ceph/src/boost/libs/math/example/f_test.cpp

   1 // Copyright John Maddock 2006
   2 // Copyright Paul A. Bristow 2007, 2008, 2010
   3
   4 // Use, modification and distribution are subject to the
   5 // Boost Software License, Version 1.0.
   6 // (See accompanying file LICENSE_1_0.txt
   7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   8
   9 #ifdef _MSC_VER
  10 #  pragma warning(disable: 4512) // assignment operator could not be generated.
  11 #  pragma warning(disable: 4510) // default constructor could not be generated.
  12 #  pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
  13 #  pragma warning(disable: 4180) // qualifier has no effect (in Fusion).
  14 #endif
  15
  16 #include <iostream>
  17 using std::cout; using std::endl;
  18 using std::left; using std::fixed; using std::right; using std::scientific;
  19 #include <iomanip>
  20 using std::setw;
  21 using std::setprecision;
  22
  23 #include <boost/math/distributions/fisher_f.hpp>
  24
  25 void f_test(
  26        double sd1,     // Sample 1 std deviation
  27        double sd2,     // Sample 2 std deviation
  28        double N1,      // Sample 1 size
  29        double N2,      // Sample 2 size
  30        double alpha)  // Significance level
  31 {
  32    //
  33    // An F test applied to two sets of data.
  34    // We are testing the null hypothesis that the
  35    // standard deviation of the samples is equal, and
  36    // that any variation is down to chance.  We can
  37    // also test the alternative hypothesis that any
  38    // difference is not down to chance.
  39    // See http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
  40    //
  41    // Avoid "using namespace boost::math;" because of potential name ambiguity.
  42    using boost::math::fisher_f;
  43
  44    // Print header:
  45    cout <<
  46       "____________________________________\n"
  47       "F test for equal standard deviations\n"
  48       "____________________________________\n\n";
  49    cout << setprecision(5);
  50    cout << "Sample 1:\n";
  51    cout << setw(55) << left << "Number of Observations" << "=  " << N1 << "\n";
  52    cout << setw(55) << left << "Sample Standard Deviation" << "=  " << sd1 << "\n\n";
  53    cout << "Sample 2:\n";
  54    cout << setw(55) << left << "Number of Observations" << "=  " << N2 << "\n";
  55    cout << setw(55) << left << "Sample Standard Deviation" << "=  " << sd2 << "\n\n";
  56    //
  57    // Now we can calculate and output some stats:
  58    //
  59    // F-statistic:
  60    double F = (sd1 / sd2);
  61    F *= F;
  62    cout << setw(55) << left << "Test Statistic" << "=  " << F << "\n\n";
  63    //
  64    // Finally define our distribution, and get the probability:
  65    //
  66    fisher_f dist(N1 - 1, N2 - 1);
  67    double p = cdf(dist, F);
  68    cout << setw(55) << left << "CDF of test statistic: " << "=  "
  69       << setprecision(3) << scientific << p << "\n";
  70    double ucv = quantile(complement(dist, alpha));
  71    double ucv2 = quantile(complement(dist, alpha / 2));
  72    double lcv = quantile(dist, alpha);
  73    double lcv2 = quantile(dist, alpha / 2);
  74    cout << setw(55) << left << "Upper Critical Value at alpha: " << "=  "
  75       << setprecision(3) << scientific << ucv << "\n";
  76    cout << setw(55) << left << "Upper Critical Value at alpha/2: " << "=  "
  77       << setprecision(3) << scientific << ucv2 << "\n";
  78    cout << setw(55) << left << "Lower Critical Value at alpha: " << "=  "
  79       << setprecision(3) << scientific << lcv << "\n";
  80    cout << setw(55) << left << "Lower Critical Value at alpha/2: " << "=  "
  81       << setprecision(3) << scientific << lcv2 << "\n\n";
  82    //
  83    // Finally print out results of null and alternative hypothesis:
  84    //
  85    cout << setw(55) << left <<
  86       "Results for Alternative Hypothesis and alpha" << "=  "
  87       << setprecision(4) << fixed << alpha << "\n\n";
  88    cout << "Alternative Hypothesis                                    Conclusion\n";
  89    cout << "Standard deviations are unequal (two sided test)          ";
  90    if((ucv2 < F) || (lcv2 > F))
  91       cout << "NOT REJECTED\n";
  92    else
  93       cout << "REJECTED\n";
  94    cout << "Standard deviation 1 is less than standard deviation 2    ";
  95    if(lcv > F)
  96       cout << "NOT REJECTED\n";
  97    else
  98       cout << "REJECTED\n";
  99    cout << "Standard deviation 1 is greater than standard deviation 2 ";
 100    if(ucv < F)
 101       cout << "NOT REJECTED\n";
 102    else
 103       cout << "REJECTED\n";
 104    cout << endl << endl;
 105 }
 106
 107 int main()
 108 {
 109    //
 110    // Run tests for ceramic strength data:
 111    // see http://www.itl.nist.gov/div898/handbook/eda/section4/eda42a1.htm
 112    // The data for this case study were collected by Said Jahanmir of the
 113    // NIST Ceramics Division in 1996 in connection with a NIST/industry
 114    // ceramics consortium for strength optimization of ceramic strength.
