public class TTest extends Object
Tests can be:
Test statistics are available for all tests. Methods including "Test" in
in their names perform tests, all other methods return t-statistics. Among
the "Test" methods, double-valued methods return p-values;
boolean-valued methods perform fixed significance level tests.
Significance levels are always specified as numbers between 0 and 0.5
(e.g. tests at the 95% level use alpha=0.05).
Input to tests can be either double[] arrays or
StatisticalSummary instances.
Uses commons-math TDistribution
implementation to estimate exact p-values.
| Constructor and Description |
|---|
TTest() |
| Modifier and Type | Method and Description |
|---|---|
protected double |
df(double v1,
double v2,
double n1,
double n2)
Computes approximate degrees of freedom for 2-sample t-test.
|
double |
homoscedasticT(double[] sample1,
double[] sample2)
Computes a 2-sample t statistic, under the hypothesis of equal
subpopulation variances.
|
protected double |
homoscedasticT(double m1,
double m2,
double v1,
double v2,
double n1,
double n2)
Computes t test statistic for 2-sample t-test under the hypothesis
of equal subpopulation variances.
|
double |
homoscedasticT(StatisticalSummary sampleStats1,
StatisticalSummary sampleStats2)
Computes a 2-sample t statistic, comparing the means of the datasets
described by two
StatisticalSummary instances, under the
assumption of equal subpopulation variances. |
double |
homoscedasticTTest(double[] sample1,
double[] sample2)
Returns the observed significance level, or
p-value, associated with a two-sample, two-tailed t-test
comparing the means of the input arrays, under the assumption that
the two samples are drawn from subpopulations with equal variances.
|
boolean |
homoscedasticTTest(double[] sample1,
double[] sample2,
double alpha)
Performs a
two-sided t-test evaluating the null hypothesis that
sample1
and sample2 are drawn from populations with the same mean,
with significance level alpha, assuming that the
subpopulation variances are equal. |
protected double |
homoscedasticTTest(double m1,
double m2,
double v1,
double v2,
double n1,
double n2)
Computes p-value for 2-sided, 2-sample t-test, under the assumption
of equal subpopulation variances.
|
double |
homoscedasticTTest(StatisticalSummary sampleStats1,
StatisticalSummary sampleStats2)
Returns the observed significance level, or
p-value, associated with a two-sample, two-tailed t-test
comparing the means of the datasets described by two StatisticalSummary
instances, under the hypothesis of equal subpopulation variances.
|
double |
pairedT(double[] sample1,
double[] sample2)
Computes a paired, 2-sample t-statistic based on the data in the input
arrays.
|
double |
pairedTTest(double[] sample1,
double[] sample2)
Returns the observed significance level, or
p-value, associated with a paired, two-sample, two-tailed t-test
based on the data in the input arrays.
|
boolean |
pairedTTest(double[] sample1,
double[] sample2,
double alpha)
Performs a paired t-test evaluating the null hypothesis that the
mean of the paired differences between
sample1 and
sample2 is 0 in favor of the two-sided alternative that the
mean paired difference is not equal to 0, with significance level
alpha. |
double |
t(double[] sample1,
double[] sample2)
Computes a 2-sample t statistic, without the hypothesis of equal
subpopulation variances.
|
double |
t(double mu,
double[] observed)
Computes a
t statistic given observed values and a comparison constant.
|
protected double |
t(double m,
double mu,
double v,
double n)
Computes t test statistic for 1-sample t-test.
|
protected double |
t(double m1,
double m2,
double v1,
double v2,
double n1,
double n2)
Computes t test statistic for 2-sample t-test.
|
double |
t(double mu,
StatisticalSummary sampleStats)
|
double |
t(StatisticalSummary sampleStats1,
StatisticalSummary sampleStats2)
Computes a 2-sample t statistic , comparing the means of the datasets
described by two
StatisticalSummary instances, without the
assumption of equal subpopulation variances. |
double |
tTest(double[] sample1,
double[] sample2)
Returns the observed significance level, or
p-value, associated with a two-sample, two-tailed t-test
comparing the means of the input arrays.
|
boolean |
tTest(double[] sample1,
double[] sample2,
double alpha)
Performs a
two-sided t-test evaluating the null hypothesis that
sample1
and sample2 are drawn from populations with the same mean,
with significance level alpha. |
double |
tTest(double mu,
double[] sample)
Returns the observed significance level, or
p-value, associated with a one-sample, two-tailed t-test
comparing the mean of the input array with the constant
mu. |
boolean |
tTest(double mu,
double[] sample,
double alpha)
Performs a
two-sided t-test evaluating the null hypothesis that the mean of the population from
which
sample is drawn equals mu. |
protected double |
tTest(double m,
double mu,
double v,
double n)
Computes p-value for 2-sided, 1-sample t-test.
|
protected double |
tTest(double m1,
double m2,
double v1,
double v2,
double n1,
double n2)
Computes p-value for 2-sided, 2-sample t-test.
|
double |
tTest(double mu,
StatisticalSummary sampleStats)
Returns the observed significance level, or
p-value, associated with a one-sample, two-tailed t-test
comparing the mean of the dataset described by
sampleStats
with the constant mu. |
boolean |
tTest(double mu,
StatisticalSummary sampleStats,
double alpha)
Performs a
two-sided t-test evaluating the null hypothesis that the mean of the
population from which the dataset described by
stats is
drawn equals mu. |
double |
tTest(StatisticalSummary sampleStats1,
StatisticalSummary sampleStats2)
Returns the observed significance level, or
p-value, associated with a two-sample, two-tailed t-test
comparing the means of the datasets described by two StatisticalSummary
instances.
|
boolean |
tTest(StatisticalSummary sampleStats1,
StatisticalSummary sampleStats2,
double alpha)
Performs a
two-sided t-test evaluating the null hypothesis that
sampleStats1 and sampleStats2 describe
datasets drawn from populations with the same mean, with significance
level alpha. |
public TTest()
public double pairedT(double[] sample1, double[] sample2) throws NullArgumentException, NoDataException, DimensionMismatchException, NumberIsTooSmallException
t(double, double[]), with
mu = 0 and the sample array consisting of the (signed)
differences between corresponding entries in sample1 and
sample2.
Preconditions:
sample1 - array of sample data valuessample2 - array of sample data valuesNullArgumentException - if the arrays are nullNoDataException - if the arrays are emptyDimensionMismatchException - if the length of the arrays is not equalNumberIsTooSmallException - if the length of the arrays is < 2public double pairedTTest(double[] sample1, double[] sample2) throws NullArgumentException, NoDataException, DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException
The number returned is the smallest significance level at which one can reject the null hypothesis that the mean of the paired differences is 0 in favor of the two-sided alternative that the mean paired difference is not equal to 0. For a one-sided test, divide the returned value by 2.
This test is equivalent to a one-sample t-test computed using
tTest(double, double[]) with mu = 0 and the sample
array consisting of the signed differences between corresponding elements of
sample1 and sample2.
Usage Note:
The validity of the p-value depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
sample1 - array of sample data valuessample2 - array of sample data valuesNullArgumentException - if the arrays are nullNoDataException - if the arrays are emptyDimensionMismatchException - if the length of the arrays is not equalNumberIsTooSmallException - if the length of the arrays is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic boolean pairedTTest(double[] sample1, double[] sample2, double alpha) throws NullArgumentException, NoDataException, DimensionMismatchException, NumberIsTooSmallException, OutOfRangeException, MaxCountExceededException
sample1 and
sample2 is 0 in favor of the two-sided alternative that the
mean paired difference is not equal to 0, with significance level
alpha.
Returns true iff the null hypothesis can be rejected with
confidence 1 - alpha. To perform a 1-sided test, use
alpha * 2
Usage Note:
The validity of the test depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
0 < alpha < 0.5
sample1 - array of sample data valuessample2 - array of sample data valuesalpha - significance level of the testNullArgumentException - if the arrays are nullNoDataException - if the arrays are emptyDimensionMismatchException - if the length of the arrays is not equalNumberIsTooSmallException - if the length of the arrays is < 2OutOfRangeException - if alpha is not in the range (0, 0.5]MaxCountExceededException - if an error occurs computing the p-valuepublic double t(double mu, double[] observed) throws NullArgumentException, NumberIsTooSmallException
This statistic can be used to perform a one sample t-test for the mean.
