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Additional t-tests (#487)
* Add integer support to t_test * Add paired samples t test * Add two sample t test * Add welch's t test * Update docs * Cleanup * Add CHECK_ULP_CLOSE tests to test battery. Fix svg * Remove all instances of ex [CI SKIP] * Remove std::distance and note in docs [CI SKIP] * Re-write test battery
This commit is contained in:
Matt Borland
GitHub
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doc/graphs/paired_sample_t_statistic.svg
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<title id="MathJax-SVG-1-Title">{\displaystyle t={\frac {{\bar {X}}_{D}-\mu _{0}}{s_{D}/{\sqrt {n}}}}}</title>
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doc/graphs/two_sample_t_statistic.svg
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<title id="MathJax-SVG-1-Title">{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{p}\cdot {\sqrt {{\frac {1}{n_{1}}}+{\frac {1}{n_{2}}}}}}}}</title>
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122
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122
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41
doc/graphs/welchs_t_statistic.svg
Normal file
41
doc/graphs/welchs_t_statistic.svg
Normal file
@@ -0,0 +1,41 @@
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<title id="MathJax-SVG-1-Title">{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{\bar {\Delta }}}}}</title>
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After Width: | Height: | Size: 5.0 KiB |
57
doc/graphs/welchs_t_variance.svg
Normal file
57
doc/graphs/welchs_t_variance.svg
Normal file
@@ -0,0 +1,57 @@
|
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="109" height="46" style="vertical-align: -2.838;" viewBox="0 -2083 7823.7 3304.9" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title">
|
||||
<title id="MathJax-SVG-1-Title">{\displaystyle s_{\bar {\Delta }}={\sqrt {{\frac {s_{1}^{2}}{n_{1}}}+{\frac {s_{2}^{2}}{n_{2}}}}}.}</title>
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|
After Width: | Height: | Size: 5.3 KiB |
@@ -1,5 +1,6 @@
|
||||
[/
|
||||
Copyright (c) 2019 Nick Thompson
|
||||
Copyright (c) 2021 Matt Borland
|
||||
Use, modification and distribution are subject to the
|
||||
Boost Software License, Version 1.0. (See accompanying file
|
||||
LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
|
||||
@@ -14,20 +15,38 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
namespace boost::math::statistics {
|
||||
|
||||
template<typename Real>
|
||||
std::pair<Real, Real> one_sample_t_test(Real sample_mean, Real sample_variance, Real num_samples, Real assumed_mean);
|
||||
template<typename Real, typename Size = Real>
|
||||
std::pair<Real, Real> one_sample_t_test(Real sample_mean, Real sample_variance, Size num_samples, Real assumed_mean);
|
||||
|
||||
template<class ForwardIterator>
|
||||
auto one_sample_t_test(ForwardIterator begin, ForwardIterator end, typename std::iterator_traits<ForwardIterator>::value_type assumed_mean);
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type>
|
||||
std::pair<Real, Real> one_sample_t_test(ForwardIterator begin, ForwardIterator end, Real assumed_mean);
|
||||
|
||||
template<class Container>
|
||||
auto one_sample_t_test(Container const & v, typename Container::value_type assumed_mean);
|
||||
template<typename Container>
|
||||
std::pair<Real, Real> one_sample_t_test(Container const & v, typename Container::value_type assumed_mean);
|
||||
|
||||
}}}
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type>
|
||||
std::pair<Real, Real> two_sample_t_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator begin_2);
|
||||
|
||||
template<typename Container, typename Real = typename Container::value_type>
|
||||
std::pair<Real, Real> two_sample_t_test(Container const & u, Container const & v);
|
||||
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type>
|
||||
std::pair<Real, Real> paired_samples_t_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator begin_2);
|
||||
|
||||
template<typename Container, typename Real = typename Container::value_type>
|
||||
std::pair<Real, Real> paired_samples_t_test(Container const & u, Container const & v);
|
||||
|
||||
}
|
||||
```
|
||||
|
||||
[heading Background]
|
||||
|
||||
A set of C++11 compatible functions for various [@https://en.wikipedia.org/wiki/Student's_t-test Student's t-tests].
|
||||
The input can be any real number or set of real numbers.
|
||||
In the event that the input is an integer or a set of integers typename Real will be deduced as a double precision type.
