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| 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: |
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| <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, 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 |
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