251 lines
9.8 KiB
C++
251 lines
9.8 KiB
C++
// Copyright John Maddock 2006
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// Copyright Paul A. Bristow 2007, 2008, 2010
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifdef _MSC_VER
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# pragma warning(disable: 4512) // assignment operator could not be generated.
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# pragma warning(disable: 4510) // default constructor could not be generated.
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# pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
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# pragma warning(disable: 4180) // qualifier has no effect (in Fusion).
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#endif
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#include <iostream>
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using std::cout; using std::endl;
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using std::left; using std::fixed; using std::right; using std::scientific;
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#include <iomanip>
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using std::setw;
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using std::setprecision;
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#include <boost/math/distributions/fisher_f.hpp>
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void f_test(
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double sd1, // Sample 1 std deviation
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double sd2, // Sample 2 std deviation
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double N1, // Sample 1 size
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double N2, // Sample 2 size
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double alpha) // Significance level
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{
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//
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// An F test applied to two sets of data.
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// We are testing the null hypothesis that the
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// standard deviation of the samples is equal, and
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// that any variation is down to chance. We can
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// also test the alternative hypothesis that any
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// difference is not down to chance.
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// See http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
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//
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// Avoid "using namespace boost::math;" because of potential name ambiguity.
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using boost::math::fisher_f;
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// Print header:
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cout <<
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"____________________________________\n"
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"F test for equal standard deviations\n"
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"____________________________________\n\n";
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cout << setprecision(5);
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cout << "Sample 1:\n";
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cout << setw(55) << left << "Number of Observations" << "= " << N1 << "\n";
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cout << setw(55) << left << "Sample Standard Deviation" << "= " << sd1 << "\n\n";
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cout << "Sample 2:\n";
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cout << setw(55) << left << "Number of Observations" << "= " << N2 << "\n";
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cout << setw(55) << left << "Sample Standard Deviation" << "= " << sd2 << "\n\n";
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//
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// Now we can calculate and output some stats:
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//
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// F-statistic:
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double F = (sd1 / sd2);
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F *= F;
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cout << setw(55) << left << "Test Statistic" << "= " << F << "\n\n";
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//
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// Finally define our distribution, and get the probability:
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//
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fisher_f dist(N1 - 1, N2 - 1);
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double p = cdf(dist, F);
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cout << setw(55) << left << "CDF of test statistic: " << "= "
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<< setprecision(3) << scientific << p << "\n";
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double ucv = quantile(complement(dist, alpha));
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double ucv2 = quantile(complement(dist, alpha / 2));
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double lcv = quantile(dist, alpha);
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double lcv2 = quantile(dist, alpha / 2);
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cout << setw(55) << left << "Upper Critical Value at alpha: " << "= "
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<< setprecision(3) << scientific << ucv << "\n";
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cout << setw(55) << left << "Upper Critical Value at alpha/2: " << "= "
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<< setprecision(3) << scientific << ucv2 << "\n";
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cout << setw(55) << left << "Lower Critical Value at alpha: " << "= "
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<< setprecision(3) << scientific << lcv << "\n";
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cout << setw(55) << left << "Lower Critical Value at alpha/2: " << "= "
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<< setprecision(3) << scientific << lcv2 << "\n\n";
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//
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// Finally print out results of null and alternative hypothesis:
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//
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cout << setw(55) << left <<
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"Results for Alternative Hypothesis and alpha" << "= "
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<< setprecision(4) << fixed << alpha << "\n\n";
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cout << "Alternative Hypothesis Conclusion\n";
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cout << "Standard deviations are unequal (two sided test) ";
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if((ucv2 < F) || (lcv2 > F))
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cout << "NOT REJECTED\n";
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else
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cout << "REJECTED\n";
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cout << "Standard deviation 1 is less than standard deviation 2 ";
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if(lcv > F)
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cout << "NOT REJECTED\n";
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else
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cout << "REJECTED\n";
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cout << "Standard deviation 1 is greater than standard deviation 2 ";
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if(ucv < F)
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cout << "NOT REJECTED\n";
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else
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cout << "REJECTED\n";
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cout << endl << endl;
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}
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int main()
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{
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//
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// Run tests for ceramic strength data:
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// see http://www.itl.nist.gov/div898/handbook/eda/section4/eda42a1.htm
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// The data for this case study were collected by Said Jahanmir of the
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// NIST Ceramics Division in 1996 in connection with a NIST/industry
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// ceramics consortium for strength optimization of ceramic strength.