|
||||
|
||||
[heading One-sample /t/-test]
|
||||
|
||||
A one-sample /t/-test attempts to answer the question "given a sample mean, is it likely that the population mean of my data is a certain value?"
|
||||
The test statistic is
|
||||
|
||||
@@ -61,6 +80,76 @@ auto [t, p] = boost::math::statistics::one_sample_t_test(v, 0.0);
|
||||
|
||||
The test statistic is the first element of the pair, and the /p/-value is the second element.
|
||||
|
||||
[heading Independent two-sample /t/-test]
|
||||
|
||||
A two-sample /t/-test determines if the means of two sets of data have a statistically significant difference from each other.
|
||||
There are two underlying implementations based off the variances of the sets of data.
|
||||
If /s/[sub 1] and /s/[sub 2] are within a factor of 2 of each other the following formulas will be used:
|
||||
|
||||
[$../graphs/two_sample_t_statistic.svg]
|
||||
|
||||
where
|
||||
|
||||
[$../graphs/two_sample_pooled_variance.svg]
|
||||
|
||||
If /s/[sub 1] and /s/[sub 2] are not within a factor of 2 of each other Welch's t-test will be used:
|
||||
|
||||
[$../graphs/welchs_t_statistic.svg]
|
||||
|
||||
where
|
||||
|
||||
[$../graphs/welchs_t_variance.svg]
|
||||
|
||||
and
|
||||
|
||||
[$../graphs/welchs_t_dof.svg]
|
||||
|
||||
An example of usage is as follows:
|
||||
|
||||
```
|
||||
#include <vector>
|
||||
#include <random>
|
||||
#include <boost/math/statistics/t_test.hpp>
|
||||
|
||||
std::random_device rd;
|
||||
std::mt19937 gen{rd()};
|
||||
std::normal_distribution<double> dis{0,1};
|
||||
std::vector<double> u(1024);
|
||||
std::vector<double> v(1024);
|
||||
for(std::size_t i = 0; i < u.size(); ++i)
|
||||
{
|
||||
u[i] = dis(gen);
|
||||
v[i] = dis(gen);
|
||||
}
|
||||
|
||||
auto [t, p] = boost::math::statistics::two_sample_t_test(u, v);
|
||||
```
|
||||
|
||||
/Nota bene:/ The sample sizes for the two sets of data do not need to be equal.
|
||||
|
||||
/Nota bene:/ std::distance is used in the implementation leading to lower performance with ForwardIterator than RandomAccessIterator.
|
||||
|
||||
[heading Dependent /t/-test for paired samples]
|
||||
|
||||
This test is used when the samples are dependent such as when one sample has been tested twice, or when two samples have been paired.
|
||||
Much like the independent t-test it is used to determine if the means of two sets of data have a statistically significant difference from each other.
|
||||
|
||||
[$../graphs/paired_sample_t_statistic.svg]
|
||||
|
||||
where /X/[sub D] and /s/[sub D] are the mean and standard deviation of the differences between all pairs.
