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| 25 | <div class="section"> | |
| 26 | <div class="titlepage"><div><div><h4 class="title"> | |
| 27 | <a name="math_toolkit.stat_tut.overview.parameters"></a><a class="link" href="parameters.html" title="Parameters can be calculated">Parameters | |
| 28 | can be calculated</a> | |
| 29 | </h4></div></div></div> | |
| 30 | <p> | |
| 31 | Sometimes it's the parameters that define the distribution that you need | |
| 32 | to find. Suppose, for example, you have conducted a Students-t test for | |
| 33 | equal means and the result is borderline. Maybe your two samples differ | |
| 34 | from each other, or maybe they don't; based on the result of the test you | |
| 35 | can't be sure. A legitimate question to ask then is "How many more | |
| 36 | measurements would I have to take before I would get an X% probability | |
| 37 | that the difference is real?" Parameter finders can answer questions | |
| 38 | like this, and are necessarily different for each distribution. They are | |
| 39 | implemented as static member functions of the distributions, for example: | |
| 40 | </p> | |
| 41 | <pre class="programlisting"><span class="identifier">students_t</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span> | |
| 42 | <span class="number">1.3</span><span class="special">,</span> <span class="comment">// difference from true mean to detect</span> | |
| 43 | <span class="number">0.05</span><span class="special">,</span> <span class="comment">// maximum risk of falsely rejecting the null-hypothesis.</span> | |
| 44 | <span class="number">0.1</span><span class="special">,</span> <span class="comment">// maximum risk of falsely failing to reject the null-hypothesis.</span> | |
| 45 | <span class="number">0.13</span><span class="special">);</span> <span class="comment">// sample standard deviation</span> | |
| 46 | </pre> | |
| 47 | <p> | |
| 48 | Returns the number of degrees of freedom required to obtain a 95% probability | |
| 49 | that the observed differences in means is not down to chance alone. In | |
| 50 | the case that a borderline Students-t test result was previously obtained, | |
| 51 | this can be used to estimate how large the sample size would have to become | |
| 52 | before the observed difference was considered significant. It assumes, | |
| 53 | of course, that the sample mean and standard deviation are invariant with | |
| 54 | sample size. | |
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| 59 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
| 60 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
| 61 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
| 62 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
| 63 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
| 64 | 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>) | |
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