F-Distribution

Fathom Reference > Fathom Operators, Functions, and Units > Distribution Functions > F-Distribution

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The F-distribution is used to compute p-values in a one-way analysis of variance. Under the null hypothesis, the test statistic in this analysis (called, appropriately enough, the F-ratio) is a random variable from an F-distribution.

The ratio referred to is the ratio of the mean square for treatments and the mean square for error. Each of these has associated with it a number of degrees of freedom. There is a different F-distribution for each distinct pair of degrees of freedom. These are labeled numDf and denomDf in the list that follows, corresponding to numerator and denominator. The function plot here shows a plot of both the density and the cumulative probability for the F-distribution, where sliders have been used to make it easy to explore the effect of the two parameters on the shape of the distribution.

F-distribution functions also take two optional parameters: scale, which defaults to 1, and min, which defaults to 0.

fCumulative(x, numDf, denomDf, scale, min)	This function computes the cumulative probability, Pr(X ≤ x), where X = min + scale*F, where F is a random variable drawn from an F-distribution with the given pair of degrees of freedom.
fDensity(x, numDf, denomDf, scale, min)	This function calculates the probability density, (d/dx)Pr(X ≤ x).
fQuantile(c, numDf, denomDf, scale, min)	This function computes the value x, such that Pr(X ≤ x) = c.