You&#x27;re absolutely right! My example was mainly for illustration, I was not sure that it would give exactly the same lower bound (but I was indeed surprised that it&#x27;s below the 29% in those papers, which I thought a &quot;hard&quot; bound).<p>It seems the bound that you are calculating (that I have reproduced, R code below) was already published more than 50 years ago for this specific case of a normal distribution. See slide 10 in  <a href="http:&#x2F;&#x2F;www.biostat.uzh.ch&#x2F;teaching&#x2F;master&#x2F;previous&#x2F;seminarbayes&#x2F;LeonhardHeld_slides.pdf" rel="nofollow">http:&#x2F;&#x2F;www.biostat.uzh.ch&#x2F;teaching&#x2F;master&#x2F;previous&#x2F;seminarba...</a><p>I have not really read the paper of Sellke et al. entirely, but it seems that the &quot;calibration&quot; they propose is more general but it makes some assumptions about the distribution of the p-value and it&#x27;s therefore approximative.<p><pre><code>  p=0.05
  null=0.5
  c0=qnorm(1-p)
  x=seq(0,5,0.01)
  y=100*dnorm(c0)&#x2F;(dnorm(c0)+dnorm(x-c0))
  calib=100&#x2F;(1-1&#x2F;(exp(1)*p*log(p)))
  actual=min(y)
  plot(x,y,type=&quot;l&quot;,ylim=c(0,100),ylab=&quot;%null&quot;,xlab=&quot;mu1&quot;,bty=&quot;l&quot;,xaxs=&quot;i&quot;,yaxs=&quot;i&quot;)
  title(paste(null*100,&quot;% null  p = &quot;,p,sep=&quot;&quot;))
  legend(&quot;topleft&quot;,c(paste(&quot;Sellke, Bayarri, Berger (2001) =&quot;,format(calib,digits=3)),
                   paste(&quot;Edwards, Lindman, Savage (1963) =&quot;,format(actual,digits=3))),
       lwd=2,col=c(&quot;red&quot;,&quot;blue&quot;),bty=&quot;n&quot;)
  abline(h=calib,col=&quot;red&quot;)
  abline(h=actual,col=&quot;blue&quot;)
  grid()</code></pre>