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The ChiSquared distribution is a right-skewed distribution bounded at zero. n is called the 'degrees of freedom' from its use in statistics below. Examples of the Chi Squared distribution are given below:




The sum of the squares of n unit-Normal distributions (i.e. Normal(0, 1)^2) is a Chisquared(n) distribution: so ChiSquared(2) = Normal(0,1)^2+Normal(0,1)^2 for example. It is this property that makes it very useful in statistics, particularly classical statistics.


In our view, the ChiSquared tests and statistics get over-used (especially the GOF statistic) because the Normality assumption is often tenuous.



The Chi Squared distribution is not directly available in Crystal Ball. However, because of its relationship to the Gamma distribution we can constructed a Chi Squared distribution by using the following equation:

Chisquared(n) = Gamma(0, n/2, 2)


As n gets large, so it is the sum of a large number of [N(0,10^2] distributions and, through Central Limit Theorem, approximates a Normal distribution itself.