|
||||
|
||||
An example of usage is as follows:
|
||||
|
||||
```
|
||||
#include <vector>
|
||||
#include <random>
|
||||
#include <boost/math/statistics/t_test.hpp>
|
||||
|
||||
std::vector<int> first_test {35, 50, 90, 78};
|
||||
std::vector<int> second_test {67, 46, 86, 91};
|
||||
|
||||
auto [t, p] = boost::math::statistics::paired_samples_t_test(first_test, second_test);
|
||||
```
|
||||
|
||||
[heading Performance]
|
||||
|
||||
|
||||
@@ -8,9 +8,12 @@
|
||||
#define BOOST_MATH_STATISTICS_T_TEST_HPP
|
||||
|
||||
#include <cmath>
|
||||
#include <cstddef>
|
||||
#include <iterator>
|
||||
#include <utility>
|
||||
#include <type_traits>
|
||||
#include <vector>
|
||||
#include <stdexcept>
|
||||
#include <boost/math/distributions/students_t.hpp>
|
||||
#include <boost/math/statistics/univariate_statistics.hpp>
|
||||
|
||||
@@ -47,6 +50,133 @@ ReturnType one_sample_t_test_impl(ForwardIterator begin, ForwardIterator end, ty
|
||||
Real s_sq = std::get<1>(temp);
|
||||
return one_sample_t_test_impl<ReturnType>(mu, s_sq, Real(std::distance(begin, end)), Real(assumed_mean));
|
||||
}
|
||||
|
||||
// https://en.wikipedia.org/wiki/Student%27s_t-test#Equal_or_unequal_sample_sizes,_unequal_variances_(sX1_%3E_2sX2_or_sX2_%3E_2sX1)
|
||||
template<typename ReturnType, typename T>
|
||||
ReturnType welchs_t_test_impl(T mean_1, T variance_1, T size_1, T mean_2, T variance_2, T size_2)
|
||||
{
|
||||
using Real = typename std::tuple_element<0, ReturnType>::type;
|
||||
using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
|
||||
using std::sqrt;
|
||||
|
||||
Real dof_num = (variance_1/size_1 + variance_2/size_2) * (variance_1/size_1 + variance_2/size_2);
|
||||
Real dof_denom = ((variance_1/size_1) * (variance_1/size_1))/(size_1 - 1) +
|
||||
((variance_2/size_2) * (variance_2/size_2))/(size_2 - 1);
|
||||
Real dof = dof_num / dof_denom;
|
||||
|
||||
Real s_estimator = sqrt((variance_1/size_1) + (variance_2/size_2));
|
||||
|
||||
Real test_statistic = (static_cast<Real>(mean_1) - static_cast<Real>(mean_2))/s_estimator;
|
||||
auto student = boost::math::students_t_distribution<Real, no_promote_policy>(dof);
|
||||
Real pvalue;
|
||||
if (test_statistic > 0)
|
||||
{
|
||||
pvalue = 2*boost::math::cdf<Real>(student, -test_statistic);;
|
||||
}
|
||||
else
|
||||
{
|
||||
pvalue = 2*boost::math::cdf<Real>(student, test_statistic);
|
||||
}
|
||||
|
||||
return std::make_pair(test_statistic, pvalue);
|
||||
}
|
||||
|
||||
// https://en.wikipedia.org/wiki/Student%27s_t-test#Equal_or_unequal_sample_sizes,_similar_variances_(1/2_%3C_sX1/sX2_%3C_2)
|
||||
template<typename ReturnType, typename T>
|
||||
ReturnType two_sample_t_test_impl(T mean_1, T variance_1, T size_1, T mean_2, T variance_2, T size_2)
|
||||
{
|
||||
using Real = typename std::tuple_element<0, ReturnType>::type;
|
||||
using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
|
||||
using std::sqrt;
|
||||
|
||||
Real dof = size_1 + size_2 - 2;
|
||||
Real pooled_std_dev = sqrt(((size_1-1)*variance_1 + (size_2-1)*variance_2) / dof);
|
||||
Real test_statistic = (mean_1-mean_2) / (pooled_std_dev*sqrt(1.0/static_cast<Real>(size_1) + 1.0/static_cast<Real>(size_2)));
|
||||
|
||||
auto student = boost::math::students_t_distribution<Real, no_promote_policy>(dof);
|
||||
Real pvalue;
|
||||
if (test_statistic > 0)
|
||||
{
|
||||
pvalue = 2*boost::math::cdf<Real>(student, -test_statistic);;
|
||||
}
|
||||
else
|
||||
{
|
||||
pvalue = 2*boost::math::cdf<Real>(student, test_statistic);
|
||||
}
|
||||
|
||||
return std::make_pair(test_statistic, pvalue);
|
||||
}
|
||||
|
||||
template<typename ReturnType, typename ForwardIterator>
|
||||
ReturnType two_sample_t_test_impl(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2)
