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Table 1 The format of a table that will be used to analyze p-values and \(\updelta\)

From: A non-parametric maximum for number of selected features: objective optima for FDR and significance threshold with application to ordinal survey analysis

Set of observations Observed p-value in the set Observed frequency of p-value Set of rejected hypotheses Cumulative expected false discoveries if set is rejected (CEFD) Cumulative expected TRUE discoveries if set is rejected (CETD) δ = CETD − CEFD
\(S_{1}\) \(p_{1}\) \(f_{1}\) \(R_{1} = S_{1}\) \(N \times p_{1}\) \(f_{1} - N \times p_{1}\) \(f_{1} - N \times p_{1} - N \times p_{1}\)
\(S_{2}\) \(p_{2}\) \(f_{2}\) \(R_{2} = S_{1} \cup S_{2}\) \(N \times p_{2}\) \(f_{1} + f_{2} - N \times p_{2}\) \(\mathop \sum \limits_{i = 1}^{2} \left( {f_{i} } \right) - 2 \times N \times p_{2}\)
\(S_{3}\) \(p_{3}\) \(f_{3}\) \(R_{3} = S_{1} \cup S_{2} \cup S_{3}\) \(N \times p_{3}\) \(f_{1} + f_{2} + f_{3} - N \times p_{3}\) \(\mathop \sum \limits_{i = 1}^{3} \left( {f_{i} } \right) - 2 \times N \times p_{3}\)
 
\(S_{k}\) \(p_{k}\) \(f_{k}\) \(R_{k} = S_{1} \cup S_{2} \cup S_{3} \cup \ldots \cup S_{k}\) 1 \(0\) − N
  \(\mathop \sum \limits_{i = 1}^{k} \left( {p_{i} } \right) = 1\) \(\mathop \sum \limits_{i = 1}^{k} \left( {f_{i} } \right)\) = N