| java.lang.Object
 org.apache.commons.math.stat.inference.TTestImpl
| Constructor Summary | |
| public | TTestImpl()
Default constructor. |
| Method Summary | |
| protected double | df(double v1, double v2, double n1, double n2)
Computes approximate degrees of freedom for 2-sample t-test. | | protected DistributionFactory | getDistributionFactory()
Gets a DistributionFactory to use in creating TDistribution instances. | | public double | homoscedasticT(double[] sample1, double[] sample2)
Computes a 2-sample t statistic, under the hypothesis of equal
subpopulation variances. | | public 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. | | 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. | | public 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.
To perform the test without the equal variances assumption, use
TTestImpl.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. | | public 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. | | public 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. | | 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. | | public double | pairedT(double[] sample1, double[] sample2)
Computes a paired, 2-sample t-statistic based on the data in the input
arrays. | | public 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.
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. | | public 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.
Returns true iff the null hypothesis can be rejected with
confidence 1 - alpha. | | public double | t(double mu, double[] observed)
Computes a
t statistic given observed values and a comparison constant. | | public double | t(double mu, StatisticalSummary sampleStats)
Computes a
t statistic to use in comparing the mean of the dataset described by
sampleStats to mu. | | public double | t(double[] sample1, double[] sample2)
Computes a 2-sample t statistic, without the hypothesis of equal
subpopulation variances. | | public 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. | | 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. | | public 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.
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. | | public 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.
Returns true iff the null hypothesis can be
rejected with confidence 1 - alpha. | | public 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.
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. | | public 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.
Returns true iff the null hypothesis can be rejected with
confidence 1 - alpha. | | public 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.
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. | | public 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. | | public 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.
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. | | public 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. | | 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.
Does not assume subpopulation variances are equal. |
| TTestImpl | | public TTestImpl()(Code) | | Default constructor.
|
| df | | protected double df(double v1, double v2, double n1, double n2)(Code) | | Computes approximate degrees of freedom for 2-sample t-test.
Parameters:
v1 - first sample variance
Parameters:
v2 - second sample variance
Parameters:
n1 - first sample n
Parameters:
n2 - second sample n approximate degrees of freedom |
| getDistributionFactory | | protected DistributionFactory getDistributionFactory()(Code) | | Gets a DistributionFactory to use in creating TDistribution instances.
a distribution factory. |
| homoscedasticT | | public double homoscedasticT(double[] sample1, double[] sample2) throws IllegalArgumentException(Code) | | Computes a 2-sample t statistic, under the hypothesis of equal
subpopulation variances. To compute a t-statistic without the
equal variances hypothesis, use
TTestImpl.t(double[],double[]) .
This statistic can be used to perform a (homoscedastic) two-sample
t-test to compare sample means.
The t-statisitc 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:
- The observed array lengths must both be at least 2.
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values t statistic
throws:
IllegalArgumentException - if the precondition is not met |
| homoscedasticT | | public double homoscedasticT(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException(Code) | | Computes a 2-sample t statistic, comparing the means of the datasets
described by two
StatisticalSummary instances, under the
assumption of equal subpopulation variances. To compute a t-statistic
without the equal variances assumption, use
TTestImpl.t(StatisticalSummary,StatisticalSummary) .
This statistic can be used to perform a (homoscedastic) two-sample
t-test to compare sample means.
The t-statisitc 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:
- The datasets described by the two Univariates must each contain
at least 2 observations.
Parameters:
sampleStats1 - StatisticalSummary describing data from the first sample
Parameters:
sampleStats2 - StatisticalSummary describing data from the second sample t statistic
throws:
IllegalArgumentException - if the precondition is not met |
| homoscedasticT | | protected double homoscedasticT(double m1, double m2, double v1, double v2, double n1, double n2)(Code) | | Computes t test statistic for 2-sample t-test under the hypothesis
of equal subpopulation variances.
