# Statistics Dictionary

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### F Distribution

The distribution of all possible values of the f statistic is called an F distribution .

The curve of the F distribution depends on the degrees of freedom, v1 and v2. When describing an F distribution, the number of degrees of freedom v1 is always stated first. Thus, f(5, 9) would refer to an F distribution with v1 = 5 and v2 = 9 degrees of freedom; whereas f(9, 5) would refer to an F distribution with v1 = 9 and v2 = 5 degrees of freedom. Note that the curve represented by f(5, 9) would differ from the curve represented by f(9, 5).

The F distribution has the following properties:

• The mean of the distribution is equal to v1 / ( v2 - 2 ).
• The variance is equal to [ v22 * ( v1 + 2 ) ] / [ v1 * ( v2 - 2 ) * ( v2 - 4 ) ].
 See also: Tutorial: F Distribution | F Distribution Calculator