Preconditions:
mu - comparison constantobserved - array of valuesNullArgumentException - if observed is nullNumberIsTooSmallException - if the length of observed is < 2public double t(double mu, StatisticalSummary sampleStats) throws NullArgumentException, NumberIsTooSmallException
sampleStats to mu.
This statistic can be used to perform a one sample t-test for the mean.
Preconditions:
observed.getN() ≥ 2.
mu - comparison constantsampleStats - DescriptiveStatistics holding sample summary statitsticsNullArgumentException - if sampleStats is nullNumberIsTooSmallException - if the number of samples is < 2public double homoscedasticT(double[] sample1, double[] sample2) throws NullArgumentException, NumberIsTooSmallException
t(double[], double[]).
This statistic can be used to perform a (homoscedastic) two-sample t-test to compare sample means.
The t-statistic is
t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))
where n1 is the size of first sample;
n2 is the size of second sample;
m1 is the mean of first sample;
m2 is the mean of second sample
and var is the pooled variance estimate:
var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))
with var1 the variance of the first sample and
var2 the variance of the second sample.
Preconditions:
sample1 - array of sample data valuessample2 - array of sample data valuesNullArgumentException - if the arrays are nullNumberIsTooSmallException - if the length of the arrays is < 2public double t(double[] sample1, double[] sample2) throws NullArgumentException, NumberIsTooSmallException
homoscedasticT(double[], double[]).
This statistic can be used to perform a two-sample t-test to compare sample means.
The t-statistic is
t = (m1 - m2) / sqrt(var1/n1 + var2/n2)
where n1 is the size of the first sample
n2 is the size of the second sample;
m1 is the mean of the first sample;
m2 is the mean of the second sample;
var1 is the variance of the first sample;
var2 is the variance of the second sample;
Preconditions:
sample1 - array of sample data valuessample2 - array of sample data valuesNullArgumentException - if the arrays are nullNumberIsTooSmallException - if the length of the arrays is < 2public double t(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws NullArgumentException, NumberIsTooSmallException
StatisticalSummary instances, without the
assumption of equal subpopulation variances. Use
homoscedasticT(StatisticalSummary, StatisticalSummary) to
compute a t-statistic under the equal variances assumption.
This statistic can be used to perform a two-sample t-test to compare sample means.
The returned t-statistic is
t = (m1 - m2) / sqrt(var1/n1 + var2/n2)
where n1 is the size of the first sample;
n2 is the size of the second sample;
m1 is the mean of the first sample;
m2 is the mean of the second sample
var1 is the variance of the first sample;
var2 is the variance of the second sample
Preconditions:
sampleStats1 - StatisticalSummary describing data from the first samplesampleStats2 - StatisticalSummary describing data from the second sampleNullArgumentException - if the sample statistics are nullNumberIsTooSmallException - if the number of samples is < 2public double homoscedasticT(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws NullArgumentException, NumberIsTooSmallException
StatisticalSummary instances, under the
assumption of equal subpopulation variances. To compute a t-statistic
without the equal variances assumption, use
t(StatisticalSummary, StatisticalSummary).
This statistic can be used to perform a (homoscedastic) two-sample t-test to compare sample means.
The t-statistic returned is
t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))
where n1 is the size of first sample;
n2 is the size of second sample;
m1 is the mean of first sample;
m2 is the mean of second sample
and var is the pooled variance estimate:
var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))
with var1 the variance of the first sample and
var2 the variance of the second sample.
Preconditions:
sampleStats1 - StatisticalSummary describing data from the first samplesampleStats2 - StatisticalSummary describing data from the second sampleNullArgumentException - if the sample statistics are nullNumberIsTooSmallException - if the number of samples is < 2public double tTest(double mu, double[] sample) throws NullArgumentException, NumberIsTooSmallException, MaxCountExceededException
mu.
The number returned is the smallest significance level
at which one can reject the null hypothesis that the mean equals
mu in favor of the two-sided alternative that the mean
is different from mu. For a one-sided test, divide the
returned value by 2.
