Looking Elsewhere and Looking Everywhere (a.k.a. Multiple Testing ...
Looking Elsewhere and Looking Everywhere (a.k.a. Multiple Testing ...
Looking Elsewhere and Looking Everywhere (a.k.a. Multiple Testing ...
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Holm-Bonferroni Method<br />
Advantage: Works for any (discrete domain) setup!<br />
Disadvantage: Too conservative when T large<br />
Holm’s modification increases average # of hypotheses rejected at level α<br />
(but does not increase power for overall rejection of H0)<br />
Holm’s Procedure<br />
1 Suppose we reject H0,t for large values of a test statistic Wt<br />
2 Order individual test statistics, largest to smallest: W (T ) ≥ . . . ≥ W (1)<br />
3 Starting from t = T <strong>and</strong> going down, reject all H 0,(t) such that W (t)<br />
supercritical at level α/t. Stop rejecting at first subcritical W (t).<br />
Genuine improvement over Bonferroni if want to detect as many signals as<br />
possible, not just existence of some signal<br />
Both Holm <strong>and</strong> Bonferroni reject the global H0 if <strong>and</strong> only if sup t Wt<br />
supercritical at level α/T wrt distribution of corresponding W under H0<br />
Victor M. Panaretos (EPFL) Progress on Statistical Issues in Searches SLAC – June 2012 8 / 25
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