Table 1 Test statistics and quality measures. For the quality-based tests, the summarized quality measure, across treatment groups, is defined by Q _g = max_w∈{1...W}$R_g^w$.

$Q_g^0$

1.0

1.0

No filtering

$Q_g^{call}$

$q_{giw}^{*}=\{\begin{array}{cc}1& ifcallisP\\ 0& otherwise\end{array}$

${\min }_{i\in \{1\dots I\}}{q}_{giw}^{*}$

All arrays must have present call to be included

$Q_g^{meanp}$

q _giw = detection p-value

$1-{\overline{q}}_{gw}=1-{\displaystyle \sum _{i\in w}(q_{giw})/n_w}$

n _w is the number of arrays in group w

$Q_g^{\exp }$

q _giw = detection p-value

$\exp \lfloor {\widehat{\lambda }}_{gw}\log \nu \rfloor$ for sensitivity parameter ν

${\widehat{\lambda }}_{gw}=-n_w/{\displaystyle \sum _{i\in w}\log }(q_{giw})$

$Q_g^{beta}$

q _giw = detection p-value

${\nu }^{{\widehat{a}}_{gw}}$

${\widehat{a}}_{gw}={\overline{q}}_{gw}/(1-{\overline{q}}_{gw})$

$Q_g^{we}$

q _giw = detection p-value

N/A

Weighted means ${\overline{x}}_{gw}$ and weighted standard deviations S _gw

$Q_g^{LPE}$

N/A

N/A

Local pooled error test [18]