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There is a following answer to an exercise in a text book:

The hypotheses are \begin{align*} H_0 &: Var_1 = Var_2\\ H_1 &: Var_1 \neq Var_2 \end{align*} Computation: $f = 78.800/913.333 = 0.086$.

Since $\text{P-value} = 2P(f < 0.086) = (2)(0.0164) =0.0328$ for $4$ and $6$ degrees of freedom, the variability of running time for company $1$ is significantly less than, at level $0.0328$, the variability of running time for company $2$. So the question is why do they multiple $\text{P-value}$ by $2$? I saw they did that when they were using $T$ or Normal distributions but the $F$ distribution is not symmetrical.

Gilles
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Nikolai Felix
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  • See the discussion [here](http://stats.stackexchange.com/q/67543/805) (which mostly covers it), and the last part of [this answer](http://stats.stackexchange.com/questions/76689/how-to-compare-the-mean-of-two-samples-whose-data-fits-exponential-distributions/76695#76695), which gives some links, and [this](http://stats.stackexchange.com/questions/94914/how-to-get-f-test-p-value/94945#94945) which gives some more discussion. Also see the comments under [this](http://stats.stackexchange.com/questions/55550/how-do-i-interpret-the-results-from-the-f-test-in-excel/55553#55553) answer. – Glen_b Aug 24 '14 at 06:40
  • Short version: it's a common approximation (dare one say 'so common to seems many people don't know how to do it any other way'?). None of those links are *quite* a duplicate - though the third one perhaps comes closest to a duplicate, the first one (which really isn't) probably comes closer to answering it. – Glen_b Aug 24 '14 at 06:43
  • Some of what's [here](http://stats.stackexchange.com/questions/64311/how-to-read-off-0-975-alpha-value-in-f-table/64313#64313) might also help. – Glen_b Aug 24 '14 at 06:51

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