Usage Note:
The validity of the test depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
mu - constant value to compare sample mean againstsample - array of sample data valuesNullArgumentException - if the sample array is nullNumberIsTooSmallException - if the length of the array is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic boolean tTest(double mu, double[] sample, double alpha) throws NullArgumentException, NumberIsTooSmallException, OutOfRangeException, MaxCountExceededException
sample is drawn equals mu.
Returns true iff the null hypothesis can be
rejected with confidence 1 - alpha. To
perform a 1-sided test, use alpha * 2
Examples:
sample mean = mu at
the 95% level, use tTest(mu, sample, 0.05)
sample mean < mu
at the 99% level, first verify that the measured sample mean is less
than mu and then use
tTest(mu, sample, 0.02)
Usage Note:
The validity of the test depends on the assumptions of the one-sample
parametric t-test procedure, as discussed
here
Preconditions:
mu - constant value to compare sample mean againstsample - array of sample data valuesalpha - significance level of the testNullArgumentException - if the sample array is nullNumberIsTooSmallException - if the length of the array is < 2OutOfRangeException - if alpha is not in the range (0, 0.5]MaxCountExceededException - if an error computing the p-valuepublic double tTest(double mu, StatisticalSummary sampleStats) throws NullArgumentException, NumberIsTooSmallException, MaxCountExceededException
sampleStats
with the constant mu.
The number returned is the smallest significance level
at which one can reject the null hypothesis that the mean equals
mu in favor of the two-sided alternative that the mean
is different from mu. For a one-sided test, divide the
returned value by 2.
Usage Note:
The validity of the test depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
mu - constant value to compare sample mean againstsampleStats - StatisticalSummary describing sample dataNullArgumentException - if sampleStats is nullNumberIsTooSmallException - if the number of samples is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic boolean tTest(double mu, StatisticalSummary sampleStats, double alpha) throws NullArgumentException, NumberIsTooSmallException, OutOfRangeException, MaxCountExceededException
stats is
drawn equals mu.
Returns true iff the null hypothesis can be rejected with
confidence 1 - alpha. To perform a 1-sided test, use
alpha * 2.
Examples:
sample mean = mu at
the 95% level, use tTest(mu, sampleStats, 0.05)
sample mean < mu
at the 99% level, first verify that the measured sample mean is less
than mu and then use
tTest(mu, sampleStats, 0.02)
Usage Note:
The validity of the test depends on the assumptions of the one-sample
parametric t-test procedure, as discussed
here
Preconditions:
mu - constant value to compare sample mean againstsampleStats - StatisticalSummary describing sample data valuesalpha - significance level of the testNullArgumentException - if sampleStats is nullNumberIsTooSmallException - if the number of samples is < 2OutOfRangeException - if alpha is not in the range (0, 0.5]MaxCountExceededException - if an error occurs computing the p-valuepublic double tTest(double[] sample1, double[] sample2) throws NullArgumentException, NumberIsTooSmallException, MaxCountExceededException
The number returned is the smallest significance level at which one can reject the null hypothesis that the two means are equal in favor of the two-sided alternative that they are different. For a one-sided test, divide the returned value by 2.
The test does not assume that the underlying popuation variances are
equal and it uses approximated degrees of freedom computed from the
sample data to compute the p-value. The t-statistic used is as defined in
t(double[], double[]) and the Welch-Satterthwaite approximation
to the degrees of freedom is used,
as described
here. To perform the test under the assumption of equal subpopulation
variances, use homoscedasticTTest(double[], double[]).
Usage Note:
The validity of the p-value depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
sample1 - array of sample data valuessample2 - array of sample data valuesNullArgumentException - if the arrays are nullNumberIsTooSmallException - if the length of the arrays is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic double homoscedasticTTest(double[] sample1, double[] sample2) throws NullArgumentException, NumberIsTooSmallException, MaxCountExceededException
tTest(double[], double[]).
The number returned is the smallest significance level at which one can reject the null hypothesis that the two means are equal in favor of the two-sided alternative that they are different. For a one-sided test, divide the returned value by 2.
