Higher criticism, Advanced Statistics

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Higher criticism is a multiple-comparison test concept arising from the situation where there are number of independent tests of significance and interest lies in the rejecting joint null hypothesis.

The fraction of the observed significances at the given α-level is compared to the expected fraction under the joint null and the difference between the two quantities is standardized and this standardized value then maximized over the range of significance levels to provide the higher criticism statistic. This statistic is efficient in assessing whether n normal means are all zero against the alternative that the small fraction is nonzero.

 


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