ceph/src/boost/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html

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   4 <title>Comparing two paired samples with the Student's t distribution</title>
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  27 <a name="math_toolkit.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
  28           two paired samples with the Student's t distribution</a>
  29 </h5></div></div></div>
  30 <p>
  31             Imagine that we have a before and after reading for each item in the
  32             sample: for example we might have measured blood pressure before and
  33             after administration of a new drug. We can't pool the results and compare
  34             the means before and after the change, because each patient will have
  35             a different baseline reading. Instead we calculate the difference between
  36             before and after measurements in each patient, and calculate the mean
  37             and standard deviation of the differences. To test whether a significant
  38             change has taken place, we can then test the null-hypothesis that the
  39             true mean is zero using the same procedure we used in the single sample
  40             cases previously discussed.
  41           </p>
  42 <p>
  43             That means we can:
  44           </p>
  45 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  46 <li class="listitem">
  47                 <a class="link" href="tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculate
  48                 confidence intervals of the mean</a>. If the endpoints of the
  49                 interval differ in sign then we are unable to reject the null-hypothesis
  50                 that there is no change.
  51               </li>
  52 <li class="listitem">
  53                 <a class="link" href="tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Test
  54                 whether the true mean is zero</a>. If the result is consistent
  55                 with a true mean of zero, then we are unable to reject the null-hypothesis
  56                 that there is no change.
  57               </li>
  58 <li class="listitem">
  59                 <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
  60                 how many pairs of readings we would need in order to obtain a significant
  61                 result</a>.
  62               </li>
  63 </ul></div>
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  67 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  68       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  69       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  70       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  71         Distributed under the Boost Software License, Version 1.0. (See accompanying
  72         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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