F-distribution
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The F-distribution is used in classical statistics for hypothesis testing involving the comparison of variances between two samples (ANOVA = ANalysis Of VAriance), or for testing whether one model (such as a regression fit) is statistically superior to another. In also goes by the names Snedecor's distribution and the Fisher-Snedecor distribution.
The F-distribution is a positive-only distribution
The ratio of two random variates each having a ChiSquared distribution has a F-distribution.
Functions
FDist(dof1, dof2)
New to Analytica 5.2
The distribution function.
DensFDist(x, dof1, dof2)
The Analytic density function. Returns the probability density at «x» of an F-distribution with «dof1» and «dof2» degrees of freedom.
CumFDist(x, dof1, dof2)
The cumulative density at «x» for the F-distribution with degrees of freedom «dof1» and «dof2». This is the area under the probability density graph falling to the left of «x».
CumFDistInv(p, dof1, dof2)
The inverse cumulative density function (quantile function) of a F-distribution with «dof1» and «dof2» degrees of freedom. Returns the p^{th} fractile/quantile/percentile.
Statistics
F-tests
Are means of two normal distributions equal?
When they are assumed to have the same standard deviation.... (TBD)
Does a regression fit describe the data well?
(TBD)
Is a regression model with more basis terms better than a simpler model?
(TBD)
Do the expected values of several groups differ from each other?
(TBD)
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