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//
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f_test(65.54909, 61.85425, 240, 240, 0.05);
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//
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// And again for the process change comparison:
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// see http://www.itl.nist.gov/div898/handbook/prc/section3/prc32.htm
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// A new procedure to assemble a device is introduced and tested for
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// possible improvement in time of assembly. The question being addressed
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// is whether the standard deviation of the new assembly process (sample 2) is
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// better (i.e., smaller) than the standard deviation for the old assembly
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// process (sample 1).
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//
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f_test(4.9082, 2.5874, 11, 9, 0.05);
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return 0;
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}
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/*
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Output:
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f_test.cpp
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F-test_example1.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\F_test_example1.exe
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____________________________________
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F test for equal standard deviations
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____________________________________
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Sample 1:
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Number of Observations = 240
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Sample Standard Deviation = 65.549
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Sample 2:
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Number of Observations = 240
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Sample Standard Deviation = 61.854
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Test Statistic = 1.123
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CDF of test statistic: = 8.148e-001
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Upper Critical Value at alpha: = 1.238e+000
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Upper Critical Value at alpha/2: = 1.289e+000
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Lower Critical Value at alpha: = 8.080e-001
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Lower Critical Value at alpha/2: = 7.756e-001
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Results for Alternative Hypothesis and alpha = 0.0500
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Alternative Hypothesis Conclusion
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Standard deviations are unequal (two sided test) REJECTED
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Standard deviation 1 is less than standard deviation 2 REJECTED
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Standard deviation 1 is greater than standard deviation 2 REJECTED
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____________________________________
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F test for equal standard deviations
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____________________________________
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Sample 1:
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Number of Observations = 11.00000
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Sample Standard Deviation = 4.90820
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Sample 2:
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Number of Observations = 9.00000
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Sample Standard Deviation = 2.58740
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Test Statistic = 3.59847
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CDF of test statistic: = 9.589e-001
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Upper Critical Value at alpha: = 3.347e+000
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Upper Critical Value at alpha/2: = 4.295e+000
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Lower Critical Value at alpha: = 3.256e-001
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Lower Critical Value at alpha/2: = 2.594e-001
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Results for Alternative Hypothesis and alpha = 0.0500
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Alternative Hypothesis Conclusion
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Standard deviations are unequal (two sided test) REJECTED
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Standard deviation 1 is less than standard deviation 2 REJECTED
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Standard deviation 1 is greater than standard deviation 2 NOT REJECTED
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____________________________________
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F test for equal standard deviations
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____________________________________
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Sample 1:
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Number of Observations = 240
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Sample Standard Deviation = 65.549
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Sample 2:
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Number of Observations = 240
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Sample Standard Deviation = 61.854
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Test Statistic = 1.123
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CDF of test statistic: = 8.148e-001
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Upper Critical Value at alpha: = 1.238e+000
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Upper Critical Value at alpha/2: = 1.289e+000
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Lower Critical Value at alpha: = 8.080e-001
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Lower Critical Value at alpha/2: = 7.756e-001
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Results for Alternative Hypothesis and alpha = 0.0500
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Alternative Hypothesis Conclusion
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Standard deviations are unequal (two sided test) REJECTED
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Standard deviation 1 is less than standard deviation 2 REJECTED
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Standard deviation 1 is greater than standard deviation 2 REJECTED
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____________________________________
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F test for equal standard deviations
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____________________________________
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Sample 1:
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Number of Observations = 11.00000
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Sample Standard Deviation = 4.90820
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Sample 2:
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Number of Observations = 9.00000
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Sample Standard Deviation = 2.58740
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Test Statistic = 3.59847
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CDF of test statistic: = 9.589e-001
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Upper Critical Value at alpha: = 3.347e+000
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Upper Critical Value at alpha/2: = 4.295e+000
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Lower Critical Value at alpha: = 3.256e-001
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Lower Critical Value at alpha/2: = 2.594e-001
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Results for Alternative Hypothesis and alpha = 0.0500
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Alternative Hypothesis Conclusion
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Standard deviations are unequal (two sided test) REJECTED
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Standard deviation 1 is less than standard deviation 2 REJECTED
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Standard deviation 1 is greater than standard deviation 2 NOT REJECTED
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*/
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