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254 lines
9.2 KiB
C++
254 lines
9.2 KiB
C++
// (C) Copyright John Maddock 2006
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <iostream>
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#include <iomanip>
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#include <boost/math/distributions/students_t.hpp>
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void two_samples_t_test(
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double Sm1,
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double Sd1,
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unsigned Sn1,
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double Sm2,
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double Sd2,
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unsigned Sn2,
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double alpha)
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{
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//
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// Sm1 = Sample Mean 1.
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// Sd1 = Sample Standard Deviation 1.
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// Sn1 = Sample Size 1.
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// Sm2 = Sample Mean 2.
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// Sd2 = Sample Standard Deviation 2.
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// Sn2 = Sample Size 2.
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// alpha = Confidence Level.
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//
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// A Students t test applied to two sets of data.
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// We are testing the null hypothesis that the two
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// samples have the same mean and that any difference
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// if due to chance.
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// See http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
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//
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using namespace std;
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using namespace boost::math;
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// Print header:
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cout <<
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"_________________________________________________\n"
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"Student t test for two samples (unequal variances)\n"
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"_________________________________________________\n\n";
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cout << setprecision(5);
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cout << setw(55) << left << "Number of Observations (Sample 1)" << "= " << Sn1 << "\n";
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cout << setw(55) << left << "Sample 1 Mean" << "= " << Sm1 << "\n";
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cout << setw(55) << left << "Sample 1 Standard Deviation" << "= " << Sd1 << "\n";
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cout << setw(55) << left << "Number of Observations (Sample 2)" << "= " << Sn2 << "\n";
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cout << setw(55) << left << "Sample 2 Mean" << "= " << Sm2 << "\n";
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cout << setw(55) << left << "Sample 2 Standard Deviation" << "= " << Sd2 << "\n";
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//
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// Now we can calculate and output some stats:
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//
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// Degrees of freedom:
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double v = Sd1 * Sd1 / Sn1 + Sd2 * Sd2 / Sn2;
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v *= v;
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double t1 = Sd1 * Sd1 / Sn1;
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t1 *= t1;
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t1 /= (Sn1 - 1);
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double t2 = Sd2 * Sd2 / Sn2;
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t2 *= t2;
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t2 /= (Sn2 - 1);
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v /= (t1 + t2);
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cout << setw(55) << left << "Degrees of Freedom" << "= " << v << "\n";
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// t-statistic:
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double t_stat = (Sm1 - Sm2) / sqrt(Sd1 * Sd1 / Sn1 + Sd2 * Sd2 / Sn2);
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cout << setw(55) << left << "T Statistic" << "= " << t_stat << "\n";
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//
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// Finally define our distribution, and get the probability:
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//
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students_t dist(v);
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double q = cdf(complement(dist, fabs(t_stat)));
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cout << setw(55) << left << "Probability that difference is due to chance" << "= "
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<< setprecision(3) << scientific << q << "\n\n";
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//
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// Finally print out results of alternative hypothesis:
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//
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cout << setw(55) << left <<
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"Results for Alternative Hypothesis and alpha" << "= "
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<< setprecision(4) << fixed << alpha << "\n\n";
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cout << "Alternative Hypothesis Conclusion\n";
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cout << "Sample 1 Mean != Sample 2 Mean " ;
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if(q < alpha)
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cout << "ACCEPTED\n";
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else
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cout << "REJECTED\n";
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cout << "Sample 1 Mean < Sample 2 Mean ";
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if(cdf(dist, t_stat) < alpha)
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cout << "ACCEPTED\n";
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else
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cout << "REJECTED\n";
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cout << "Sample 1 Mean > Sample 2 Mean ";
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if(cdf(complement(dist, t_stat)) < alpha)
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cout << "ACCEPTED\n";
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else
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cout << "REJECTED\n";
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cout << endl << endl;
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}
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void two_samples_t_test_equal_sd(
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double Sm1,
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double Sd1,
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unsigned Sn1,
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double Sm2,
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double Sd2,
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unsigned Sn2,
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double alpha)
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{
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//
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// Sm1 = Sample Mean 1.
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// Sd1 = Sample Standard Deviation 1.
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// Sn1 = Sample Size 1.
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// Sm2 = Sample Mean 2.
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// Sd2 = Sample Standard Deviation 2.
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// Sn2 = Sample Size 2.
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// alpha = Confidence Level.
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//
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// A Students t test applied to two sets of data.
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// We are testing the null hypothesis that the two
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// samples have the same mean and that any difference
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// if due to chance.
