You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
| You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
|
Table of Contents  Univariate Data Sampling Distributions Chi-Square Distribution |
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| See also: sampling distributions, t-distribution, F-distribution |   |
In order to make inferences about the population variance on the basis
of the sample variance, we have to consider a special distribution, called
chi-square (
)
distribution: if a random variable Y is normally distributed with mean
µ and variance s2, then the
quantity
shows a
distribution with n-1 degrees of freedom for a random sample of size n.
Several examples of
distributions for different degrees of freedom are shown in the figure
below.
As you can see, the
distribution is skewed and is always positive. The mean of the
distribution is equal to the number of degrees of freedom n-1, the variance
is twice the degrees of freedom. The
distribution is tabulated in statistical tables, or can be calculated online
by means of the distribution calculator.
The
distribution is used to test differences between population and sample
variances, and between theoretical and observed distributions.
An important property of the distribution is its additivity: if two independent variables follow a distribution (exihibiting the degrees of freedom f1 and f2), then the sum of the two variables is also -distributed with a degree of freedom of f1+f2.
Last Update: 2005-Jän-25