Difference between revisions of "Chi-squared distribution"
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== ChiSquared(d) ==
 
== 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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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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:<math>\Chi^2 \sum_{i=1}^n {y_i}^2</math>
  
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where each ''y<sub>i</sub>'' is independently sampled from a standard normal distribution and ''d = n -1'' . The distribution is defined over nonnegative values.
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where each ''y<sub>i</sub>'' 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.
 
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.

Revision as of 01:39, 28 January 2016


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.

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