A pooled variance estimate is used to compute the t-statistic. See
homoscedasticT(double[], double[]). The sum of the sample sizes
minus 2 is used as the degrees of freedom.
Usage Note:
The validity of the p-value depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
sample1 - array of sample data valuessample2 - array of sample data valuesNullArgumentException - if the arrays are nullNumberIsTooSmallException - if the length of the arrays is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic boolean tTest(double[] sample1, double[] sample2, double alpha) throws NullArgumentException, NumberIsTooSmallException, OutOfRangeException, MaxCountExceededException
sample1
and sample2 are drawn from populations with the same mean,
with significance level alpha. This test does not assume
that the subpopulation variances are equal. To perform the test assuming
equal variances, use
homoscedasticTTest(double[], double[], double).
Returns true iff the null hypothesis that the means are
equal can be rejected with confidence 1 - alpha. To
perform a 1-sided test, use alpha * 2
See t(double[], double[]) for the formula used to compute the
t-statistic. Degrees of freedom are approximated using the
Welch-Satterthwaite approximation.
Examples:
mean 1 = mean 2 at
the 95% level, use
tTest(sample1, sample2, 0.05).
mean 1 < mean 2 ,
at the 99% level, first verify that the measured mean of sample 1
is less than the mean of sample 2 and then use
tTest(sample1, sample2, 0.02)
Usage Note:
The validity of the test depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
0 < alpha < 0.5
sample1 - array of sample data valuessample2 - array of sample data valuesalpha - significance level of the testNullArgumentException - if the arrays are nullNumberIsTooSmallException - if the length of the arrays is < 2OutOfRangeException - if alpha is not in the range (0, 0.5]MaxCountExceededException - if an error occurs computing the p-valuepublic boolean homoscedasticTTest(double[] sample1, double[] sample2, double alpha) throws NullArgumentException, NumberIsTooSmallException, OutOfRangeException, MaxCountExceededException
sample1
and sample2 are drawn from populations with the same mean,
with significance level alpha, assuming that the
subpopulation variances are equal. Use
tTest(double[], double[], double) to perform the test without
the assumption of equal variances.
Returns true iff the null hypothesis that the means are
equal can be rejected with confidence 1 - alpha. To
perform a 1-sided test, use alpha * 2. To perform the test
without the assumption of equal subpopulation variances, use
tTest(double[], double[], double).
A pooled variance estimate is used to compute the t-statistic. See
t(double[], double[]) for the formula. The sum of the sample
sizes minus 2 is used as the degrees of freedom.
Examples:
mean 1 = mean 2 at
the 95% level, use tTest(sample1, sample2, 0.05).
mean 1 < mean 2,
at the 99% level, first verify that the measured mean of
sample 1 is less than the mean of sample 2
and then use
tTest(sample1, sample2, 0.02)
Usage Note:
The validity of the test depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
0 < alpha < 0.5
sample1 - array of sample data valuessample2 - array of sample data valuesalpha - significance level of the testNullArgumentException - if the arrays are nullNumberIsTooSmallException - if the length of the arrays is < 2OutOfRangeException - if alpha is not in the range (0, 0.5]MaxCountExceededException - if an error occurs computing the p-valuepublic double tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws NullArgumentException, NumberIsTooSmallException, MaxCountExceededException
The number returned is the smallest significance level at which one can reject the null hypothesis that the two means are equal in favor of the two-sided alternative that they are different. For a one-sided test, divide the returned value by 2.
The test does not assume that the underlying population variances are
equal and it uses approximated degrees of freedom computed from the
sample data to compute the p-value. To perform the test assuming
equal variances, use
homoscedasticTTest(StatisticalSummary, StatisticalSummary).
Usage Note:
The validity of the p-value depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
sampleStats1 - StatisticalSummary describing data from the first samplesampleStats2 - StatisticalSummary describing data from the second sampleNullArgumentException - if the sample statistics are nullNumberIsTooSmallException - if the number of samples is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic double homoscedasticTTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws NullArgumentException, NumberIsTooSmallException, MaxCountExceededException
tTest(StatisticalSummary, StatisticalSummary).
