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<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>
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<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>
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<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 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>)
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