| // 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 |
| |
| |
| |
| */ |
| |
