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<h1 class="title toc-ignore">Histogram of correlated <span class="math inline">\(z\)</span> scores, Part 2</h1>
<h4 class="author"><em>Lei Sun</em></h4>
<h4 class="date"><em>2017-03-06</em></h4>
</div>
<p><strong>Last updated:</strong> 2017-03-10</p>
<p><strong>Code version:</strong> 894c395</p>
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Following <a href="correlated_z.html">previous simulation</a> on randomly selected data sets, this time we first apply <code>ash</code> on <span class="math inline">\(z\)</span> scores for every data set, and take a second look at those data sets on which <code>ash</code> makes most mistakes, or in other words, produces smallest <span class="math inline">\(\hat\pi_0\)</span>.</p>
</div>
<div id="simulation-and-ash" class="section level2">
<h2>Simulation and <code>ash</code></h2>
<pre class="r"><code>z = read.table("../output/z_null_liver_777.txt")</code></pre>
<pre class="r"><code>library(ashr)
n = dim(z)[1]
pihat0 = c()
for (i in 1:n) {
ash.fit = ash(as.numeric(z[i, ]), 1, method = "fdr")
pihat0[i] = get_pi0(ash.fit)
}</code></pre>
</div>
<div id="histograms-of-z-scores-in-100-most-ash-hostile-data-sets" class="section level2">
<h2>Histograms of <span class="math inline">\(z\)</span> scores in 100 most “<code>ash</code>-hostile” data sets</h2>
<pre class="r"><code>I = order(pihat0)[1:100]
x = seq(-10, 10, 0.01)
y = dnorm(x)
k = 1
for (j in I) {
cat("N0.", k, ": Data Set", j, "pihat0 =", pihat0[j])
hist(as.numeric(z[j, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), main = "10000 z scores, default")
lines(x, y, col = "red")
hist(as.numeric(z[j, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), nclass = 100, main = "10000 z scores, 100 bins")
lines(x, y, col = "red")
k = k + 1
}</code></pre>
<pre><code>N0. 1 : Data Set 724 pihat0 = 0.01606004</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 2 : Data Set 33 pihat0 = 0.01680632</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 3 : Data Set 537 pihat0 = 0.01681555</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 4 : Data Set 522 pihat0 = 0.02083846</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-7.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 5 : Data Set 693 pihat0 = 0.02122591</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-9.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 6 : Data Set 840 pihat0 = 0.02316832</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-11.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 7 : Data Set 749 pihat0 = 0.02583276</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-13.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 8 : Data Set 269 pihat0 = 0.02787007</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-15.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 9 : Data Set 360 pihat0 = 0.0308234</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-17.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 10 : Data Set 23 pihat0 = 0.03139009</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-19.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 11 : Data Set 389 pihat0 = 0.03156173</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-21.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 12 : Data Set 923 pihat0 = 0.03239883</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-23.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 13 : Data Set 22 pihat0 = 0.03271534</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-25.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 14 : Data Set 885 pihat0 = 0.03413736</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-27.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-28.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 15 : Data Set 705 pihat0 = 0.03438913</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-29.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-30.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 16 : Data Set 40 pihat0 = 0.03668824</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-31.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-32.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 17 : Data Set 338 pihat0 = 0.0393062</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-33.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-34.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 18 : Data Set 379 pihat0 = 0.03958053</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-35.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-36.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 19 : Data Set 649 pihat0 = 0.04041784</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-37.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-38.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 20 : Data Set 627 pihat0 = 0.04041922</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-39.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-40.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 21 : Data Set 133 pihat0 = 0.04064386</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-41.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-42.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 22 : Data Set 915 pihat0 = 0.04083527</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-43.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-44.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 23 : Data Set 999 pihat0 = 0.04218153</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-45.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-46.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 24 : Data Set 182 pihat0 = 0.04223457</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-47.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-48.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 25 : Data Set 511 pihat0 = 0.04232901</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-49.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-50.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 26 : Data Set 122 pihat0 = 0.04301549</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-51.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-52.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 27 : Data Set 937 pihat0 = 0.04305909</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-53.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-54.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 28 : Data Set 771 pihat0 = 0.04316169</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-55.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-56.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 29 : Data Set 495 pihat0 = 0.04395344</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-57.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-58.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 30 : Data Set 41 pihat0 = 0.04491135</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-59.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-60.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 31 : Data Set 984 pihat0 = 0.04567195</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-61.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-62.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 32 : Data Set 3 pihat0 = 0.0465218</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-63.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-64.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 33 : Data Set 907 pihat0 = 0.04653847</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-65.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-66.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 34 : Data Set 355 pihat0 = 0.04750946</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-67.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-68.