, we can use the ShapiroWilk test. This test tests the null hypothesis // that samples come from a Normal distribution, vs. the alternative hypothesis that // the samples do not come from such distribution. In other words, should this test // come out significant, it means our samples do not come from a Normal distribution. // Create a new ShapiroWilk test: var sw = new ShapiroWilkTest(samples); double W = sw.Statistic; // should be 0.90050 double p = sw.PValue; // should be 0.04209 bool significant = sw.Significant; // should be true // The test is significant, therefore we should reject the null // hypothesis that the samples come from a Normal distribution.