Pub. date: 2008 | Online Pub. Date: November 27, 2007 | DOI:
10.4135/9781412953948 | Print ISBN: 9781412928168 | Online ISBN:
9781412953948| Publisher:SAGE Publications, Inc.About this
encyclopedia Marjorie E. Bond The F test is used for hypotheses
concerning variances. It is used to test whether two variances
are equal and is also used in the analysis of variance (ANOVA).
Let U and V be two independent chi-square random variables
having m and n degrees of freedom ( df ), respectively. The
ratio F = ( U = m )/( V = n )hasan F distribution with numerator
df equal to m and denominator df equal to n . Two properties of
the F distribution are as follows If X ∼ F m,n , then 1/X ∼ F
n,m , that is, the reciprocal of an F random variable is again
an F random variable. If X ∼ t m (X has a t distribution with df
= m ), then X 2 ∼ F 1,m . The F test is H ...