mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-10-25 01:50:30 -04:00
121 lines
4.6 KiB
C++
121 lines
4.6 KiB
C++
// students_t_example3.cpp
|
|
// Copyright Paul A. Bristow 2006, 2007.
|
|
|
|
// 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 3 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 two-sided test is from:
|
|
// B. M. Smith & M. B. Griffiths, Analyst, 1982, 107, 253,
|
|
// from Statistics for Analytical Chemistry, 3rd ed. (1994), pp 58-59
|
|
// J. C. Miller and J. N. Miller, Ellis Horwood ISBN 0 13 0309907
|
|
|
|
// Concentrations of lead (ug/l) determined by two different methods
|
|
// for each of four test portions,
|
|
// the concentration of each portion is significantly different,
|
|
// the values may NOT be pooled.
|
|
// (Called a 'paired test' by Miller and Miller
|
|
// because each portion analysed has a different concentration.)
|
|
|
|
// Portion Wet oxidation Direct Extraction
|
|
// 1 71 76
|
|
// 2 61 68
|
|
// 3 50 48
|
|
// 4 60 57
|
|
|
|
const int portions = 4;
|
|
const int methods = 2;
|
|
float data [portions][methods] = {{71, 76}, {61,68}, {50, 48}, {60, 57}};
|
|
float diffs[portions];
|
|
|
|
int main()
|
|
{
|
|
cout << "Example3 using Student's t function. " << endl;
|
|
float mean_diff = 0.f;
|
|
cout << "\n""Portion wet_oxidation Direct_extraction difference" << endl;
|
|
for (int portion = 0; portion < portions; portion++)
|
|
{ // Echo data and differences.
|
|
diffs[portion] = data[portion][0] - data[portion][1];
|
|
mean_diff += diffs[portion];
|
|
cout << setw(4) << portion << ' ' << setw(14) << data[portion][0] << ' ' << setw(18)<< data[portion][1] << ' ' << setw(9) << diffs[portion] << endl;
|
|
}
|
|
mean_diff /= portions;
|
|
cout << "Mean difference = " << mean_diff << endl; // -1.75
|
|
|
|
float sd_diffs = 0.f;
|
|
for (int portion = 0; portion < portions; portion++)
|
|
{ // Calculate standard deviation of differences.
|
|
sd_diffs +=(diffs[portion] - mean_diff) * (diffs[portion] - mean_diff);
|
|
}
|
|
int degrees_of_freedom = portions-1; // Use the n-1 formula.
|
|
sd_diffs /= degrees_of_freedom;
|
|
sd_diffs = sqrt(sd_diffs);
|
|
cout << "Standard deviation of differences = " << sd_diffs << endl; // 4.99166
|
|
// Standard deviation of differences = 4.99166
|
|
double t = mean_diff * sqrt(static_cast<double>(portions))/ sd_diffs; // -0.70117
|
|
cout << "Student's t = " << t << ", if " << degrees_of_freedom << " degrees of freedom." << endl;
|
|
// Student's t = -0.70117, if 3 degrees of freedom.
|
|
cout << "Probability of the means being different is "
|
|
<< 2.F * cdf(students_t(degrees_of_freedom), t) << "."<< endl; // 0.266846 * 2 = 0.533692
|
|
// Double the probability because using a 'two-sided test' because
|
|
// mean for 'Wet oxidation' could be either
|
|
// greater OR LESS THAN for 'Direct extraction'.
|
|
|
|
return 0;
|
|
} // int main()
|
|
|
|
/*
|
|
|
|
Output is:
|
|
|
|
Example3 using Student's t function.
|
|
Portion wet_oxidation Direct_extraction difference
|
|
0 71 76 -5
|
|
1 61 68 -7
|
|
2 50 48 2
|
|
3 60 57 3
|
|
Mean difference = -1.75
|
|
Standard deviation of differences = 4.99166
|
|
Student's t = -0.70117, if 3 degrees of freedom.
|
|
Probability of the means being different is 0.533692.
|
|
|
|
*/
|
|
|
|
|
|
|
|
|