com.numericalmethod.suanshu.stats.test.mean

Class T

java.lang.Object

com.numericalmethod.suanshu.stats.test.HypothesisTest

com.numericalmethod.suanshu.stats.test.mean.T

All Implemented Interfaces:

java.io.Serializable

public class T
extends HypothesisTest

Student's TDistribution-test tests for the equality of means, for the one-sample case, against a hypothetical mean, and for two-sample case, of two populations.

Welch's t test is an adaptation of Student's t-test intended for use with two samples having possibly unequal variances.

The R equivalent function is t.test.

See Also:

• Richard D. De Veaux, Paul F. Velleman, David E. Bock. "Stats: Data and Models", Chapter 24.
• Student's t-test
• Welch's t test
• Welch–Satterthwaite equation

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	df degree of freedom
double	mean1 mean for sample 1
double	mean2 mean for sample 2
double	pValue1SidedGreater right, one-sided p-value
double	pValue1SidedLess left, one-sided p-value
ProbabilityDistribution	T the associated TDistribution distribution
double	var1 variance for sample 1
double	var2 variance for sample 2

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Constructor Summary

Constructors

Constructor and Description
T(double[] sample, double mu) Construct a one-sample location test of whether the mean of a normally distributed population has a value specified in a null hypothesis.
T(double[] sample1, double[] sample2) Construct Welch's t test, an adaptation of Student's t-test, for the use with two samples having possibly unequal variances.
T(double[] sample1, double[] sample2, boolean isEqualVar, double mu) Construct a two sample location test of the null hypothesis that the means of two normally distributed populations are equal.
T(double[] sample1, double[] sample2, double mu) Construct Welch's t test, an adaptation of Student's t-test, for the use with two samples having possibly unequal variances.

Method Summary

Modifier and Type	Method and Description
double[]	confidenceInterval(double confidence) Compute the confidence interval.
java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
double	leftConfidenceInterval(double confidence) Compute the one sided left confidence interval, [0, a]
double	rightConfidenceInterval(double confidence) Compute the one sided right confidence interval, [a, ∞)

Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, oneSidedPvalue, pValue, statistics

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

df

public final double df

degree of freedom

mean1

public final double mean1

mean for sample 1

var1

public final double var1

variance for sample 1

mean2

public final double mean2

mean for sample 2

var2

public final double var2

variance for sample 2

pValue1SidedLess

public final double pValue1SidedLess

left, one-sided p-value

pValue1SidedGreater

public final double pValue1SidedGreater

right, one-sided p-value

T

public final ProbabilityDistribution T

the associated TDistribution distribution

Constructor Detail

T

public T(double[] sample,
         double mu)

Construct a one-sample location test of whether the mean of a normally distributed population has a value specified in a null hypothesis.

Parameters:

sample - sample

mu - the hypothetical mean in the null hypothesis

T

public T(double[] sample1,
         double[] sample2)

Construct Welch's t test, an adaptation of Student's t-test, for the use with two samples having possibly unequal variances.

Parameters:

sample1 - sample 1

sample2 - sample 2

T

public T(double[] sample1,
         double[] sample2,
         double mu)

Construct Welch's t test, an adaptation of Student's t-test, for the use with two samples having possibly unequal variances.

Parameters:

sample1 - sample 1

sample2 - sample 2

mu - the hypothetical mean-difference in the null hypothesis

T

public T(double[] sample1,
         double[] sample2,
         boolean isEqualVar,
         double mu)

Construct a two sample location test of the null hypothesis that the means of two normally distributed populations are equal.

Parameters:

sample1 - sample 1

sample2 - sample 2

isEqualVar - true if we assume the variances of the two samples are equal; false otherwise

mu - the hypothetical mean-difference in the null hypothesis. Default value is 0.

Method Detail

getNullHypothesis

public java.lang.String getNullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

getNullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public java.lang.String getAlternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

confidenceInterval

public double[] confidenceInterval(double confidence)

Compute the confidence interval.

Parameters:

confidence - the confidence level, e.g., for a 2-sided 95% confidence interval, we use 0.975 because 1 - 0.95 = 2 * (1 - 0.025)

Returns:

the left and right interval values

rightConfidenceInterval

public double rightConfidenceInterval(double confidence)

Compute the one sided right confidence interval, [a, ∞)

Parameters:

confidence - the confidence level, e.g., 0.95 for 95% confidence interval

Returns:

the left interval value

leftConfidenceInterval

public double leftConfidenceInterval(double confidence)

Compute the one sided left confidence interval, [0, a]

Parameters:

confidence - the confidence level, e.g., 0.95 for 95% confidence interval

Returns:

the right interval value