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Diffstat (limited to 'src/boost/libs/math/example/f_test.cpp')
| -rw-r--r-- | src/boost/libs/math/example/f_test.cpp | 250 |
1 files changed, 250 insertions, 0 deletions
diff --git a/src/boost/libs/math/example/f_test.cpp b/src/boost/libs/math/example/f_test.cpp new file mode 100644 index 00000000..f7fabdee --- /dev/null +++ b/src/boost/libs/math/example/f_test.cpp @@ -0,0 +1,250 @@ +// 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 + + + +*/ + |