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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 ==========
+
+*/
+
+
+
+
+