# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.test.mean

## Class T

• public class T
extends HypothesisTest
Student's t-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.

• ### 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

All Methods
Modifier and Type Method and Description
double[] confidenceInterval(double confidence)
Get the confidence interval.
double df()
Get the degree of freedom.
String getAlternativeHypothesis()
Get the description of the alternative hypothesis.
String getNullHypothesis()
Get a description of the null hypothesis.
double leftConfidenceInterval(double confidence)
Get the one sided left confidence interval, [0, a]
double leftOneSidedPvalue()
Get the left, one-sided p-value.
double mean1()
Get the mean of the first sample.
double mean2()
Get the mean of the second sample.
double pValue()
Get the p-value for the test statistics.
double rightConfidenceInterval(double confidence)
Get the one sided right confidence interval, [a, ∞)
double rightOneSidedPvalue()
Get the right, one-sided p-value.
double statistics()
Get the test statistics.
• ### Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, nGroups, nObs, oneSidedPvalue
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### 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 - a 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. The default value is 0.
• ### Method Detail

• #### getNullHypothesis

public 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
Wikipedia: Null hypothesis
• #### getAlternativeHypothesis

public String getAlternativeHypothesis()
Description copied from class: HypothesisTest
Get the description of the alternative hypothesis.
Specified by:
getAlternativeHypothesis in class HypothesisTest
Returns:
the alternative hypothesis description
Wikipedia: Alternative hypothesis
• #### statistics

public double statistics()
Description copied from class: HypothesisTest
Get the test statistics.
Specified by:
statistics in class HypothesisTest
Returns:
the test statistics
Wikipedia: Test statistic
• #### pValue

public double pValue()
Description copied from class: HypothesisTest
Get the p-value for the test statistics.
Specified by:
pValue in class HypothesisTest
Returns:
the p-value
Wikipedia: P-value
• #### rightOneSidedPvalue

public double rightOneSidedPvalue()
Get the right, one-sided p-value.
Returns:
the right, one-sided p-value.
• #### leftOneSidedPvalue

public double leftOneSidedPvalue()
Get the left, one-sided p-value.
Returns:
the left, one-sided p-value.
• #### confidenceInterval

public double[] confidenceInterval(double confidence)
Get 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)
Get 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)
Get 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
• #### df

public double df()
Get the degree of freedom.
Returns:
the degree of freedom
• #### mean1

public double mean1()
Get the mean of the first sample.
Returns:
the mean of the first sample
• #### mean2

public double mean2()
Get the mean of the second sample.
Returns:
the mean of the second sample