Chi-Square Distribution

Fathom Reference > Fathom Operators, Functions, and Units > Distribution Functions > Chi-Square Distribution

The chi-square distribution is used in Fathom when you are testing for goodness of fit or independence of two categorical attributes. The distribution has a degrees of freedom parameter, df, that determines its shape and that must be a positive integer. In a goodness of fit test, for example, the number of degrees of freedom is one less than the number of categories.

These functions take optional parameters that determine a minimum value and a scale so that Pr(X ≤ x), where X = min + scale× C and C is a random variable from a chi-square distribution with df degrees of freedom. Scale defaults to 1. Min defaults to 0.

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A plot of two chi-square probability densities, one with three and the other with five degrees of freedom

chiSquareCumulative (x,

df, scale, min)

The cumulative chi-square distribution function calculates the cumulative probability, Pr(X ≤ x).

chiSquareDensity (x,

df, scale, min)

The chi-square density function calculates the probability density, (d/dx)Pr(X ≤ x).

chiSquareQuantile (c,

df, scale, min)

The chi-square quantile function computes the value x, such that Pr(X ≤ x) = c.