Difference between revisions of "Chi-squared distribution"
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| − | = ChiSquared(d) = | + | == ChiSquared(d) == |
| − | The ChiSquared distribution with | + | The ChiSquared distribution with «d» degrees of freedom describes the distribution of a Chi-Squared metric defined as |
<math>\Chi^2 \sum_{i=1}^n {y_i}^2</math> | <math>\Chi^2 \sum_{i=1}^n {y_i}^2</math> | ||
| − | where each | + | 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. |
| − | distribution and d = n -1 . The distribution is defined over nonnegative | ||
| − | values. | ||
| − | The Chi-squared distribution is commonly used for analyses of | + | 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. |
| − | second moments, such as analyses of variance and contingency | ||
| − | table analyses. It can also be used to generate the F distribution. | ||
Suppose | Suppose | ||
| − | + | :<code>Variable V := ChiSquared(k)</code> | |
| − | + | :<code>Variable W := ChiSquared(m)</code> | |
| − | + | :<code>Variable S := (V/k)*(W/m)</code> | |
| − | S is distributed as an F distribution with k and m degrees of freedom | + | <code>S</code> is distributed as an F distribution with <code>k</code> and <code>m</code> 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 | Distributions | ||
| − | = See Also = | + | == See Also == |
| − | |||
* [[Dens_ChiSquared]] | * [[Dens_ChiSquared]] | ||
| + | * [[CumChiSquared]] | ||
| + | * [[Parametric continuous distributions]] | ||
| + | * [[Distribution Densities Library]] | ||
Revision as of 23:49, 26 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.
Library
Distributions
See Also
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