The number returned is the smallest significance level at which one can reject the null hypothesis that the two means are equal in favor of the two-sided alternative that they are different. For a one-sided test, divide the returned value by 2.
See homoscedasticT(double[], double[]) for the formula used to
compute the t-statistic. The sum of the sample sizes minus 2 is used as
the degrees of freedom.
Usage Note:
The validity of the p-value depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
sampleStats1 - StatisticalSummary describing data from the first samplesampleStats2 - StatisticalSummary describing data from the second sampleNullArgumentException - if the sample statistics are nullNumberIsTooSmallException - if the number of samples is < 2MaxCountExceededException - if an error occurs computing the p-valuepublic boolean tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2, double alpha) throws NullArgumentException, NumberIsTooSmallException, OutOfRangeException, MaxCountExceededException
sampleStats1 and sampleStats2 describe
datasets drawn from populations with the same mean, with significance
level alpha. This test does not assume that the
subpopulation variances are equal. To perform the test under the equal
variances assumption, use
homoscedasticTTest(StatisticalSummary, StatisticalSummary).
Returns true iff the null hypothesis that the means are
equal can be rejected with confidence 1 - alpha. To
perform a 1-sided test, use alpha * 2
See t(double[], double[]) for the formula used to compute the
t-statistic. Degrees of freedom are approximated using the
Welch-Satterthwaite approximation.
Examples:
mean 1 = mean 2 at
the 95%, use
tTest(sampleStats1, sampleStats2, 0.05)
mean 1 < mean 2
at the 99% level, first verify that the measured mean of
sample 1 is less than the mean of sample 2
and then use
tTest(sampleStats1, sampleStats2, 0.02)
Usage Note:
The validity of the test depends on the assumptions of the parametric
t-test procedure, as discussed
here
Preconditions:
0 < alpha < 0.5
sampleStats1 - StatisticalSummary describing sample data valuessampleStats2 - StatisticalSummary describing sample data valuesalpha - significance level of the testNullArgumentException - if the sample statistics are nullNumberIsTooSmallException - if the number of samples is < 2OutOfRangeException - if alpha is not in the range (0, 0.5]MaxCountExceededException - if an error occurs computing the p-valueprotected double df(double v1, double v2, double n1, double n2)
v1 - first sample variancev2 - second sample variancen1 - first sample nn2 - second sample nprotected double t(double m, double mu, double v, double n)
m - sample meanmu - constant to test againstv - sample variancen - sample nprotected double t(double m1, double m2, double v1, double v2, double n1, double n2)
Does not assume that subpopulation variances are equal.
m1 - first sample meanm2 - second sample meanv1 - first sample variancev2 - second sample variancen1 - first sample nn2 - second sample nprotected double homoscedasticT(double m1, double m2, double v1, double v2, double n1, double n2)
m1 - first sample meanm2 - second sample meanv1 - first sample variancev2 - second sample variancen1 - first sample nn2 - second sample nprotected double tTest(double m, double mu, double v, double n) throws MaxCountExceededException, MathIllegalArgumentException
m - sample meanmu - constant to test againstv - sample variancen - sample nMaxCountExceededException - if an error occurs computing the p-valueMathIllegalArgumentException - if n is not greater than 1protected double tTest(double m1, double m2, double v1, double v2, double n1, double n2) throws MaxCountExceededException, NotStrictlyPositiveException
Does not assume subpopulation variances are equal. Degrees of freedom are estimated from the data.
m1 - first sample meanm2 - second sample meanv1 - first sample variancev2 - second sample variancen1 - first sample nn2 - second sample nMaxCountExceededException - if an error occurs computing the p-valueNotStrictlyPositiveException - if the estimated degrees of freedom is not
strictly positiveprotected double homoscedasticTTest(double m1, double m2, double v1, double v2, double n1, double n2) throws MaxCountExceededException, NotStrictlyPositiveException
The sum of the sample sizes minus 2 is used as degrees of freedom.
m1 - first sample meanm2 - second sample meanv1 - first sample variancev2 - second sample variancen1 - first sample nn2 - second sample nMaxCountExceededException - if an error occurs computing the p-valueNotStrictlyPositiveException - if the estimated degrees of freedom is not
strictly positiveCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.