|
||||
{
|
||||
using Real = typename std::tuple_element<0, ReturnType>::type;
|
||||
using std::sqrt;
|
||||
auto n1 = std::distance(begin_1, end_1);
|
||||
auto n2 = std::distance(begin_2, end_2);
|
||||
|
||||
ReturnType temp_1 = mean_and_sample_variance(begin_1, end_1);
|
||||
Real mean_1 = std::get<0>(temp_1);
|
||||
Real variance_1 = std::get<1>(temp_1);
|
||||
Real std_dev_1 = sqrt(variance_1);
|
||||
|
||||
ReturnType temp_2 = mean_and_sample_variance(begin_2, end_2);
|
||||
Real mean_2 = std::get<0>(temp_2);
|
||||
Real variance_2 = std::get<1>(temp_2);
|
||||
Real std_dev_2 = sqrt(variance_2);
|
||||
|
||||
if(std_dev_1 > 2 * std_dev_2 || std_dev_2 > 2 * std_dev_1)
|
||||
{
|
||||
return welchs_t_test_impl<ReturnType>(mean_1, variance_1, Real(n1), mean_2, variance_2, Real(n2));
|
||||
}
|
||||
else
|
||||
{
|
||||
return two_sample_t_test_impl<ReturnType>(mean_1, variance_1, Real(n1), mean_2, variance_2, Real(n2));
|
||||
}
|
||||
}
|
||||
|
||||
// https://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples
|
||||
template<typename ReturnType, typename ForwardIterator>
|
||||
ReturnType paired_samples_t_test_impl(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2)
|
||||
{
|
||||
using Real = typename std::tuple_element<0, ReturnType>::type;
|
||||
using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
|
||||
using std::sqrt;
|
||||
|
||||
std::vector<Real> delta;
|
||||
ForwardIterator it_1 = begin_1;
|
||||
ForwardIterator it_2 = begin_2;
|
||||
std::size_t n = 0;
|
||||
while(it_1 != end_1 && it_2 != end_2)
|
||||
{
|
||||
delta.emplace_back(static_cast<Real>(*it_1++) - static_cast<Real>(*it_2++));
|
||||
++n;
|
||||
}
|
||||
|
||||
if(it_1 != end_1 || it_2 != end_2)
|
||||
{
|
||||
throw std::domain_error("Both sets must have the same number of values.");
|
||||
}
|
||||
|
||||
std::pair<Real, Real> temp = mean_and_sample_variance(delta.begin(), delta.end());
|
||||
Real delta_mean = std::get<0>(temp);
|
||||
Real delta_std_dev = sqrt(std::get<1>(temp));
|
||||
|
||||
Real test_statistic = delta_mean/(delta_std_dev/sqrt(n));
|
||||
|
||||
auto student = boost::math::students_t_distribution<Real, no_promote_policy>(n - 1);
|
||||
Real pvalue;
|
||||
if (test_statistic > 0)
|
||||
{
|
||||
pvalue = 2*boost::math::cdf<Real>(student, -test_statistic);;
|
||||
}
|
||||
else
|
||||
{
|
||||
pvalue = 2*boost::math::cdf<Real>(student, test_statistic);
|
||||
}
|
||||
|
||||
return std::make_pair(test_statistic, pvalue);
|
||||
}
|
||||
} // namespace detail
|
||||
|
||||
template<typename Real, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
|
||||
@@ -89,5 +219,57 @@ inline auto one_sample_t_test(Container const & v, Real assumed_mean) -> std::pa
|
||||
return detail::one_sample_t_test_impl<std::pair<Real, Real>>(std::begin(v), std::end(v), assumed_mean);
|
||||
}
|
||||
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
||||
typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto two_sample_t_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<double, double>
|
||||
{
|
||||
return detail::two_sample_t_test_impl<std::pair<double, double>>(begin_1, end_1, begin_2, end_2);
|
||||
}
|
||||
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
||||
typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto two_sample_t_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<Real, Real>
|
||||
{
|
||||
return detail::two_sample_t_test_impl<std::pair<Real, Real>>(begin_1, end_1, begin_2, end_2);
|
||||
}
|
||||
|
||||
template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto two_sample_t_test(Container const & u, Container const & v) -> std::pair<double, double>
|
||||
{
|
||||