Parameters:
m1 - first sample mean
Parameters:
m2 - second sample mean
Parameters:
v1 - first sample variance
Parameters:
v2 - second sample variance
Parameters:
n1 - first sample n
Parameters:
n2 - second sample n t test statistic |
| homoscedasticTTest | | public double homoscedasticTTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException(Code) | | 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.
To perform the test without the equal variances assumption, use
TTestImpl.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
TTestImpl.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:
- The observed array lengths must both be at least 2.
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values p-value for t-test
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| homoscedasticTTest | | public boolean homoscedasticTTest(double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException(Code) | | 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. Use
TTestImpl.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
TTestImpl.tTest(double[],double[],double) .
A pooled variance estimate is used to compute the t-statistic. See
TTestImpl.t(double[],double[]) for the formula. The sum of the sample
sizes minus 2 is used as the degrees of freedom.
Examples:
- To test the (2-sided) hypothesis
mean 1 = mean 2 at
the 95% level, use
tTest(sample1, sample2, 0.05).
- To test the (one-sided) hypothesis
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:
- The observed array lengths must both be at least 2.
-
0 < alpha < 0.5
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values
Parameters:
alpha - significance level of the test true if the null hypothesis can be rejected with confidence 1 - alpha
throws:
IllegalArgumentException - if the preconditions are not met
throws:
MathException - if an error occurs performing the test |
| homoscedasticTTest | | public double homoscedasticTTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException, MathException(Code) | | 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. To
perform a test without the equal variances assumption, use
TTestImpl.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
TTestImpl.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:
- The datasets described by the two Univariates must each contain
at least 2 observations.
Parameters:
sampleStats1 - StatisticalSummary describing data from the first sample
Parameters:
sampleStats2 - StatisticalSummary describing data from the second sample p-value for t-test
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| homoscedasticTTest | | protected double homoscedasticTTest(double m1, double m2, double v1, double v2, double n1, double n2) throws MathException(Code) | | Computes p-value for 2-sided, 2-sample t-test, under the assumption
of equal subpopulation variances.
The sum of the sample sizes minus 2 is used as degrees of freedom.
Parameters:
m1 - first sample mean
Parameters:
m2 - second sample mean
Parameters:
v1 - first sample variance
Parameters:
v2 - second sample variance
Parameters:
n1 - first sample n
Parameters:
n2 - second sample n p-value
throws:
MathException - if an error occurs computing the p-value |
| pairedT | | public double pairedT(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException(Code) | | Computes a paired, 2-sample t-statistic based on the data in the input
arrays. The t-statistic returned is equivalent to what would be returned by
computing the one-sample t-statistic
TTestImpl.t(double,double[]) , with
mu = 0 and the sample array consisting of the (signed)
differences between corresponding entries in sample1 and
sample2.
Preconditions:
- The input arrays must have the same length and their common length
must be at least 2.
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values t statistic
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if the statistic can not be computed do to aconvergence or other numerical error. |
| pairedTTest | | public double pairedTTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException(Code) | | 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.
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
TTestImpl.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:
- The input array lengths must be the same and their common length must
be at least 2.
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values p-value for t-test
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| pairedTTest | | public boolean pairedTTest(double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException(Code) | | 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.
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:
- The input array lengths must be the same and their common length
must be at least 2.
-
0 < alpha < 0.5
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values
Parameters:
alpha - significance level of the test true if the null hypothesis can be rejected with confidence 1 - alpha
throws:
IllegalArgumentException - if the preconditions are not met
throws:
MathException - if an error occurs performing the test |
| t | | public double t(double mu, double[] observed) throws IllegalArgumentException(Code) | | Computes a
t statistic given observed values and a comparison constant.
This statistic can be used to perform a one sample t-test for the mean.
Preconditions:
- The observed array length must be at least 2.
