Sample Size Calculation for Controlling False Discovery Proportion

<table>Plots of sd(FDP) at different <svg height="18.5875" id="M102" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 8.8500004 18.5875" width="8.8500004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.5875)">
<g transform="translate(72,-57.13)">
<g>
<path d="m -71.95,70.71 6.98,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,59.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
</text>
</g>
</g>
</svg> and <svg height="19.799999" id="M103" style="vertical-align:-3.27548pt" version="1.1" viewbox="0 0 17.6875 19.799999" width="17.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8)">
<g transform="translate(72,-56.16)">
<g>
<path d="m -71.95,70.71 6.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,59.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.4,56.35)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑉</tspan>
</text>
</g>
</g>
</svg>. <svg height="7.1374998" id="M104" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1375)">
<g transform="translate(72,-66.29)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
</text>
</g>
</g>
</svg> = 10000, <svg height="10.875" id="M105" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.9375 10.875" width="14.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜋</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.97,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
</g>
</g>
</svg> = 0.7, <svg height="10.9125" id="M106" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 63.487499 10.9125" width="63.487499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.806911" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.932661" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.184162" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="44.435661" y="0">4</tspan>
</text>
</g>
</g>
</svg>, <svg height="19.775" id="M107" style="vertical-align:-3.24916pt" version="1.1" viewbox="0 0 17.85 19.775" width="17.85" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.775)">
<g transform="translate(72,-56.18)">
<g>
<path d="m -71.95,70.71 6.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,59.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.4,56.35)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑈</tspan>
</text>
</g>
</g>
</svg> = 0.001 and <svg height="19.799999" id="M108" style="vertical-align:-3.27548pt" version="1.1" viewbox="0 0 25.4 19.799999" width="25.4" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8)">
<g transform="translate(72,-56.16)">
<g>
<path d="m -71.95,70.71 6.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,59.47)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.4,56.35)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑈</tspan>
<tspan style="font-size: 8.75px; " x="6.1701598" y="0">𝑉</tspan>
</text>
</g>
</g>
</svg> = 0. </table>

Journal of Probability and Statistics

Sample Size Calculation for Controlling False Discovery Proportion

Figure 3