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 |  |  |  |  |