1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Parameters can be calculated</title> 5<link rel="stylesheet" href="../../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../overview.html" title="Overview of Statistical Distributions"> 9<link rel="prev" href="complements.html" title="Complements are supported too - and when to use them"> 10<link rel="next" href="summary.html" title="Summary"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="complements.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../overview.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="summary.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 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. 55 </p> 56</div> 57<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 58<td align="left"></td> 59<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 60 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 61 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 62 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 63 Daryle Walker and Xiaogang Zhang<p> 64 Distributed under the Boost Software License, Version 1.0. (See accompanying 65 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>) 66 </p> 67</div></td> 68</tr></table> 69<hr> 70<div class="spirit-nav"> 71<a accesskey="p" href="complements.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../overview.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="summary.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 72</div> 73</body> 74</html> 75
