246 lines
9.4 KiB
C++
246 lines
9.4 KiB
C++
// Copyright John Maddock 2006.
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// Copyright Paul A. Bristow 2007, 2010
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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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#ifdef _MSC_VER
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# pragma warning(disable: 4512) // assignment operator could not be generated.
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# pragma warning(disable: 4510) // default constructor could not be generated.
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# pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
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#endif
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#include <iostream>
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using std::cout; using std::endl;
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using std::left; using std::fixed; using std::right; using std::scientific;
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#include <iomanip>
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using std::setw;
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using std::setprecision;
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#include <boost/math/distributions/students_t.hpp>
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using boost::math::students_t;
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void two_samples_t_test_equal_sd(
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double Sm1, // Sm1 = Sample Mean 1.
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double Sd1, // Sd1 = Sample Standard Deviation 1.
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unsigned Sn1, // Sn1 = Sample Size 1.
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double Sm2, // Sm2 = Sample Mean 2.
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double Sd2, // Sd2 = Sample Standard Deviation 2.
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unsigned Sn2, // Sn2 = Sample Size 2.
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double alpha) // alpha = Significance 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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using boost::math::students_t;
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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 and hence standard deviation:
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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" << "= " << sp << "\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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// 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 << 2 * 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 / 2)
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cout << "NOT REJECTED\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 << "NOT REJECTED\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 << "NOT REJECTED\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_unequal_sd(
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double Sm1, // Sm1 = Sample Mean 1.
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double Sd1, // Sd1 = Sample Standard Deviation 1.
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unsigned Sn1, // Sn1 = Sample Size 1.
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double Sm2, // Sm2 = Sample Mean 2.
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double Sd2, // Sd2 = Sample Standard Deviation 2.
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unsigned Sn2, // Sn2 = Sample Size 2.
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double alpha) // alpha = Significance 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
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// that any difference is 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 boost::math::students_t;
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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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// 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 << 2 * 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 / 2)
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cout << "NOT REJECTED\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 << "NOT REJECTED\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 << "NOT REJECTED\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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int main()
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{
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//
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// Run tests for Car Mileage sample data
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3531.htm
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// from the NIST website http://www.itl.nist.gov. The data compares
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// miles per gallon of US cars with miles per gallon of Japanese cars.
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//
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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_t_test_unequal_sd(20.14458, 6.414700, 249, 30.48101, 6.107710, 79, 0.05);
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return 0;
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} // int main()
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/*
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Output is:
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_______________________________________________
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Student t test for two samples (equal variances)
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_______________________________________________
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Number of Observations (Sample 1) = 249
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Sample 1 Mean = 20.145
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Sample 1 Standard Deviation = 6.4147
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Number of Observations (Sample 2) = 79
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Sample 2 Mean = 30.481
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Sample 2 Standard Deviation = 6.1077
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Degrees of Freedom = 326
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Pooled Standard Deviation = 6.3426
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T Statistic = -12.621
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Probability that difference is due to chance = 5.273e-030
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Results for Alternative Hypothesis and alpha = 0.0500
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Alternative Hypothesis Conclusion
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Sample 1 Mean != Sample 2 Mean NOT REJECTED
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Sample 1 Mean < Sample 2 Mean NOT REJECTED
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Sample 1 Mean > Sample 2 Mean REJECTED
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_________________________________________________
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Student t test for two samples (unequal variances)
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_________________________________________________
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Number of Observations (Sample 1) = 249
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Sample 1 Mean = 20.14458
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Sample 1 Standard Deviation = 6.41470
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Number of Observations (Sample 2) = 79
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Sample 2 Mean = 30.48101
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Sample 2 Standard Deviation = 6.10771
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Degrees of Freedom = 136.87499
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T Statistic = -12.94627
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Probability that difference is due to chance = 1.571e-025
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Results for Alternative Hypothesis and alpha = 0.0500
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Alternative Hypothesis Conclusion
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Sample 1 Mean != Sample 2 Mean NOT REJECTED
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Sample 1 Mean < Sample 2 Mean NOT REJECTED
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Sample 1 Mean > Sample 2 Mean REJECTED
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*/
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