holm_adjust — n4m.metrics.multiple_testing.holm_adjust¶
Namespace: n4m.metrics.multiple_testing · Fully-qualified: n4m.metrics.multiple_testing.holm_adjust · Catalog id: diagnostics.holm_adjust
API surface¶
C ABI (ABI 2): n4m_preflight_holm_adjust. Use the linked public header for the exact signature, configuration, and result handles.
R: no current source-verified entry point was found for this catalog method.
MATLAB / Octave: no current source-verified entry point was found for this catalog method.
Explanations¶
Bibliographic source¶
Holm (1979), A Simple Sequentially Rejective Multiple Test Procedure, Scandinavian Journal of Statistics 6(2), 65–70, https://www.jstor.org/stable/4615733.
Mathematical principle¶
For one family of \(m\) p-values sorted ascending as \(p_{(1)}\le\dots\le p_{(m)}\), the adjusted value of the hypothesis of rank \(i\) is \(\min(1,\max_{j\le i}(m-j+1)p_{(j)})\). The sort is stable, so tied p-values keep their input order, as in R p.adjust(method = "holm").
Appropriate uses¶
Controlling the family-wise error rate when several Preflight factor-association tests are reported together, without assuming independence between the tests.
Limits and validation¶
Holm controls the family-wise error rate, not the false discovery rate, and is conservative for many correlated tests. The caller defines the family. Inputs must lie in \([0,1]\) and \(m\ge 1\).
Implementation¶
The ABI-2 symbol n4m_preflight_holm_adjust in n4m/metrics.h is implemented in cpp/src/c_api/c_api_preflight.cpp and wrapped in JS/WASM by preflightHolmAdjust. R p.adjust reference values are pinned in cpp/tests/test_preflight.cpp.
Sources and provenance¶
https://www.jstor.org/stable/4615733; https://github.com/GBeurier/nirs4all-methods/blob/main/cpp/src/c_api/c_api_preflight.cpp; https://github.com/GBeurier/nirs4all-methods/blob/main/cpp/tests/test_preflight.cpp
Catalog note¶
Holm step-down adjusted p-values for one hypothesis family, matching R p.adjust(method = “holm”) with a stable ascending order.
See also: methods index.