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

java.lang.Object
  com.numericalmethod.suanshu.stats.test.HypothesisTest
      com.numericalmethod.suanshu.stats.test.mean.T

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

Field Summary

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
UnivariateDistribution	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

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

java.lang.String	alternativeHypothesis() Get a description of the alternative hypothesis.
double[]	confidenceInterval(double confidence) Compute the confidence interval.
double	leftConfidenceInterval(double confidence) Compute the one sided left confidence interval, [0, a]
java.lang.String	nullHypothesis() Get a description of the null hypothesis.
double	rightConfidenceInterval(double confidence) Compute the one sided right confidence interval, [a, ∞)

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

oneSidedPvalue, pValue, rejectNull, testStatistics

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 UnivariateDistribution 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

nullHypothesis

public java.lang.String nullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

nullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

alternativeHypothesis

public java.lang.String alternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

alternativeHypothesis 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