Difference between revisions of "Chi-squared distribution"
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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. | 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]]. |
Suppose | Suppose | ||
Revision as of 19:56, 4 August 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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