 115    //
 116    f_test(65.54909, 61.85425, 240, 240, 0.05);
 117    //
 118    // And again for the process change comparison:
 119    // see http://www.itl.nist.gov/div898/handbook/prc/section3/prc32.htm
 120    // A new procedure to assemble a device is introduced and tested for
 121    // possible improvement in time of assembly. The question being addressed
 122    // is whether the standard deviation of the new assembly process (sample 2) is
 123    // better (i.e., smaller) than the standard deviation for the old assembly
 124    // process (sample 1).
 125    //
 126    f_test(4.9082, 2.5874, 11, 9, 0.05);
 127    return 0;
 128 }
 129
 130 /*
 131
 132 Output:
 133
 134   f_test.cpp
 135   F-test_example1.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\F_test_example1.exe
 136   ____________________________________
 137   F test for equal standard deviations
 138   ____________________________________
 139
 140   Sample 1:
 141   Number of Observations                                 =  240
 142   Sample Standard Deviation                              =  65.549
 143
 144   Sample 2:
 145   Number of Observations                                 =  240
 146   Sample Standard Deviation                              =  61.854
 147
 148   Test Statistic                                         =  1.123
 149
 150   CDF of test statistic:                                 =  8.148e-001
 151   Upper Critical Value at alpha:                         =  1.238e+000
 152   Upper Critical Value at alpha/2:                       =  1.289e+000
 153   Lower Critical Value at alpha:                         =  8.080e-001
 154   Lower Critical Value at alpha/2:                       =  7.756e-001
 155
 156   Results for Alternative Hypothesis and alpha           =  0.0500
 157
 158   Alternative Hypothesis                                    Conclusion
 159   Standard deviations are unequal (two sided test)          REJECTED
 160   Standard deviation 1 is less than standard deviation 2    REJECTED
 161   Standard deviation 1 is greater than standard deviation 2 REJECTED
 162
 163
 164   ____________________________________
 165   F test for equal standard deviations
 166   ____________________________________
 167
 168   Sample 1:
 169   Number of Observations                                 =  11.00000
 170   Sample Standard Deviation                              =  4.90820
 171
 172   Sample 2:
 173   Number of Observations                                 =  9.00000
 174   Sample Standard Deviation                              =  2.58740
 175
 176   Test Statistic                                         =  3.59847
 177
 178   CDF of test statistic:                                 =  9.589e-001
 179   Upper Critical Value at alpha:                         =  3.347e+000
 180   Upper Critical Value at alpha/2:                       =  4.295e+000
 181   Lower Critical Value at alpha:                         =  3.256e-001
 182   Lower Critical Value at alpha/2:                       =  2.594e-001
 183
 184   Results for Alternative Hypothesis and alpha           =  0.0500
 185
 186   Alternative Hypothesis                                    Conclusion
 187   Standard deviations are unequal (two sided test)          REJECTED
 188   Standard deviation 1 is less than standard deviation 2    REJECTED
 189   Standard deviation 1 is greater than standard deviation 2 NOT REJECTED
 190
 191
 192   ____________________________________
 193   F test for equal standard deviations
 194   ____________________________________
 195
 196   Sample 1:
 197   Number of Observations                                 =  240
 198   Sample Standard Deviation                              =  65.549
 199
 200   Sample 2:
 201   Number of Observations                                 =  240
 202   Sample Standard Deviation                              =  61.854
 203
 204   Test Statistic                                         =  1.123
 205
 206   CDF of test statistic:                                 =  8.148e-001
 207   Upper Critical Value at alpha:                         =  1.238e+000
 208   Upper Critical Value at alpha/2:                       =  1.289e+000
 209   Lower Critical Value at alpha:                         =  8.080e-001
 210   Lower Critical Value at alpha/2:                       =  7.756e-001
 211
 212   Results for Alternative Hypothesis and alpha           =  0.0500
 213
 214   Alternative Hypothesis                                    Conclusion
 215   Standard deviations are unequal (two sided test)          REJECTED
 216   Standard deviation 1 is less than standard deviation 2    REJECTED
 217   Standard deviation 1 is greater than standard deviation 2 REJECTED
 218
 219
 220   ____________________________________
 221   F test for equal standard deviations
 222   ____________________________________
 223
 224   Sample 1:
 225   Number of Observations                                 =  11.00000
 226   Sample Standard Deviation                              =  4.90820
 227
 228   Sample 2:
 229   Number of Observations                                 =  9.00000
 230   Sample Standard Deviation                              =  2.58740
 231
 232   Test Statistic                                         =  3.59847
 233
 234   CDF of test statistic:                                 =  9.589e-001
 235   Upper Critical Value at alpha:                         =  3.347e+000
 236   Upper Critical Value at alpha/2:                       =  4.295e+000
 237   Lower Critical Value at alpha:                         =  3.256e-001
 238   Lower Critical Value at alpha/2:                       =  2.594e-001
 239
 240   Results for Alternative Hypothesis and alpha           =  0.0500
 241
 242   Alternative Hypothesis                                    Conclusion
 243   Standard deviations are unequal (two sided test)          REJECTED
 244   Standard deviation 1 is less than standard deviation 2    REJECTED
 245   Standard deviation 1 is greater than standard deviation 2 NOT REJECTED
 246
 247
 248
 249 */
 250