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| <div class="section" lang="en"> |
| <div class="titlepage"><div><div><h6 class="title"> |
| <a name="math_toolkit.dist.stat_tut.weg.nccs_eg.nccs_power_eg"></a><a class="link" href="nccs_power_eg.html" title="Tables of the power function of the χ2 test."> |
| Tables of the power function of the χ<sup>2</sup> test.</a> |
| </h6></div></div></div> |
| <p> |
| </p> |
| <p> |
| This example computes a table of the power of the χ<sup>2</sup> |
| 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 χ<sup>2</sup> and F-Distributions and their applications.", P. |
| B. Patnaik, Biometrika, Vol. 36, No. 1/2 (June 1949), 202-232. |
| </p> |
| <p> |
| </p> |
| <p> |
| First we need some includes to access the non-central chi squared |
| distribution (and some basic std output of course). |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">chi_squared</span><span class="special">;</span> |
| <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">non_central_chi_squared</span><span class="special">;</span> |
| |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> |
| <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> |
| <span class="special">{</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Create a table of the power of the χ<sup>2</sup> test at 5% significance level, |
| start with a table header: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[table\n[[[nu]]"</span><span class="special">;</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[[lambda]="</span> <span class="special"><<</span> <span class="identifier">lam</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"]\n"</span><span class="special">;</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook). |
| </p> |
| <p> |
| </p> |
| <p> |
| Enumerate the rows and columns and print the power of the test for |
| each table cell: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">n</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">n</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[["</span> <span class="special"><<</span> <span class="identifier">n</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span> |
| <span class="special">{</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Calculate the χ<sup>2</sup> statistic for a 5% significance: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cs</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| The power of the test is given by the complement of the CDF of the |
| non-central χ<sup>2</sup> distribution: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">beta</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">lam</span><span class="special">),</span> <span class="identifier">cs</span><span class="special">));</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Then output the cell value: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"> <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"["</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">beta</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"]"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"]"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| <span class="special">}</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| The output from this program is a table in Boost.Quickbook format |
| as shown below. |
| </p> |
| <p> |
| </p> |
| <p> |
| We can interpret this as follows - for example if ν=10 and λ=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): |
| </p> |
| <p> |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| ν |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=2 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=4 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=6 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=8 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=10 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=12 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=14 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=16 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=18 |
| </p> |
| </th> |
| <th> |
| <p> |
| λ=20 |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| 2 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.226 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.415 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.584 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.718 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.815 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.883 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.928 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.957 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.974 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.985 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 3 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.192 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.359 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.518 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.654 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.761 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.84 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.896 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.934 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.959 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.975 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 4 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.171 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.32 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.47 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.605 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.716 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.802 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.866 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.912 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.943 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.964 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 5 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.157 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.292 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.433 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.564 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.677 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.769 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.839 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.89 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.927 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.952 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 6 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.146 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.27 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.403 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.531 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.644 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.738 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.813 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.869 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.911 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.94 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 7 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.138 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.252 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.378 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.502 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.614 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.71 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.788 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.849 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.895 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.928 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 8 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.131 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.238 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.357 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.477 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.588 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.685 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.765 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.829 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.879 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.915 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 9 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.125 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.225 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.339 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.454 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.564 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.661 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.744 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.811 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.863 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.903 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 10 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.121 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.215 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.323 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.435 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.542 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.64 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.723 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.793 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.848 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.891 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 11 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.117 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.206 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.309 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.417 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.523 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.62 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.704 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.775 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.833 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.878 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 12 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.113 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.198 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.297 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.402 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.505 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.601 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.686 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.759 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.818 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.866 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 13 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.11 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.191 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.286 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.387 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.488 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.584 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.669 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.743 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.804 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.854 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 14 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.108 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.185 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.276 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.374 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.473 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.567 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.653 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.728 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.791 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.842 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 15 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.105 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.179 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.267 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.362 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.459 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.552 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.638 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.713 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.777 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.83 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 16 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.103 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.174 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.259 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.351 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.446 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.538 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.623 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.699 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.764 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.819 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 17 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.101 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.169 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.251 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.341 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.434 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.525 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.609 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.686 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.752 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.807 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 18 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.0992 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.165 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.244 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.332 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.423 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.512 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.596 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.673 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.74 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.796 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 19 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.0976 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.161 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.238 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.323 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.412 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.5 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.584 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.66 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.728 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.786 |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| 20 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.0961 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.158 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.232 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.315 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.402 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.489 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.572 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.648 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.716 |
| </p> |
| </td> |
| <td> |
| <p> |
| 0.775 |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <p> |
| </p> |
| <p> |
| See <a href="../../../../../../../../example/nc_chi_sq_example.cpp" target="_top">nc_chi_sq_example.cpp</a> |
| for the full C++ source code. |
| </p> |
| <p> |
| </p> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
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