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 ...