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[SVN r39653]
This commit is contained in:
Paul A. Bristow
2007-10-02 17:12:33 +00:00
parent 1c5fffdd28
commit cabc722e56
2 changed files with 29 additions and 96 deletions
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41
example/students_t_example1.cpp
View File

@@ -1,6 +1,6 @@
// students_t_example1.cpp
// Copyright Paul A. Bristow 2006.
// Copyright Paul A. Bristow 2006, 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
@@ -46,8 +46,7 @@ double value[values] = {38.9, 37.4, 37.1};
using boost::math::students_t; // Probability of students_t(df, t).
#include <iostream>
using std::cout;
using std::endl;
using std::cout; using std::endl;
#include <iomanip>
using std::setprecision;
#include <cmath>
@@ -55,18 +54,15 @@ double value[values] = {38.9, 37.4, 37.1};
int main()
{
cout << "Example 1 using Student's t function. ";
#if defined(__FILE__) && defined(__TIMESTAMP__)
cout << " " << __FILE__ << ' ' << __TIMESTAMP__ << ' '<< _MSC_FULL_VER;
#endif
cout << endl;
cout << "Example 1 using Student's t function. " << endl;
// Example/test using tabulated value (deliberately coded as naively as possible).
// Example/test using tabulated value
// (deliberately coded as naively as possible).
// Null hypothesis is that there is no difference (greater or less) between measured and standard.
// Null hypothesis is that there is no difference (greater or less)
// between measured and standard.
double degrees_of_freedom = values-1; // 3-1 = 2
cout << "Measurement 1 = " << value[0] << ", measurement 2 = " << value[1] << ", measurement 3 = " << value[2] << endl;
double mean = (value[0] + value[1] + value[2]) / static_cast<double>(values);
cout << "Standard = " << standard << ", mean = " << mean << ", (mean - standard) = " << mean - standard << endl;
@@ -80,10 +76,10 @@ int main()
}
double t = (mean - standard) * std::sqrt(static_cast<double>(values)) / sd;
// cout << "Student's t = " << t << endl;
cout.precision(5); // Useful accuracy is only a few decimal digits, but seems to give at least 5.
cout << "Probability of Student's t is " << cdf(students_t(degrees_of_freedom), std::abs(t)) << endl; // 0.90657, is 1 tailed.
cout << "Student's t = " << t << endl;
cout.precision(2); // Useful accuracy is only a few decimal digits.
cout << "Probability of Student's t is " << cdf(students_t(degrees_of_freedom), std::abs(t)) << endl;
// 0.91, is 1 tailed.
// So there is insufficient evidence of a difference to meet a 95% (1 in 20) criterion.
return 0;
@@ -93,21 +89,12 @@ int main()
Output is:
------ Build started: Project: students_t_example1, Configuration: Debug Win32 ------
Compiling...
students_t_example1.cpp
Linking...
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\students_t_example1.exe"
Example 1 using Student's t function. ..\..\..\..\..\..\boost-sandbox\libs\math_functions\example\students_t_example1.cpp Sat Aug 12 16:54:41 2006 140050727
Example 1 using Student's t function.
Measurement 1 = 38.9, measurement 2 = 37.4, measurement 3 = 37.1
Standard = 38.9, mean = 37.8, (mean - standard) = -1.1
Standard deviation = 0.964365
Probability of Student's t is 0.90657
Build Time 0:03
Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\students_t_example1\Debug\BuildLog.htm"
students_t_example1 - 0 error(s), 0 warning(s)
========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
Student's t = -1.97566
Probability of Student's t is 0.91
*/

84
example/students_t_example3.cpp
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@@ -1,5 +1,5 @@
// students_t_example3.cpp
// Copyright Paul A. Bristow 2006.
// Copyright Paul A. Bristow 2006, 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
@@ -26,11 +26,6 @@
// but to his employer - the company insisted on the pseudonym
// so that it could turn a blind eye to the breach of its rules.
#ifdef _MSC_VER
# pragma warning(disable: 4702) // unreachable code
#endif
// 4996 4512
// The Students't distribution function is described at
// http://en.wikipedia.org/wiki/Student%27s_t_distribution
@@ -38,11 +33,9 @@
using boost::math::students_t; // Probability of students_t(df, t).
#include <iostream>
using std::cout;
using std::endl;
using std::cout; using std::endl;
#include <iomanip>
using std::setprecision;
using std::setw;
using std::setprecision; using std::setw;
#include <cmath>
using std::sqrt;
@@ -55,6 +48,8 @@
// 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
@@ -69,11 +64,7 @@ float diffs[portions];
int main()
{
cout << "Example3 using Student's t function. ";
#if defined(__FILE__) && defined(__TIMESTAMP__)
cout << " " << __FILE__ << ' ' << __TIMESTAMP__ << ' '<< _MSC_FULL_VER;
#endif
cout << endl;
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++)
@@ -92,44 +83,26 @@ int main()
}
int degrees_of_freedom = portions-1; // Use the n-1 formula.
sd_diffs /= degrees_of_freedom;
sd_diffs = sqrt(sd_diffs);
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; //
cout << "Probability of the means being different is " << 2.F * cdf(students_t(degrees_of_freedom), t) << "."<< endl; // 0.266846 * 2 =
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'.
// mean for 'Wet oxidation' could be either
// greater OR LESS THAN for 'Direct extraction'.
return 0;
} // int main()
/*
Check using http://faculty.vassar.edu/lowry/VassarStats.html
Output from avoid data using
Independent samples is
n = 4,
sum 242 and 249 total 491
sumsq 14862 15953 30815
SS 221 452.75 679.875
means 60.5 62.25 61.375
Mean diff = -1.75, t = -0.23, df 6,
independent samples: p 1-tailed 0.4128665, 2-tailed 0.825733
correlated samples: p 1-tailed 0.261635, 2-tailed 0.534327
(Called a paired test in Miller and Miller because each portion analysed has a different concentration.)
Output is:
------ Build started: Project: students_t_example3, Configuration: Debug Win32 ------
Compiling...
students_t_example3.cpp
Linking...
Atuorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\students_t_example3.exe"
Example3 using Student's t function. ..\..\..\..\..\..\boost-sandbox\libs\math_functions\example\students_t_example3.cpp Sat Aug 12 16:57:50 2006 140050727
Example3 using Student's t function.
Portion wet_oxidation Direct_extraction difference
0 71 76 -5
1 61 68 -7
@@ -139,33 +112,6 @@ 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.
Build Time 0:03
Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\students_t_example3\Debug\BuildLog.htm"
students_t_example3 - 0 error(s), 0 warning(s)
========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
------ Build started: Project: students_t_example3, Configuration: Release Win32 ------
Compiling...
students_t_example3.cpp
Linking...
Generating code
Finished generating code
Autorun "i:\boost-06-05-03-1300\libs\math\test\math_test\release\students_t_example3.exe"
Example3 using Student's t function. ..\..\..\..\..\..\boost-sandbox\libs\math_functions\example\students_t_example3.cpp Sat Aug 12 17:01:52 2006 140050727
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.
Build Time 0:04
Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\students_t_example3\Release\BuildLog.htm"
students_t_example3 - 0 error(s), 0 warning(s)
========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
*/