libs/math/example/f_test.cpp
// Copyright John Maddock 2006 // Copyright Paul A. Bristow 2007, 2008, 2010 // 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) #ifdef _MSC_VER # pragma warning(disable: 4512) // assignment operator could not be generated. # pragma warning(disable: 4510) // default constructor could not be generated. # pragma warning(disable: 4610) // can never be instantiated - user defined constructor required. # pragma warning(disable: 4180) // qualifier has no effect (in Fusion). #endif #include <iostream> using std::cout; using std::endl; using std::left; using std::fixed; using std::right; using std::scientific; #include <iomanip> using std::setw; using std::setprecision; #include <boost/math/distributions/fisher_f.hpp> void f_test( double sd1, // Sample 1 std deviation double sd2, // Sample 2 std deviation double N1, // Sample 1 size double N2, // Sample 2 size double alpha) // Significance level { // // An F test applied to two sets of data. // We are testing the null hypothesis that the // standard deviation of the samples is equal, and // that any variation is down to chance. We can // also test the alternative hypothesis that any // difference is not down to chance. // See http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm // // Avoid "using namespace boost::math;" because of potential name ambiguity. using boost::math::fisher_f; // Print header: cout << "____________________________________\n" "F test for equal standard deviations\n" "____________________________________\n\n"; cout << setprecision(5); cout << "Sample 1:\n"; cout << setw(55) << left << "Number of Observations" << "= " << N1 << "\n"; cout << setw(55) << left << "Sample Standard Deviation" << "= " << sd1 << "\n\n"; cout << "Sample 2:\n"; cout << setw(55) << left << "Number of Observations" << "= " << N2 << "\n"; cout << setw(55) << left << "Sample Standard Deviation" << "= " << sd2 << "\n\n"; // // Now we can calculate and output some stats: // // F-statistic: double F = (sd1 / sd2); F *= F; cout << setw(55) << left << "Test Statistic" << "= " << F << "\n\n"; // // Finally define our distribution, and get the probability: // fisher_f dist(N1 - 1, N2 - 1); double p = cdf(dist, F); cout << setw(55) << left << "CDF of test statistic: " << "= " << setprecision(3) << scientific << p << "\n"; double ucv = quantile(complement(dist, alpha)); double ucv2 = quantile(complement(dist, alpha / 2)); double lcv = quantile(dist, alpha); double lcv2 = quantile(dist, alpha / 2); cout << setw(55) << left << "Upper Critical Value at alpha: " << "= " << setprecision(3) << scientific << ucv << "\n"; cout << setw(55) << left << "Upper Critical Value at alpha/2: " << "= " << setprecision(3) << scientific << ucv2 << "\n"; cout << setw(55) << left << "Lower Critical Value at alpha: " << "= " << setprecision(3) << scientific << lcv << "\n"; cout << setw(55) << left << "Lower Critical Value at alpha/2: " << "= " << setprecision(3) << scientific << lcv2 << "\n\n"; // // Finally print out results of null and alternative hypothesis: // cout << setw(55) << left << "Results for Alternative Hypothesis and alpha" << "= " << setprecision(4) << fixed << alpha << "\n\n"; cout << "Alternative Hypothesis Conclusion\n"; cout << "Standard deviations are unequal (two sided test) "; if((ucv2 < F) || (lcv2 > F)) cout << "NOT REJECTED\n"; else cout << "REJECTED\n"; cout << "Standard deviation 1 is less than standard deviation 2 "; if(lcv > F) cout << "NOT REJECTED\n"; else cout << "REJECTED\n"; cout << "Standard deviation 1 is greater than standard deviation 2 "; if(ucv < F) cout << "NOT REJECTED\n"; else cout << "REJECTED\n"; cout << endl << endl; } int main() { // // Run tests for ceramic strength data: // see http://www.itl.nist.gov/div898/handbook/eda/section4/eda42a1.htm // The data for this case study were collected by Said Jahanmir of the // NIST Ceramics Division