Parameters:
mu - comparison constant
Parameters:
observed - array of values t statistic
throws:
IllegalArgumentException - if input array length is less than 2 |
| t | | public double t(double mu, StatisticalSummary sampleStats) throws IllegalArgumentException(Code) | | Computes a
t statistic to use in comparing the mean of the dataset described by
sampleStats to mu.
This statistic can be used to perform a one sample t-test for the mean.
Preconditions:
Parameters:
mu - comparison constant
Parameters:
sampleStats - DescriptiveStatistics holding sample summary statitstics t statistic
throws:
IllegalArgumentException - if the precondition is not met |
| t | | public double t(double[] sample1, double[] sample2) throws IllegalArgumentException(Code) | | Computes a 2-sample t statistic, without the hypothesis of equal
subpopulation variances. To compute a t-statistic assuming equal
variances, use
TTestImpl.homoscedasticT(double[],double[]) .
This statistic can be used to perform a two-sample t-test to compare
sample means.
The t-statisitc 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:
- The observed array lengths must both be at least 2.
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values t statistic
throws:
IllegalArgumentException - if the precondition is not met |
| t | | public double t(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException(Code) | | Computes a 2-sample t statistic , comparing the means of the datasets
described by two
StatisticalSummary instances, without the
assumption of equal subpopulation variances. Use
TTestImpl.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-statisitc 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:
- The datasets described by the two Univariates must each contain
at least 2 observations.
Parameters:
sampleStats1 - StatisticalSummary describing data from the first sample
Parameters:
sampleStats2 - StatisticalSummary describing data from the second sample t statistic
throws:
IllegalArgumentException - if the precondition is not met |
| t | | protected double t(double m, double mu, double v, double n)(Code) | | Computes t test statistic for 1-sample t-test.
Parameters:
m - sample mean
Parameters:
mu - constant to test against
Parameters:
v - sample variance
Parameters:
n - sample n t test statistic |
| t | | protected double t(double m1, double m2, double v1, double v2, double n1, double n2)(Code) | | Computes t test statistic for 2-sample t-test.
Does not assume that subpopulation variances are equal.
Parameters:
m1 - first sample mean
Parameters:
m2 - second sample mean
Parameters:
v1 - first sample variance
Parameters:
v2 - second sample variance
Parameters:
n1 - first sample n
Parameters:
n2 - second sample n t test statistic |
| tTest | | public double tTest(double mu, double[] sample) throws IllegalArgumentException, MathException(Code) | | 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.
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:
- The observed array length must be at least 2.
Parameters:
mu - constant value to compare sample mean against
Parameters:
sample - array of sample data values p-value
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| tTest | | public boolean tTest(double mu, double[] sample, double alpha) throws IllegalArgumentException, MathException(Code) | | Performs a
two-sided t-test evaluating the null hypothesis that the mean of the population from
which 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:
- To test the (2-sided) hypothesis
sample mean = mu at
the 95% level, use
tTest(mu, sample, 0.05)
- To test the (one-sided) hypothesis
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:
- The observed array length must be at least 2.
Parameters:
mu - constant value to compare sample mean against
Parameters:
sample - array of sample data values
Parameters:
alpha - significance level of the test p-value
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error computing the p-value |
| tTest | | public double tTest(double mu, StatisticalSummary sampleStats) throws IllegalArgumentException, MathException(Code) | | 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.
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:
- The sample must contain at least 2 observations.
Parameters:
mu - constant value to compare sample mean against
Parameters:
sampleStats - StatisticalSummary describing sample data p-value
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| tTest | | public boolean tTest(double mu, StatisticalSummary sampleStats, double alpha) throws IllegalArgumentException, MathException(Code) | | 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.
Returns true iff the null hypothesis can be rejected with
confidence 1 - alpha. To perform a 1-sided test, use
alpha * 2.
Examples:
- To test the (2-sided) hypothesis
sample mean = mu at
the 95% level, use
tTest(mu, sampleStats, 0.05)
- To test the (one-sided) hypothesis
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:
- The sample must include at least 2 observations.
