Statistics and Probability Glossary
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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 ) ].
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