TTestTwoSample Class

Two-sample t-test of the null hypothesis that data in the samples are random samples from independent normal distributions with equal means, against the alternative that the means are different.

http://en.wikipedia.org/wiki/Student's_t-test#Independent_two-sample_t-test

Tail	Alternative hypothesis
Tail.Both	Mean of the first distribution is not equal to mean of the second distribution.
Tail.Left	Mean of the first distribution is less than mean of the second distribution.
Tail.Right	Mean of the first distribution is greater than mean of the second distribution.

By defaul means are supposed to be equal.

Note. Welch-Satterthwaite equation is used for approximation of degrees of freedom for unequal variances case.

Inheritance Hierarchy

SystemObject
  FinMath.Statistics.HypothesisTestingHypothesisTest
    FinMath.Statistics.HypothesisTestingTwoSampleTest
      FinMath.Statistics.HypothesisTestingTTestTwoSample

Namespace: FinMath.Statistics.HypothesisTesting
Assembly: FinMath (in FinMath.dll) Version: 2.4.7-0a995bd0ea1854c2c868ec3f8dae606c5777e170

Syntax

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[SerializableAttribute]
public class TTestTwoSample : TwoSampleTest

The TTestTwoSample type exposes the following members.

Constructors

	Name	Description
	TTestTwoSample	Creates TTestTwoSample instance with default significance level for two-tailed test.
	TTestTwoSample(Double)	Creates TTestTwoSample instance for two-tailed test.
	TTestTwoSample(Tail)	Creates TTestTwoSample instance with default significance level.
	TTestTwoSample(Double, Tail)	Creates TTestTwoSample instance.

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Properties

Name

Description

AcceptanceRegionLeft

Region of acceptance left border. We fail to reject null hypothesis if test statistics is between left and right borders of region of acceptance. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Definition_of_terms

(Overrides HypothesisTestAcceptanceRegionLeft.)

AcceptanceRegionRight

Region of acceptance right border. We fail to reject null hypothesis if test statistics is between left and right borders of region of acceptance. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Definition_of_terms

(Overrides HypothesisTestAcceptanceRegionRight.)

Decision

Decision about null hypothesis.

true	if the null hypothesis is failed to be rejected.
false	if the null hypothesis is rejected.

(Inherited from HypothesisTest.)

DecisionPrinciple

Marks whether decision should be made comparing P-value with Significance level or test statistics with critical value.

(Inherited from HypothesisTest.)

PValue

The probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. http://en.wikipedia.org/wiki/P-value

(Overrides HypothesisTestPValue.)

SignificanceLevel

Significance level. http://en.wikipedia.org/wiki/Statistical_significance

(Inherited from HypothesisTest.)

Statistics

Test statistics. http://en.wikipedia.org/wiki/Test_statistic

(Inherited from HypothesisTest.)

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	Update(Double, Double)	Updates test statistic using provided sample. (Inherited from TwoSampleTest.)
	Update(Vector, Vector)	Updates test statistic using provided sample. (Inherited from TwoSampleTest.)
	Update(Double, Double, Boolean)	Updates test statistic using provided samples.
	Update(Vector, Vector, Boolean)	Updates test statistic using provided samples.
	Update(Double, Int32, Int32, Double, Int32, Int32)	Updates test statistic using provided samples. (Overrides TwoSampleTestUpdate(Double, Int32, Int32, Double, Int32, Int32).)

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Reference

FinMath.Statistics.HypothesisTesting Namespace