(Fisher-Snedecor) F Distribution
This applet illustrates the F distribution. There are two slider
bars which allow changing the numerator and denominator degree of
freedom parameters of the distribution. In general, we use the F
distribution to compare variances.
The numerator degree of freedom
parameter is related to the number of populations that we compare
and the denominator degrees of freedom relates to the total number of
observations in our samples. As such, the denominator degree of
freedom parameter is almost always larger than the numerator
degree of freedom parameter. Verify that the mean, variance, skewness,
and kurtosis are not always defined.
The mean is defined only when the denominator degree of freedom
parameter is larger than 2. The variance is defined only when the
denominator degree of freedom is larger than 4. The skewness
is defined only when the denominator degree of freedom parameter is
larger than 6. The kurtosis is defined only when the denominator
degree of freedom parameter is larger than 8.
Note how changing either parameter alters the shape
and the center of the distribution. Also note that this distribution is
only valid for nonnegative numbers unlike the normal and the Student's
t distributions.
Several statistics are shown for the distribution below the illustration
of the density and distribution plots.
Click the Run button below when the applet has completed loading.