Difference between revisions of "Chi-squared distribution"

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= ChiSquared(d) =
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The ChiSquared distribution with d degrees of freedom describes the distribution of a Chi-Squared metric defined as
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<math>\Chi^2 \sum_{i=1}^n {y_i}^2</math>
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where each yi is independently sampled from a standard normal
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distribution and d = n -1 . The distribution is defined over nonnegative
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values.
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The Chi-squared distribution is commonly used for analyses of
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second moments, such as analyses of variance and contingency
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table analyses. It can also be used to generate the F distribution.
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Suppose
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Variable V := ChiSquared(k)
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Variable W := ChiSquared(m)
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Variable S := (V/k)*(W/m)
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S is distributed as an F distribution with k and m degrees of freedom.
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The F distribution is useful for the analysis of ratios of variance,
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such as a one-factor between-subjects analysis of
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variance.
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= Library =
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Distributions
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= See Also =
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* [[Dens_ChiSquared]]

Revision as of 20:07, 3 October 2007


ChiSquared(d)

The ChiSquared distribution with d degrees of freedom describes the distribution of a Chi-Squared metric defined as

[math]\displaystyle{ \Chi^2 \sum_{i=1}^n {y_i}^2 }[/math]

where each yi is independently sampled from a standard normal distribution and d = n -1 . The distribution is defined over nonnegative values.

The Chi-squared distribution is commonly used for analyses of second moments, such as analyses of variance and contingency table analyses. It can also be used to generate the F distribution.

Suppose 

Variable V := ChiSquared(k)
Variable W := ChiSquared(m)
Variable S := (V/k)*(W/m)

S is distributed as an F distribution with k and m degrees of freedom. The F distribution is useful for the analysis of ratios of variance, such as a one-factor between-subjects analysis of variance.

Library

Distributions

See Also

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