return detail::two_sample_t_test_impl<std::pair<double, double>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
|
||||
}
|
||||
|
||||
template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto two_sample_t_test(Container const & u, Container const & v) -> std::pair<Real, Real>
|
||||
{
|
||||
return detail::two_sample_t_test_impl<std::pair<Real, Real>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
|
||||
}
|
||||
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
||||
typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto paired_samples_t_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<double, double>
|
||||
{
|
||||
return detail::paired_samples_t_test_impl<std::pair<double, double>>(begin_1, end_1, begin_2, end_2);
|
||||
}
|
||||
|
||||
template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
||||
typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto paired_samples_t_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<Real, Real>
|
||||
{
|
||||
return detail::paired_samples_t_test_impl<std::pair<Real, Real>>(begin_1, end_1, begin_2, end_2);
|
||||
}
|
||||
|
||||
template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto paired_samples_t_test(Container const & u, Container const & v) -> std::pair<double, double>
|
||||
{
|
||||
return detail::paired_samples_t_test_impl<std::pair<double, double>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
|
||||
}
|
||||
|
||||
template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
|
||||
inline auto paired_samples_t_test(Container const & u, Container const & v) -> std::pair<Real, Real>
|
||||
{
|
||||
return detail::paired_samples_t_test_impl<std::pair<Real, Real>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
|
||||
}
|
||||
|
||||
}}} // namespace boost::math::statistics
|
||||
#endif
|
||||
|
||||
@@ -11,6 +11,9 @@
|
||||
#include <random>
|
||||
#include <boost/math/statistics/univariate_statistics.hpp>
|
||||
#include <boost/math/statistics/t_test.hpp>
|
||||
#include <boost/multiprecision/cpp_bin_float.hpp>
|
||||
|
||||
using quad = boost::multiprecision::cpp_bin_float_quad;
|
||||
|
||||
template<typename Real>
|
||||
void test_exact_mean()
|
||||
@@ -34,6 +37,24 @@ void test_exact_mean()
|
||||
CHECK_ULP_CLOSE(Real(1), computed_pvalue, 9);
|
||||
}
|
||||
|
||||
template<typename Real>
|
||||
void test_multiprecision_exact_mean()
|
||||
{
|
||||
std::mt19937 gen{5125122};
|
||||
std::normal_distribution<long double> dis{0,3};
|
||||
std::vector<Real> v(1024);
|
||||
for (auto & x : v) {
|
||||
x = dis(gen);
|
||||
}
|
||||
|
||||
Real mu = boost::math::statistics::mean(v);
|
||||
|
||||
auto [computed_statistic, computed_pvalue] = boost::math::statistics::one_sample_t_test(v, mu);
|
||||
|
||||
CHECK_MOLLIFIED_CLOSE(Real(0), computed_statistic, 10*std::numeric_limits<Real>::epsilon());
|
||||
CHECK_ULP_CLOSE(Real(1), computed_pvalue, 9);
|
||||
}
|
||||
|
||||
template<typename Z>
|
||||
void test_integer()
|
||||
{
|
||||
@@ -95,15 +116,117 @@ void test_agreement_with_mathematica()
|
||||
}
|
||||
}
|
||||
|
||||
template<typename Real>
|
||||
void test_two_sample_t()
|
||||
{
|
||||
auto [computed_statistic, computed_pvalue] =
|
||||
boost::math::statistics::detail::two_sample_t_test_impl<std::pair<Real, Real>>(Real(10.0), Real(1.0), Real(20), Real(5.0), Real(0.25), Real(20));
|
||||
|
||||
CHECK_ULP_CLOSE(Real(20), computed_statistic, 5);
|
||||
CHECK_MOLLIFIED_CLOSE(Real(0), computed_pvalue, 1e-21);
|
||||
|
||||
std::vector<Real> set_1 {301, 298, 295, 297, 304, 305, 309, 298, 291, 299, 293, 304};
|
||||
|
||||
auto [computed_statistic_2, computed_pvalue_2] = boost::math::statistics::two_sample_t_test(set_1, set_1);
|
||||
