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TTest Class

One-sample Student's T test.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.TestingHypothesisTestTDistribution
    Accord.Statistics.TestingTTest

Namespace:  Accord.Statistics.Testing
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.5.0
Syntax
[SerializableAttribute]
public class TTest : HypothesisTest<TDistribution>
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The TTest type exposes the following members.

Constructors
  NameDescription
Protected methodTTest
Creates a T-Test.
Public methodTTest(Double, Double, OneSampleHypothesis)
Tests the null hypothesis that the population mean is equal to a specified value.
Public methodTTest(Double, Double, OneSampleHypothesis)
Tests the null hypothesis that the population mean is equal to a specified value.
Public methodTTest(Double, Double, Double, Double, OneSampleHypothesis)
Tests the null hypothesis that the population mean is equal to a specified value.
Public methodTTest(Double, Double, Int32, Double, OneSampleHypothesis)
Tests the null hypothesis that the population mean is equal to a specified value.
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Properties
  NameDescription
Public propertyAnalysis
Gets the power analysis for the test, if available.
Public propertyConfidence
Gets the 95% confidence interval for the EstimatedValue.
Public propertyCriticalValue
Gets the critical value for the current significance level.
(Inherited from HypothesisTestTDistribution.)
Public propertyEstimatedValue
Gets the estimated parameter value, such as the sample's mean value.
Public propertyHypothesis
Gets the alternative hypothesis under test. If the test is Significant, the null hypothesis can be rejected in favor of this alternative hypothesis.
Public propertyHypothesizedValue
Gets the hypothesized parameter value.
Public propertyPValue
Gets the P-value associated with this test.
(Inherited from HypothesisTestTDistribution.)
Public propertySignificant
Gets whether the null hypothesis should be rejected.
(Inherited from HypothesisTestTDistribution.)
Public propertySize
Gets the significance level for the test. Default value is 0.05 (5%).
(Inherited from HypothesisTestTDistribution.)
Public propertyStandardError
Gets the standard error of the estimated value.
Public propertyStatistic
Gets the test statistic.
(Inherited from HypothesisTestTDistribution.)
Public propertyStatisticDistribution
Gets the distribution associated with the test statistic.
(Inherited from HypothesisTestTDistribution.)
Public propertyTail
Gets the test type.
(Inherited from HypothesisTestTDistribution.)
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Methods
  NameDescription
Protected methodCompute(Double, Double, OneSampleHypothesis)
Computes the T-test.
Protected methodCompute(Int32, Double, Double, Double, OneSampleHypothesis)
Computes the T-Test.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetConfidenceInterval
Gets a confidence interval for the estimated value within the given confidence level percentage.
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Protected methodOnSizeChanged
Update event.
(Overrides HypothesisTestTDistributionOnSizeChanged.)
Public methodPValueToStatistic(Double)
Converts a given p-value to a test statistic.
(Overrides HypothesisTestTDistributionPValueToStatistic(Double).)
Public methodStatic memberPValueToStatistic(Double, TDistribution, DistributionTail)
Converts a given p-value to a test statistic.
Public methodStatisticToPValue(Double)
Converts a given test statistic to a p-value.
(Overrides HypothesisTestTDistributionStatisticToPValue(Double).)
Public methodStatic memberStatisticToPValue(Double, TDistribution, DistributionTail)
Converts a given test statistic to a p-value.
Public methodToString
Converts the numeric P-Value of this test to its equivalent string representation.
(Inherited from HypothesisTestTDistribution.)
Public methodToString(String, IFormatProvider)
Converts the numeric P-Value of this test to its equivalent string representation.
(Inherited from HypothesisTestTDistribution.)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToTOverloaded.
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.)
Public Extension MethodToTOverloaded.
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 Matrix.)
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Remarks
Examples
// Consider a sample generated from a Gaussian
// distribution with mean 0.5 and unit variance.

double[] sample = 
{ 
    -0.849886940156521,    3.53492346633185,  1.22540422494611, 0.436945126810344, 1.21474290382610,
     0.295033941700225, 0.375855651783688, 1.98969760778547, 1.90903448980048,    1.91719241342961
};

// One may rise the hypothesis that the mean of the sample is not
// significantly different from zero. In other words, the fact that
// this particular sample has mean 0.5 may be attributed to chance.

double hypothesizedMean = 0;

// Create a T-Test to check this hypothesis
TTest test = new TTest(sample, hypothesizedMean,
       OneSampleHypothesis.ValueIsDifferentFromHypothesis);

// Check if the mean is significantly different
test.Significant should be true

// Now, we would like to test if the sample mean is
// significantly greater than the hypothesized zero.

// Create a T-Test to check this hypothesis
TTest greater = new TTest(sample, hypothesizedMean,
       OneSampleHypothesis.ValueIsGreaterThanHypothesis);

// Check if the mean is significantly larger
greater.Significant should be true

// Now, we would like to test if the sample mean is
// significantly smaller than the hypothesized zero.

// Create a T-Test to check this hypothesis
TTest smaller = new TTest(sample, hypothesizedMean,
       OneSampleHypothesis.ValueIsSmallerThanHypothesis);

// Check if the mean is significantly smaller
smaller.Significant should be false
See Also