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Unformatted text preview: is symmetric about zero and tends asymptotically to the standard normal distribution. Its critical values can be found in statistical tables. The F distribution is deﬁned in terms of two independent χ 2 variables. Let u and υ be independently distributed χ 2 variables with ν 1 and ν 2 degrees of freedom, respectively. Then the statistic F = u/ν 1 υ/ν 2 (2) has the F distribution with ( ν 1 ,ν 2 ) degrees of freedom (critical values can be found in statistical tables). If we square the expression for t , the result may be written as t 2 = z 2 / 1 υ/ν 2 (3) where z 2 , being the square of a standard normal variable, has the χ 2 (1) distribution. Thus t 2 = F (1 ,ν ), that is, the square of a t variable with ν degrees of freedom is an F distribution with (1 .ν ) degrees of freedom. 1...
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 Spring '10
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