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| <a name="math_toolkit.stat_tut.overview.parameters"></a><a class="link" href="parameters.html" title="Parameters can be calculated">Parameters |
| can be calculated</a> |
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| <p> |
| Sometimes it's the parameters that define the distribution that you need |
| to find. Suppose, for example, you have conducted a Students-t test for |
| equal means and the result is borderline. Maybe your two samples differ |
| from each other, or maybe they don't; based on the result of the test you |
| can't be sure. A legitimate question to ask then is "How many more |
| measurements would I have to take before I would get an X% probability |
| that the difference is real?" Parameter finders can answer questions |
| like this, and are necessarily different for each distribution. They are |
| implemented as static member functions of the distributions, for example: |
| </p> |
| <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> |
| <span class="number">1.3</span><span class="special">,</span> <span class="comment">// difference from true mean to detect</span> |
| <span class="number">0.05</span><span class="special">,</span> <span class="comment">// maximum risk of falsely rejecting the null-hypothesis.</span> |
| <span class="number">0.1</span><span class="special">,</span> <span class="comment">// maximum risk of falsely failing to reject the null-hypothesis.</span> |
| <span class="number">0.13</span><span class="special">);</span> <span class="comment">// sample standard deviation</span> |
| </pre> |
| <p> |
| Returns the number of degrees of freedom required to obtain a 95% probability |
| that the observed differences in means is not down to chance alone. In |
| the case that a borderline Students-t test result was previously obtained, |
| this can be used to estimate how large the sample size would have to become |
| before the observed difference was considered significant. It assumes, |
| of course, that the sample mean and standard deviation are invariant with |
| sample size. |
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