<title>F Distribution Examples</title>
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The test statistic for an F-test is simply the ratio of the square of the
two standard deviations:
</p>
-<p>
- F = s<sub>1</sub><sup>2</sup> / s<sub>2</sub><sup>2</sup>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">F = s<sub>1</sub><sup>2</sup> / s<sub>2</sub><sup>2</sup></span>
+ </p></blockquote></div>
<p>
where s<sub>1</sub> is the standard deviation of the first sample and s<sub>2</sub>
is the standard
The upper and lower critical values can be computed using the quantile
function:
</p>
-<p>
- F<sub>(1-alpha; N1-1, N2-1)</sub> = <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">fisher_f</span><span class="special">(</span><span class="identifier">N1</span><span class="special">-</span><span class="number">1</span><span class="special">,</span> <span class="identifier">N2</span><span class="special">-</span><span class="number">1</span><span class="special">),</span>
- <span class="identifier">alpha</span><span class="special">)</span></code>
- </p>
-<p>
- F<sub>(alpha; N1-1, N2-1)</sub> = <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">fisher_f</span><span class="special">(</span><span class="identifier">N1</span><span class="special">-</span><span class="number">1</span><span class="special">,</span> <span class="identifier">N2</span><span class="special">-</span><span class="number">1</span><span class="special">),</span>
- <span class="identifier">alpha</span><span class="special">))</span></code>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">F<sub>(1-alpha; N1-1, N2-1)</sub> = <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">fisher_f</span><span class="special">(</span><span class="identifier">N1</span><span class="special">-</span><span class="number">1</span><span class="special">,</span>
+ <span class="identifier">N2</span><span class="special">-</span><span class="number">1</span><span class="special">),</span> <span class="identifier">alpha</span><span class="special">)</span></code></span>
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">F<sub>(alpha; N1-1, N2-1)</sub> = <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">fisher_f</span><span class="special">(</span><span class="identifier">N1</span><span class="special">-</span><span class="number">1</span><span class="special">,</span>
+ <span class="identifier">N2</span><span class="special">-</span><span class="number">1</span><span class="special">),</span> <span class="identifier">alpha</span><span class="special">))</span></code></span>
+ </p></blockquote></div>
<p>
In our example program we need both upper and lower critical values for
alpha and for alpha/2: