Condition for Variance Ratio to have F-Distribution

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Theorem

Let $V$ be the variance ratio obtained as the result of an analysis of variance exercise.

Suppose that the errors are:

independently normally distributed
with zero expectation
with equal variances.

Under the null hypothesis of no difference between treatment means, $V$ has an F-distribution.


High values of variance ratio indicate rejection of the null hypothesis.


Proof


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Sources

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