Extensions of Fisher's method: Difference between revisions
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====Brown's method: [[normal distribution|Gaussian approximation]] ==== |
====Brown's method: [[normal distribution|Gaussian approximation]] ==== |
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Fisher's method showed that the log-sum of |
Fisher's method showed that the log-sum of ''k'' independent p-values follow a {{nowrap|1='''[[chi (letter)|<span style="font-family:serif">''χ''</span>]]<sup>2</sup>-distribution'''}} of 2''k'' degrees of freedom: |
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: <math>X = -2\sum_{i=1}^k \log_e(p_i) \sim \chi^2(2k) </math> |
: <math>X = -2\sum_{i=1}^k \log_e(p_i) \sim \chi^2(2k) </math> |
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Brown proposed the idea of approximating ''X'' using a scaled ''χ''²-distribution, ''cχ''<sup>2</sup>(''k’''), with ''k’'' degrees of freedom. This approximation is shown to be accurate up to two moments. |
In the case that these p-values are not independent, Brown proposed the idea of approximating ''X'' using a scaled ''χ''²-distribution, ''cχ''<sup>2</sup>(''k’''), with ''k’'' degrees of freedom. This approximation is shown to be accurate up to two moments. |
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<ref>{{cite journal | last1 = Brown | first1 = M. | title = A method for combining non-independent, one-sided tests of significance | journal = Biometrics | volume = 31 | pages = 987–992 | year = 1975 }}</ref> |
<ref>{{cite journal | last1 = Brown | first1 = M. | title = A method for combining non-independent, one-sided tests of significance | journal = Biometrics | volume = 31 | pages = 987–992 | year = 1975 }}</ref> |
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Revision as of 17:55, 22 September 2011
 | This article has no lead section. (September 2011) |
(Introductory block)
Dependent statistics
A principle limitation of Fisher's method is its exclusive design to combine independent p-values, which renders it an unreliable technique to combine dependent p-values. To overcome this limitation, a number of methods were developed to extend its utility.
Known covariance
Brown's method: Gaussian approximation
Fisher's method showed that the log-sum of k independent p-values follow a χ2-distribution of 2k degrees of freedom:
In the case that these p-values are not independent, Brown proposed the idea of approximating X using a scaled χ²-distribution, cχ2(k’), with k’ degrees of freedom. This approximation is shown to be accurate up to two moments.