in 1996 in connection with a NIST/industry // ceramics consortium for strength optimization of ceramic strength. // f_test(65.54909, 61.85425, 240, 240, 0.05); // // And again for the process change comparison: // see http://www.itl.nist.gov/div898/handbook/prc/section3/prc32.htm // A new procedure to assemble a device is introduced and tested for // possible improvement in time of assembly. The question being addressed // is whether the standard deviation of the new assembly process (sample 2) is // better (i.e., smaller) than the standard deviation for the old assembly // process (sample 1). // f_test(4.9082, 2.5874, 11, 9, 0.05); return 0; } /* Output: f_test.cpp F-test_example1.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\F_test_example1.exe ____________________________________ F test for equal standard deviations ____________________________________ Sample 1: Number of Observations = 240 Sample Standard Deviation = 65.549 Sample 2: Number of Observations = 240 Sample Standard Deviation = 61.854 Test Statistic = 1.123 CDF of test statistic: = 8.148e-001 Upper Critical Value at alpha: = 1.238e+000 Upper Critical Value at alpha/2: = 1.289e+000 Lower Critical Value at alpha: = 8.080e-001 Lower Critical Value at alpha/2: = 7.756e-001 Results for Alternative Hypothesis and alpha = 0.0500 Alternative Hypothesis Conclusion Standard deviations are unequal (two sided test) REJECTED Standard deviation 1 is less than standard deviation 2 REJECTED Standard deviation 1 is greater than standard deviation 2 REJECTED ____________________________________ F test for equal standard deviations ____________________________________ Sample 1: Number of Observations = 11.00000 Sample Standard Deviation = 4.90820 Sample 2: Number of Observations = 9.00000 Sample Standard Deviation = 2.58740 Test Statistic = 3.59847 CDF of test statistic: = 9.589e-001 Upper Critical Value at alpha: = 3.347e+000 Upper Critical Value at alpha/2: = 4.295e+000 Lower Critical Value at alpha: = 3.256e-001 Lower Critical Value at alpha/2: = 2.594e-001 Results for Alternative Hypothesis and alpha = 0.0500 Alternative Hypothesis Conclusion Standard deviations are unequal (two sided test) REJECTED Standard deviation 1 is less than standard deviation 2 REJECTED Standard deviation 1 is greater than standard deviation 2 NOT REJECTED ____________________________________ F test for equal standard deviations ____________________________________ Sample 1: Number of Observations = 240 Sample Standard Deviation = 65.549 Sample 2: Number of Observations = 240 Sample Standard Deviation = 61.854 Test Statistic = 1.123 CDF of test statistic: = 8.148e-001 Upper Critical Value at alpha: = 1.238e+000 Upper Critical Value at alpha/2: = 1.289e+000 Lower Critical Value at alpha: = 8.080e-001 Lower Critical Value at alpha/2: = 7.756e-001 Results for Alternative Hypothesis and alpha = 0.0500 Alternative Hypothesis Conclusion Standard deviations are unequal (two sided test) REJECTED Standard deviation 1 is less than standard deviation 2 REJECTED Standard deviation 1 is greater than standard deviation 2 REJECTED ____________________________________ F test for equal standard deviations ____________________________________ Sample 1: Number of Observations = 11.00000 Sample Standard Deviation = 4.90820 Sample 2: Number of Observations = 9.00000 Sample Standard Deviation = 2.58740 Test Statistic = 3.59847 CDF of test statistic: = 9.589e-001 Upper Critical Value at alpha: = 3.347e+000 Upper Critical Value at alpha/2: = 4.295e+000 Lower Critical Value at alpha: = 3.256e-001 Lower Critical Value at alpha/2: = 2.594e-001 Results for Alternative Hypothesis and alpha = 0.0500 Alternative Hypothesis Conclusion Standard deviations are unequal (two sided test) REJECTED Standard deviation 1 is less than standard deviation 2 REJECTED Standard deviation 1 is greater than standard deviation 2 NOT REJECTED */