Parameters:
mu - constant value to compare sample mean against
Parameters:
sampleStats - StatisticalSummary describing sample data values
Parameters:
alpha - significance level of the test p-value
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| tTest | | public double tTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException(Code) | | Returns the observed significance level, or
p-value, associated with a two-sample, two-tailed t-test
comparing the means of the input arrays.
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
TTestImpl.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
TTestImpl.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:
- The observed array lengths must both be at least 2.
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values p-value for t-test
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| tTest | | public boolean tTest(double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException(Code) | | 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. This test does not assume
that the subpopulation variances are equal. To perform the test assuming
equal variances, use
TTestImpl.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
TTestImpl.t(double[],double[]) for the formula used to compute the
t-statistic. Degrees of freedom are approximated using the
Welch-Satterthwaite approximation.
Examples:
- To test the (2-sided) hypothesis
mean 1 = mean 2 at
the 95% level, use
tTest(sample1, sample2, 0.05).
- To test the (one-sided) hypothesis
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:
- The observed array lengths must both be at least 2.
-
0 < alpha < 0.5
Parameters:
sample1 - array of sample data values
Parameters:
sample2 - array of sample data values
Parameters:
alpha - significance level of the test true if the null hypothesis can be rejected with confidence 1 - alpha
throws:
IllegalArgumentException - if the preconditions are not met
throws:
MathException - if an error occurs performing the test |
| tTest | | public double tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException, MathException(Code) | | 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.
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. To perform the test assuming
equal variances, use
TTestImpl.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:
- The datasets described by the two Univariates must each contain
at least 2 observations.
Parameters:
sampleStats1 - StatisticalSummary describing data from the first sample
Parameters:
sampleStats2 - StatisticalSummary describing data from the second sample p-value for t-test
throws:
IllegalArgumentException - if the precondition is not met
throws:
MathException - if an error occurs computing the p-value |
| tTest | | public boolean tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2, double alpha) throws IllegalArgumentException, MathException(Code) | | 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. This test does not assume that the
subpopulation variances are equal. To perform the test under the equal
variances assumption, use
TTestImpl.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
TTestImpl.t(double[],double[]) for the formula used to compute the
t-statistic. Degrees of freedom are approximated using the
Welch-Satterthwaite approximation.
Examples:
- To test the (2-sided) hypothesis
mean 1 = mean 2 at
the 95%, use
tTest(sampleStats1, sampleStats2, 0.05)
- To test the (one-sided) hypothesis
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:
- The datasets described by the two Univariates must each contain
at least 2 observations.
-
0 < alpha < 0.5
Parameters:
sampleStats1 - StatisticalSummary describing sample data values
Parameters:
sampleStats2 - StatisticalSummary describing sample data values
Parameters:
alpha - significance level of the test true if the null hypothesis can be rejected with confidence 1 - alpha
throws:
IllegalArgumentException - if the preconditions are not met
throws:
MathException - if an error occurs performing the test |
| tTest | | protected double tTest(double m, double mu, double v, double n) throws MathException(Code) | | Computes p-value for 2-sided, 1-sample t-test.
Parameters:
m - sample mean
Parameters:
mu - constant to test against
Parameters:
v - sample variance
Parameters:
n - sample n p-value
throws:
MathException - if an error occurs computing the p-value |
| tTest | | protected double tTest(double m1, double m2, double v1, double v2, double n1, double n2) throws MathException(Code) | | Computes p-value for 2-sided, 2-sample t-test.
Does not assume subpopulation variances are equal. Degrees of freedom
are estimated from the data.
Parameters:
m1 - first sample mean
Parameters:
m2 - second sample mean
Parameters:
v1 - first sample variance
Parameters:
v2 - second sample variance
Parameters:
n1 - first sample n
Parameters:
n2 - second sample n p-value
throws:
MathException - if an error occurs computing the p-value |
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