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