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127 lines
4.5 KiB
C++
127 lines
4.5 KiB
C++
// students_t_example2.cpp
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// Copyright Paul A. Bristow 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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// Example 2 of using Student's t
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// A general guide to Student's t is at
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// http://en.wikipedia.org/wiki/Student's_t-test
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// (and many other elementary and advanced statistics texts).
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// It says:
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// The t statistic was invented by William Sealy Gosset
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// for cheaply monitoring the quality of beer brews.
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// "Student" was his pen name.
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// Gosset was statistician for Guinness brewery in Dublin, Ireland,
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// hired due to Claude Guinness's innovative policy of recruiting the
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// best graduates from Oxford and Cambridge for applying biochemistry
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// and statistics to Guinness's industrial processes.
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// Gosset published the t test in Biometrika in 1908,
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// but was forced to use a pen name by his employer who regarded the fact
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// that they were using statistics as a trade secret.
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// In fact, Gosset's identity was unknown not only to fellow statisticians
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// but to his employer - the company insisted on the pseudonym
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// so that it could turn a blind eye to the breach of its rules.
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// The Students't distribution function is described at
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// http://en.wikipedia.org/wiki/Student%27s_t_distribution
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#include <boost/math/distributions/students_t.hpp>
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using boost::math::students_t; // Probability of students_t(df, t).
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#include <iostream>
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using std::cout;
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using std::endl;
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#include <iomanip>
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using std::setprecision;
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using std::setw;
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#include <cmath>
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using std::sqrt;
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// This example of a one-sided test is from:
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//
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// from Statistics for Analytical Chemistry, 3rd ed. (1994), pp 59-60
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// J. C. Miller and J. N. Miller, Ellis Horwood ISBN 0 13 0309907.
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// An acid-base titrimetric method has a significant indicator error and
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// thus tends to give results with a positive systematic error (+bias).
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// To test this an exactly 0.1 M solution of acid is used to titrate
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// 25.00 ml of exactly 0.1 M solution of alkali,
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// with the following results (ml):
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double reference = 25.00; // 'True' result.
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const int values = 6; // titrations.
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double data [values] = {25.06, 25.18, 24.87, 25.51, 25.34, 25.41};
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int main()
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{
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cout << "Example2 using Student's t function. ";
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#if defined(__FILE__) && defined(__TIMESTAMP__) && defined(_MSC_FULL_VER)
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cout << " " << __FILE__ << ' ' << __TIMESTAMP__ << ' '<< _MSC_FULL_VER;
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#endif
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cout << endl;
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double sum = 0.;
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for (int value = 0; value < values; value++)
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{ // Echo data and calculate mean.
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sum += data[value];
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cout << setw(4) << value << ' ' << setw(14) << data[value] << endl;
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}
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double mean = sum /static_cast<double>(values);
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cout << "Mean = " << mean << endl; // 25.2283
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double sd = 0.;
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for (int value = 0; value < values; value++)
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{ // Calculate standard deviation.
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sd +=(data[value] - mean) * (data[value] - mean);
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}
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int degrees_of_freedom = values - 1; // Use the n-1 formula.
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sd /= degrees_of_freedom; // == variance.
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sd= sqrt(sd);
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cout << "Standard deviation = " << sd<< endl; // = 0.238279
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double t = (mean - reference) * sqrt(static_cast<double>(values))/ sd; //
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cout << "Student's t = " << t << ", with " << degrees_of_freedom << " degrees of freedom." << endl; // = 2.34725
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cout << "Probability of positive bias is " << cdf(students_t(degrees_of_freedom), t) << "."<< endl; // = 0.967108.
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// A 1-sided test because only testing for a positive bias.
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// If > 0.95 then greater than 1 in 20 conventional (arbitrary) requirement.
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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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------ Build started: Project: students_t_example2, Configuration: Debug Win32 ------
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Compiling...
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students_t_example2.cpp
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Linking...
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Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\students_t_example2.exe"
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Example2 using Student's t function. ..\..\..\..\..\..\boost-sandbox\libs\math_functions\example\students_t_example2.cpp Sat Aug 12 16:55:59 2006 140050727
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0 25.06
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1 25.18
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2 24.87
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3 25.51
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4 25.34
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5 25.41
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Mean = 25.2283
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Standard deviation = 0.238279
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Student's t = 2.34725, with 5 degrees of freedom.
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Probability of positive bias is 0.967108.
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Build Time 0:03
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Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\students_t_example2\Debug\BuildLog.htm"
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students_t_example2 - 0 error(s), 0 warning(s)
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========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
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*/
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