CHECK_ULP_CLOSE(Real(0), computed_statistic_2, 5);
|
||||
CHECK_ULP_CLOSE(Real(1), computed_pvalue_2, 5);
|
||||
}
|
||||
|
||||
template<typename Z>
|
||||
void test_integer_two_sample_t()
|
||||
{
|
||||
auto [computed_statistic, computed_pvalue] =
|
||||
boost::math::statistics::detail::two_sample_t_test_impl<std::pair<double, double>>(Z(10), Z(4), Z(20), Z(5), Z(1), Z(20));
|
||||
|
||||
CHECK_ULP_CLOSE(10.0, computed_statistic, 5);
|
||||
|
||||
std::vector<Z> set_1 {301, 298, 295, 297, 304, 305, 309, 298, 291, 299, 293, 304};
|
||||
|
||||
auto [computed_statistic_2, computed_pvalue_2] = boost::math::statistics::two_sample_t_test(set_1, set_1);
|
||||
CHECK_ULP_CLOSE(0.0, computed_statistic_2, 5);
|
||||
CHECK_ULP_CLOSE(1.0, computed_pvalue_2, 5);
|
||||
}
|
||||
|
||||
template<typename Real>
|
||||
void test_welch()
|
||||
{
|
||||
using std::sqrt;
|
||||
|
||||
auto [computed_statistic, computed_pvalue] =
|
||||
boost::math::statistics::detail::welchs_t_test_impl<std::pair<Real, Real>>(Real(10.0), Real(1.0), Real(20), Real(5.0), Real(0.25), Real(20));
|
||||
|
||||
CHECK_ULP_CLOSE(Real(20), computed_statistic, 5);
|
||||
CHECK_MOLLIFIED_CLOSE(Real(0), computed_pvalue, 5e-18);
|
||||
|
||||
auto [computed_statistic_2, computed_pvalue_2] =
|
||||
boost::math::statistics::detail::welchs_t_test_impl<std::pair<Real, Real>>(Real(10.0), Real(0.5), Real(20), Real(10.0), Real(0.5), Real(20));
|
||||
|
||||
CHECK_ULP_CLOSE(Real(0), computed_statistic_2, 5);
|
||||
CHECK_ULP_CLOSE(Real(1), computed_pvalue_2, 5);
|
||||
}
|
||||
|
||||
template<typename Z>
|
||||
void test_integer_welch()
|
||||
{
|
||||
auto [computed_statistic, computed_pvalue] =
|
||||
boost::math::statistics::detail::welchs_t_test_impl<std::pair<double, double>>(10.0, 4.0, 20.0, 5.0, 1.0, 20.0);
|
||||
|
||||
CHECK_ULP_CLOSE(Z(10), computed_statistic, 5);
|
||||
|
||||
auto [computed_statistic_2, computed_pvalue_2] =
|
||||
boost::math::statistics::detail::welchs_t_test_impl<std::pair<double, double>>(10.0, 0.5, 20.0, 10.0, 0.5, 20.0);
|
||||
CHECK_ULP_CLOSE(Z(0), computed_statistic_2, 5);
|
||||
CHECK_ULP_CLOSE(Z(1), computed_pvalue_2, 5);
|
||||
}
|
||||
|
||||
template<typename Real>
|
||||
void test_paired_samples()
|
||||
{
|
||||
std::vector<Real> set_1 {2,4};
|
||||
std::vector<Real> set_2 {1,2};
|
||||
|
||||
auto [computed_statistic, computed_pvalue] = boost::math::statistics::paired_samples_t_test(set_1, set_2);
|
||||
|
||||
CHECK_ULP_CLOSE(Real(3), computed_statistic, 5);
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
test_agreement_with_mathematica();
|
||||
|
||||
test_exact_mean<float>();
|
||||
test_exact_mean<double>();
|
||||
test_multiprecision_exact_mean<quad>();
|
||||
|
||||
test_integer<int>();
|
||||
test_integer<int32_t>();
|
||||
test_integer<int64_t>();
|
||||
test_integer<uint32_t>();
|
||||
|
||||
test_two_sample_t<float>();
|
||||
test_two_sample_t<double>();
|
||||
test_two_sample_t<quad>();
|
||||
|
||||
test_integer_two_sample_t<int>();
|
||||
test_integer_two_sample_t<int32_t>();
|
||||
test_integer_two_sample_t<int64_t>();
|
||||
test_integer_two_sample_t<uint32_t>();
|
||||
|
||||
test_welch<float>();
|
||||
test_welch<double>();
|
||||
test_welch<quad>();
|
||||
|
||||
test_integer_welch<int>();
|
||||
test_integer_welch<int32_t>();
|
||||
test_integer_welch<int64_t>();
|
||||
test_integer_welch<uint32_t>();
|
||||
|
||||
test_paired_samples<float>();
|
||||
test_paired_samples<double>();
|
||||
test_paired_samples<int>();
|
||||
test_paired_samples<int32_t>();
|
||||
test_paired_samples<int64_t>();
|
||||
test_paired_samples<uint32_t>();
|
||||
|
||||
return boost::math::test::report_errors();
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user