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 35 : Data Set 485 pihat0 = 0.04794909</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-69.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-70.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 36 : Data Set 56 pihat0 = 0.04829662</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-71.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-72.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 37 : Data Set 809 pihat0 = 0.04880257</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-73.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-74.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 38 : Data Set 404 pihat0 = 0.05059485</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-75.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-76.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 39 : Data Set 858 pihat0 = 0.05110069</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-77.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-78.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 40 : Data Set 77 pihat0 = 0.05151585</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-79.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-80.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 41 : Data Set 800 pihat0 = 0.05218407</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-81.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-82.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 42 : Data Set 562 pihat0 = 0.05247834</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-83.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-84.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 43 : Data Set 893 pihat0 = 0.05252202</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-85.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-86.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 44 : Data Set 403 pihat0 = 0.0531628</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-87.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-88.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 45 : Data Set 780 pihat0 = 0.05426134</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-89.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-90.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 46 : Data Set 538 pihat0 = 0.05493143</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-91.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-92.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 47 : Data Set 324 pihat0 = 0.05506971</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-93.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-94.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 48 : Data Set 176 pihat0 = 0.05513259</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-95.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-96.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 49 : Data Set 972 pihat0 = 0.05539611</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-97.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-98.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 50 : Data Set 644 pihat0 = 0.0557842</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-99.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-100.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 51 : Data Set 977 pihat0 = 0.0564768</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-101.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-102.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 52 : Data Set 467 pihat0 = 0.06112237</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-103.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-104.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 53 : Data Set 857 pihat0 = 0.06183555</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-105.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-106.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 54 : Data Set 783 pihat0 = 0.06208376</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-107.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-108.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 55 : Data Set 976 pihat0 = 0.06343862</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-109.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-110.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 56 : Data Set 968 pihat0 = 0.06385437</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-111.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-112.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 57 : Data Set 942 pihat0 = 0.06399678</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-113.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-114.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 58 : Data Set 402 pihat0 = 0.06468693</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-115.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-116.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 59 : Data Set 341 pihat0 = 0.06681535</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-117.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-118.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 60 : Data Set 411 pihat0 = 0.06812445</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-119.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-120.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 61 : Data Set 484 pihat0 = 0.06857855</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-121.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-122.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 62 : Data Set 476 pihat0 = 0.06944478</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-123.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-124.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 63 : Data Set 407 pihat0 = 0.07139176</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-125.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-126.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 64 : Data Set 871 pihat0 = 0.07236197</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-127.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-128.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 65 : Data Set 638 pihat0 = 0.07281058</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-129.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-130.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 66 : Data Set 232 pihat0 = 0.07317683</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-131.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-132.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 67 : Data Set 778 pihat0 = 0.07619716</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-133.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-134.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 68 : Data Set 349 pihat0 = 0.07627442</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-135.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-136.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 69 : Data Set 985 pihat0 = 0.07865805</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-137.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-138.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 70 : Data Set 259 pihat0 = 0.0794454</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-139.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-140.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 71 : Data Set 452 pihat0 = 0.079703</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-141.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-142.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 72 : Data Set 268 pihat0 = 0.08182634</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-143.