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// See http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
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//
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using namespace std;
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using namespace boost::math;
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// Print header:
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cout <<
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"_______________________________________________\n"
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"Student t test for two samples (equal variances)\n"
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"_______________________________________________\n\n";
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cout << setprecision(5);
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cout << setw(55) << left << "Number of Observations (Sample 1)" << "= " << Sn1 << "\n";
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cout << setw(55) << left << "Sample 1 Mean" << "= " << Sm1 << "\n";
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cout << setw(55) << left << "Sample 1 Standard Deviation" << "= " << Sd1 << "\n";
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cout << setw(55) << left << "Number of Observations (Sample 2)" << "= " << Sn2 << "\n";
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cout << setw(55) << left << "Sample 2 Mean" << "= " << Sm2 << "\n";
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cout << setw(55) << left << "Sample 2 Standard Deviation" << "= " << Sd2 << "\n";
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//
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// Now we can calculate and output some stats:
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//
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// Degrees of freedom:
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double v = Sn1 + Sn2 - 2;
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cout << setw(55) << left << "Degrees of Freedom" << "= " << v << "\n";
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// Pooled variance:
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double sp = sqrt(((Sn1-1) * Sd1 * Sd1 + (Sn2-1) * Sd2 * Sd2) / v);
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cout << setw(55) << left << "Pooled Standard Deviation" << "= " << v << "\n";
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// t-statistic:
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double t_stat = (Sm1 - Sm2) / (sp * sqrt(1.0 / Sn1 + 1.0 / Sn2));
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cout << setw(55) << left << "T Statistic" << "= " << t_stat << "\n";
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//
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// Finally define our distribution, and get the probability:
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//
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students_t dist(v);
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double q = cdf(complement(dist, fabs(t_stat)));
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cout << setw(55) << left << "Probability that difference is due to chance" << "= "
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<< setprecision(3) << scientific << q << "\n\n";
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//
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// Finally print out results of alternative hypothesis:
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//
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cout << setw(55) << left <<
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"Results for Alternative Hypothesis and alpha" << "= "
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<< setprecision(4) << fixed << alpha << "\n\n";
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cout << "Alternative Hypothesis Conclusion\n";
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cout << "Sample 1 Mean != Sample 2 Mean " ;
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if(q < alpha)
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cout << "ACCEPTED\n";
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else
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cout << "REJECTED\n";
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cout << "Sample 1 Mean < Sample 2 Mean ";
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if(cdf(dist, t_stat) < alpha)
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cout << "ACCEPTED\n";
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else
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cout << "REJECTED\n";
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cout << "Sample 1 Mean > Sample 2 Mean ";
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if(cdf(complement(dist, t_stat)) < alpha)
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cout << "ACCEPTED\n";
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else
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cout << "REJECTED\n";
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cout << endl << endl;
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}
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void two_samples_estimate_df(
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double m1, // m1 = Sample 1 Mean.
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double s1, // s1 = Sample 1 Standard Deviation.
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unsigned n1, // n1 = Sample 1 Size.
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double m2, // m2 = Sample 2 Mean.
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double s2) // s2 = Sample 2 Standard Deviation.
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{
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using namespace std;
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using namespace boost::math;
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// Print out general info:
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cout <<
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"_____________________________________________________________\n"
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"Estimated sample sizes required for various confidence levels\n"
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"_____________________________________________________________\n\n";
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cout << setprecision(5);
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cout << setw(40) << left << "Sample 1 Mean" << "= " << m1 << "\n";
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cout << setw(40) << left << "Sample 1 Standard Deviation" << "= " << s1 << "\n";
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cout << setw(40) << left << "Sample 1 Size" << "= " << n1 << "\n";
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cout << setw(40) << left << "Sample 2 Mean" << "= " << m2 << "\n";
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cout << setw(40) << left << "Sample 2 Standard Deviation" << "= " << s2 << "\n";
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//
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// Define a table of confidence intervals:
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//
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double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
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//
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// Print table header:
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//
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cout << "\n\n"
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"_______________________________________________________________________\n"
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"Confidence Estimated Sample Size Estimated Sample 2 Size\n"
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" Value (%) (With Two Equal Sizes) (With Fixed Sample 1 Size)\n"
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"_______________________________________________________________________\n";
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//
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// Now print out the data for the table rows.
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//
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for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
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{
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// Confidence value:
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cout << fixed << setprecision(3) << setw(10) << right << 100 * (1-alpha[i]);
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// calculate df assuming equal sample sizes:
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double df = students_t::estimate_two_equal_degrees_of_freedom(
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complement(m1, s1, m2, s2, alpha[i]));
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// convert to sample size:
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double size = (ceil(df) + 2) / 2;
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// Print size:
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cout << fixed << setprecision(0) << setw(28) << right << size;
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// calculate df with sample 1 fixed:
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df = students_t::estimate_two_unequal_degrees_of_freedom(
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complement(m1, s1, n1, m2, s2, alpha[i]));
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// convert to sample size:
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size = (ceil(df) + 2) - n1;
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// Print size:
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cout << fixed << setprecision(0) << setw(28) << right << size << endl;
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}
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cout << endl;
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}
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int main()
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{
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//
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// Run tests for Heat Flow Meter data
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// see http://www.itl.nist.gov/div898/handbook/eda/section4/eda428.htm
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// The data was collected while calibrating a heat flow meter
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// against a known value.
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//
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two_samples_t_test(20.14458, 6.414700, 249, 30.48101, 6.107710, 79, 0.05);
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two_samples_t_test_equal_sd(20.14458, 6.414700, 249, 30.48101, 6.107710, 79, 0.05);
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two_samples_estimate_df(20.14458, 6.414700, 249, 30.48101, 6.107710);
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return 0;
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}
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