# 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.

## Contents

## 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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