| <html> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> |
| <title>Comparing two paired samples with the Student's t distribution</title> |
| <link rel="stylesheet" href="../../../../../../../../../../doc/src/boostbook.css" type="text/css"> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> |
| <link rel="home" href="../../../../../index.html" title="Math Toolkit"> |
| <link rel="up" href="../st_eg.html" title="Student's t Distribution Examples"> |
| <link rel="prev" href="two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test"> |
| <link rel="next" href="../cs_eg.html" title="Chi Squared Distribution Examples"> |
| </head> |
| <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> |
| <table cellpadding="2" width="100%"><tr> |
| <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../../../boost.png"></td> |
| <td align="center"><a href="../../../../../../../../../../index.html">Home</a></td> |
| <td align="center"><a href="../../../../../../../../../../libs/libraries.htm">Libraries</a></td> |
| <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../../../../../../../more/index.htm">More</a></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="two_sample_students_t.html"><img src="../../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../st_eg.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="../cs_eg.html"><img src="../../../../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| <div class="section" lang="en"> |
| <div class="titlepage"><div><div><h6 class="title"> |
| <a name="math_toolkit.dist.stat_tut.weg.st_eg.paired_st"></a><a class="link" href="paired_st.html" title="Comparing two paired samples with the Student's t distribution"> |
| Comparing two paired samples with the Student's t distribution</a> |
| </h6></div></div></div> |
| <p> |
| Imagine that we have a before and after reading for each item in the |
| sample: for example we might have measured blood pressure before and |
| after administration of a new drug. We can't pool the results and compare |
| the means before and after the change, because each patient will have |
| a different baseline reading. Instead we calculate the difference between |
| before and after measurements in each patient, and calculate the mean |
| and standard deviation of the differences. To test whether a significant |
| change has taken place, we can then test the null-hypothesis that the |
| true mean is zero using the same procedure we used in the single sample |
| cases previously discussed. |
| </p> |
| <p> |
| That means we can: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| <a class="link" href="tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculate |
| confidence intervals of the mean</a>. If the endpoints of the |
| interval differ in sign then we are unable to reject the null-hypothesis |
| that there is no change. |
| </li> |
| <li> |
| <a class="link" href="tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Test |
| whether the true mean is zero</a>. If the result is consistent |
| with a true mean of zero, then we are unable to reject the null-hypothesis |
| that there is no change. |
| </li> |
| <li> |
| <a class="link" href="tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Calculate |
| how many pairs of readings we would need in order to obtain a significant |
| result</a>. |
| </li> |
| </ul></div> |
| </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> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="two_sample_students_t.html"><img src="../../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../st_eg.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="../cs_eg.html"><img src="../../../../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| </body> |
| </html> |
