Control of the False Discovery Proportion for Independently Tested Null Hypotheses

<table>A blowup of Figure <a href="../fig2/">2</a>. This shows the part of the probability <svg height="19.012501" id="M392" style="vertical-align:-3.20526pt" version="1.1" viewbox="0 0 69.962502 19.012501" width="69.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.0125)">
<g transform="translate(72,-56.79)">
<text transform="matrix(1,0,0,-1,-71.95,60.03)">
<tspan style="font-size: 12.50px; " x="16.34" y="-2.54"></tspan>
<tspan style="font-size: 12.50px; " x="14.58" y="0">𝑍</tspan>
<tspan style="font-size: 12.50px; " x="0" y="0">p</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">r</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">(</tspan>
</text>
<text transform="matrix(1,0,0,-1,-46.84,56.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
</text>
<text transform="matrix(1,0,0,-1,-38.52,60.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">≤</tspan>
<tspan style="font-size: 12.50px; " x="18.654476" y="0">̃</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">)</tspan>
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</svg> that is close to 1 as 1−<svg height="10.325" id="M393" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
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</svg> is drawn on a log scale for the <svg height="9.8625002" id="M394" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.8625)">
<g transform="translate(72,-64.11)">
<text transform="matrix(1,0,0,-1,-71.95,66.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
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</g>
</g>
</svg>-axis.</table>

Journal of Probability and Statistics

fig3

Figure 3

Figure 3: Control of the False Discovery Proportion for Independently Tested Null Hypotheses 