July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short CourseBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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13.9 The F Distribution
Suppose we conduct a random sampling experiment whose outcome is a set of observations on two independent chi-square random variables X and Y with degrees of freedom v1 and v2, respectively. If we define a new variable
as the ratio of two independent chi-square random variables, each divided by its degrees of freedom, then F is said to follow an F distribution with v1 and v2 degrees of freedom and will be denoted as 
. As this notation reveals, the F distribution is a two-parameter family of distributions; and as we vary the parameters v1 and v2, we generate a whole assortment of different F distributions. It can be demonstrated that the F distribution is positively skewed for any values of v1 and v2, with
Moreover, unlike the t or Z distributions, the F distribution can only assume positive values.
What is the connection between Equation (13.24) and sampling from a normal population? Suppose a random sample of size n1 with variance 
is drawn from a N(μ ...
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