Example:
Prob( X^2 >=
Characteristics:
This is not a test, but a distribution. The Chisquare distribution, is
derived from the
>
Normal distribution. It is the distribution of a sum of squared Normal
distributed variables. That is, if all Xi are independent and all have an
identical, standard Normal distribution then X^2 = X1*X1 +
X2*X2 + X3*X3 + ... + Xv*Xv is Chisquare distributed with
v degrees of freedom with mean = v and variance = 2*v.
The importance of the Chisquare distribution stems from the fact that it
describes the distribution of the Variance of a sample taken from a
Normal distributed population.
Note that X^2 is a Sum of Squares and should be tested OneSided only.
H0:
The distribution of the underlying sample values X has mean = 0
and variance = 1, i.e., is Standard Normal. As a consequence,
X^2 has mean equal to the Degrees of Freedom and a variance
equal to 2 * Degrees of Freedom.
Assumptions:
The values from which X^2 is calculated are themselves Normal
distributed with unit variance.
Scale:
Interval
Procedure:

Level of significance:
Use a table to look up the level of significance associated with X^2 and
the Degrees of Freedom.
Approximation:
If the Degrees of Freedom > 30, the distribution of
Z = {(X^2/DoF)^(1/3)  (1  2/(9*DoF))}/SQRT(2/(9*DoF))
can be approximated by a > Standard Normal Distribution.
Remarks:
The ChiSquare distribution is based on a sum of squares, therefore the value
of X^2 will always be larger than (or equal to) zero. This means that all
testing should be done OneTailed only. This is in fact done in the
above example.
WARNING: the level of significance given here is only an
approximation, take care when using it! (use a table if necessary)