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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

   Â