| // Copyright John Maddock 2008 |
| // Copyright Paul A. Bristow 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) |
| |
| // Caution: this file contains Quickbook markup as well as code |
| // and comments, don't change any of the special comment markups! |
| |
| //[nccs_eg |
| |
| /*` |
| |
| This example computes a table of the power of the [chi][super 2] |
| test at the 5% significance level, for various degrees of freedom |
| and non-centrality parameters. The table is deliberately the same |
| as Table 6 from "The Non-Central [chi][super 2] and F-Distributions and |
| their applications.", P. B. Patnaik, Biometrika, Vol. 36, No. 1/2 (June 1949), |
| 202-232. |
| |
| First we need some includes to access the non-central chi squared distribution |
| (and some basic std output of course). |
| |
| */ |
| |
| #include <boost/math/distributions/non_central_chi_squared.hpp> |
| using boost::math::chi_squared; |
| using boost::math::non_central_chi_squared; |
| |
| #include <iostream> |
| using std::cout; using std::endl; |
| using std::setprecision; |
| |
| int main() |
| { |
| /*` |
| Create a table of the power of the [chi][super 2] test at |
| 5% significance level, start with a table header: |
| */ |
| cout << "[table\n[[[nu]]"; |
| for(int lam = 2; lam <= 20; lam += 2) |
| { |
| cout << "[[lambda]=" << lam << "]"; |
| } |
| cout << "]\n"; |
| |
| /*` |
| (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook). |
| |
| Enumerate the rows and columns and print the power of the test |
| for each table cell: |
| */ |
| |
| for(int n = 2; n <= 20; ++n) |
| { |
| cout << "[[" << n << "]"; |
| for(int lam = 2; lam <= 20; lam += 2) |
| { |
| /*` |
| Calculate the [chi][super 2] statistic for a 5% significance: |
| */ |
| double cs = quantile(complement(chi_squared(n), 0.05)); |
| /*` |
| The power of the test is given by the complement of the CDF |
| of the non-central [chi][super 2] distribution: |
| */ |
| double beta = cdf(complement(non_central_chi_squared(n, lam), cs)); |
| /*` |
| Then output the cell value: |
| */ |
| cout << "[" << setprecision(3) << beta << "]"; |
| } |
| cout << "]" << endl; |
| } |
| cout << "]" << endl; |
| } |
| |
| /*` |
| The output from this program is a table in Boost.Quickbook format as shown below. |
| |
| We can interpret this as follows - for example if [nu]=10 and [lambda]=10 |
| then the power of the test is 0.542 - so we have only a 54% chance of |
| correctly detecting that our null hypothesis is false, and a 46% chance |
| of incurring a type II error (failing to reject the null hypothesis when |
| it is in fact false): |
| |
| [table |
| [[[nu]][[lambda]=2][[lambda]=4][[lambda]=6][[lambda]=8][[lambda]=10][[lambda]=12][[lambda]=14][[lambda]=16][[lambda]=18][[lambda]=20]] |
| [[2][0.226][0.415][0.584][0.718][0.815][0.883][0.928][0.957][0.974][0.985]] |
| [[3][0.192][0.359][0.518][0.654][0.761][0.84][0.896][0.934][0.959][0.975]] |
| [[4][0.171][0.32][0.47][0.605][0.716][0.802][0.866][0.912][0.943][0.964]] |
| [[5][0.157][0.292][0.433][0.564][0.677][0.769][0.839][0.89][0.927][0.952]] |
| [[6][0.146][0.27][0.403][0.531][0.644][0.738][0.813][0.869][0.911][0.94]] |
| [[7][0.138][0.252][0.378][0.502][0.614][0.71][0.788][0.849][0.895][0.928]] |
| [[8][0.131][0.238][0.357][0.477][0.588][0.685][0.765][0.829][0.879][0.915]] |
| [[9][0.125][0.225][0.339][0.454][0.564][0.661][0.744][0.811][0.863][0.903]] |
| [[10][0.121][0.215][0.323][0.435][0.542][0.64][0.723][0.793][0.848][0.891]] |
| [[11][0.117][0.206][0.309][0.417][0.523][0.62][0.704][0.775][0.833][0.878]] |
| [[12][0.113][0.198][0.297][0.402][0.505][0.601][0.686][0.759][0.818][0.866]] |
| [[13][0.11][0.191][0.286][0.387][0.488][0.584][0.669][0.743][0.804][0.854]] |
| [[14][0.108][0.185][0.276][0.374][0.473][0.567][0.653][0.728][0.791][0.842]] |
| [[15][0.105][0.179][0.267][0.362][0.459][0.552][0.638][0.713][0.777][0.83]] |
| [[16][0.103][0.174][0.259][0.351][0.446][0.538][0.623][0.699][0.764][0.819]] |
| [[17][0.101][0.169][0.251][0.341][0.434][0.525][0.609][0.686][0.752][0.807]] |
| [[18][0.0992][0.165][0.244][0.332][0.423][0.512][0.596][0.673][0.74][0.796]] |
| [[19][0.0976][0.161][0.238][0.323][0.412][0.5][0.584][0.66][0.728][0.786]] |
| [[20][0.0961][0.158][0.232][0.315][0.402][0.489][0.572][0.648][0.716][0.775]] |
| ] |
| |
| See [@../../../example/nc_chi_sq_example.cpp nc_chi_sq_example.cpp] for the full C++ source code. |
| |
| */ |
| |
| //] |