Ftable - Working with the F Distribution The random variable F n1 n 2 has an F-distribution with numerator degrees of freedom n1 and denominator degrees

Ftable - Working with the F Distribution The random...

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Working with the F Distribution The random variable ) 2 n , 1 n ( F has an F-distribution with numerator degrees of freedom n1 and denominator degrees of freedom n2. For a critical value c F such that α = > ) F F ( P c ) 2 n , 1 n ( then α = < c ) 1 n , 2 n ( F 1 F P Tables that follow give F-distribution critical values for α = 0.05 and α = 0.01 (generated with the SHAZAM Econometrics Software). Example: 05 . 0 ) 22 . 3 F ( P ) 10 , 6 ( = > and 05 . 0 ) 246 . 0 F ( P 06 . 4 1 F P ) 10 , 6 ( ) 10 , 6 ( = < = < This is illustrated in the figure. Additional Note: For denominator degrees of freedom 1 n F 2 ) 1 n ( ) , 1 n ( χ = where 2 ) 1 n ( χ has a chi-square distribution with n1 degrees of freedom. Figure Probability density function of the F- distribution with 6 numerator degrees of freedom and 10 denominator degrees of freedom showing the skewed shape of the distribution. Properties of the F-distribution are: mean 2 2 n 2 n - = , (n2>2) ; mode ) 2 2 n ( 1 n ) 2 1 n ( 2 n + - = , (n1>2) For the example: mean 25 . 1 8 10 = = and mode 556 . 0
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