Fig. 4

Measures of power of the three p-value alternatives for \( {\widehat{er}}_{up\;}^{*} \). Observations for control subjects followed a log-normal (0,1) distribution while those of experimental subjects where drawn from a log-normal (\( \mu \),1) distribution where \( \mu \) assumed values ranging between 0 and 2. The number of simulation repetitions was a hundred thousand with \( {\pi}_0 \) and \( {\pi}_1 \) pairs selected as indicated (i.e. the top row \( {\pi}_0=0.25;{\pi}_1=0 \) and the bottom row \( {\pi}_0={\pi}_1=0.25 \)). The graphs represent the two group size and weigh scenarios as indicated (left panel: \( {N}_0={N}_1=20;{w}_0={w}_1=0.5 \) and right panel: \( {N}_0=31;{N}_1=17;{w}_0=0.35;{w}_1=0.65 \)). The lines represent the averages of the three p-value estimates (i) \( {p}_0 \) in dark blue; (ii) \( {p}_{max} \) in purple; and (iii) \( {p}_{obs} \) in light blue, conditioned on a 10% significance level. The red lines correspond to \( {p}_{\pi} \)