Table 3 Formulation that distinguishes between distributional and locational hypotheses for both self-contained and competitive schemes
From: Roastgsa: a comparison of rotation-based scores for gene set enrichment analysis
type | Distributional hypothesis | Locational hypothesis |
|---|---|---|
self-contained | \(H_{D}: [E[\delta _i] = 0, \forall i\in S]\) | \(H_{L}: \text {avg}_S(E[\delta _i]) = 0\) |
competitive | \(H_{D}: [F_{\delta _i}, i \in S] = [F_{\delta _i}, i \in C]\) | \(H_{L}: \text {avg}_S(E[\delta _i]) = \text {avg}_C(E[\delta _i])\) |
Notation | \([\delta _i] \equiv \hbox {modt-statistics, } i\in \Omega = [1,\ldots ,q]\) | |
\(S \equiv \hbox {Testing gene set, } S\subset \Omega , \,\,\, m_0 = |S|,\,\, C = \Omega \setminus S\) | ||