#include <boost/math/distributions/students_t.hpp>
//From www.richelbilderbeek.nl/CppAreMeansSame.htm
//
// mean1 - mean2
// t = ----------------------------------------------------
// SQRT (pooled_variance * ( (1.0/size1) + (1.0/size2) )
//
// Difference_due_to_chance = t * 2.0
//
// ((size1-1)*stddev1*stddev1) + ((size2-1)*stddev2*stddev2)
// Pooled_variance = --------------------------------------------------------- )
// size1 + size2 - 2
// Degrees of freedom = size1 + size2 - 2
//
bool AreMeansSame(
const double mean1,
const double stddev1,
const std::size_t size1,
const double mean2,
const double stddev2,
const std::size_t size2,
const double significance_level)
{
const double degrees_of_freedom = static_cast<double>(size1 + size2 - 2);
const double pooled_variance
= ((static_cast<double>(size1-1) * stddev1 * stddev1)
+ (static_cast<double>(size2-1) * stddev2 * stddev2))
/ degrees_of_freedom;
const double t_statistic
= std::fabs(mean1 - mean2)
/ std::sqrt(pooled_variance * (
(1.0 / static_cast<double>(size1))
+ (1.0 / static_cast<double>(size2)) ) );
//std::cout << "t_statistic: " << t_statistic << '\n';
const boost::math::students_t distribution(degrees_of_freedom);
const double critical_value
= boost::math::quantile(boost::math::complement(distribution,
significance_level / 2.0));
//std::cout << "critical_value: " << critical_value << '\n';
return (t_statistic < critical_value);
}
#include <iostream>
int main()
{
//Values from
// * David Heath. An introduction to experimental
// design and statistics for biology. 1995.
// ISBN: 1-85728-132-2 PB. Page 246, box 9.12:
// The t test for difference in means of two populations
// using small samples: mean activty of
// acid phosphatase at pH3 and pH5
if (AreMeansSame(11.24,1.26,5,14.12,1.45,5,0.05))
{
std::cout << "It cannot be rejected that means are the same" << std::endl;
}
else
{
std::cout << "It can be rejected that means are the same" << std::endl;
}
}
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