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-144.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 73 : Data Set 526 pihat0 = 0.08340671</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-145.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-146.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 74 : Data Set 274 pihat0 = 0.08580661</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-147.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-148.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 75 : Data Set 685 pihat0 = 0.08592309</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-149.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-150.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 76 : Data Set 499 pihat0 = 0.08826948</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-151.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-152.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 77 : Data Set 982 pihat0 = 0.08854547</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-153.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-154.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 78 : Data Set 582 pihat0 = 0.08899861</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-155.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-156.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 79 : Data Set 953 pihat0 = 0.08900989</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-157.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-158.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 80 : Data Set 811 pihat0 = 0.08962902</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-159.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-160.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 81 : Data Set 575 pihat0 = 0.0946117</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-161.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-162.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 82 : Data Set 997 pihat0 = 0.09560788</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-163.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-164.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 83 : Data Set 231 pihat0 = 0.09686204</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-165.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-166.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 84 : Data Set 781 pihat0 = 0.09690435</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-167.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-168.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 85 : Data Set 853 pihat0 = 0.09889116</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-169.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-170.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 86 : Data Set 868 pihat0 = 0.09918104</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-171.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-172.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 87 : Data Set 502 pihat0 = 0.1001788</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-173.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-174.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 88 : Data Set 606 pihat0 = 0.1033893</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-175.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-176.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 89 : Data Set 912 pihat0 = 0.106048</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-177.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-178.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 90 : Data Set 659 pihat0 = 0.1065714</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-179.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-180.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 91 : Data Set 501 pihat0 = 0.1090034</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-181.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-182.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 92 : Data Set 296 pihat0 = 0.1115216</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-183.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-184.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 93 : Data Set 895 pihat0 = 0.1119629</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-185.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-186.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 94 : Data Set 153 pihat0 = 0.1148195</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-187.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-188.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 95 : Data Set 477 pihat0 = 0.1172838</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-189.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-190.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 96 : Data Set 769 pihat0 = 0.1187511</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-191.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-192.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 97 : Data Set 555 pihat0 = 0.1210902</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-193.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-194.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 98 : Data Set 475 pihat0 = 0.1273824</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-195.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-196.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 99 : Data Set 584 pihat0 = 0.1291777</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-197.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-198.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 100 : Data Set 949 pihat0 = 0.1308901</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-199.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-3-200.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="take-a-closer-look-at-the-p-values-in-100-most-ash-hostile-data-sets" class="section level2">
<h2>Take a closer look at the <span class="math inline">\(p\)</span> values in 100 most “<code>ash</code>-hostile” data sets</h2>
<p>We take a closer look at the behavior of <span class="math inline">\(p\)</span> values in these most “<code>ash</code>-hostile” data sets, and also apply Benjamini-Hochberg’s FDR procedure on them, to see if BH is robust enough against the foes that make <code>ash</code> fail badly. False discoveries produced by BH are indicated as green points.</p>
<pre class="r"><code>p = read.table("../output/p_null_liver_777.txt")</code></pre>
<pre class="r"><code>fd.bh = c()
for (i in 1 : n[1]) {
p_BH = p.adjust(p[i, ], method = "BH")
fd.bh[i] = sum(p_BH <= 0.05)
}</code></pre>
<pre class="r"><code>I = order(pihat0)[1:100]
x = seq(-10, 10, 0.01)
y = dnorm(x)
k = 1
m = dim(p)[2]
for (j in I) {
cat("N0.", k, ": Data Set", j, "; pihat0 =", pihat0[j], "; Number of False Discoveries:", fd.bh[j])
hist(as.numeric(z[j, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), nclass = 100, main = "10000 z scores, 100 bins")
lines(x, y, col = "red")
qqnorm(as.numeric(z[j, ]), main = "Normal Q-Q plot for z scores")
abline(0, 1)
plot(sort(as.numeric(p[j, ])), xlab = "Order", ylab = "Ordered p value", main = "All p values")
abline(0, 1 / m, col = "blue")
abline(0, 0.05 / m, col = "red")
legend("top", lty = 1, col = c("blue", "red"), c("Uniform", "BH, FDR = 0.05"))
pj = sort(as.numeric(p[j, ]))
plot(pj[1:max(100, fd.bh[j])], xlab = "Order", ylab = "Ordered p value", main = "Zoom-in to 100 smallest p values", ylim = c(0, pj[max(100, fd.bh[j])]))
abline(0, 1 / m, col = "blue")
points(pj[1:fd.bh[j]], col = "green", pch = 19)
abline(0, 0.05 / m, col = "red")
legend("top", lty = 1, col = c("blue", "red"), c("Uniform", "BH, FDR = 0.05"))
plot(pj[pj <= 0.01], xlab = "Order", ylab = "Ordered p value", main = "Zoom-in to p values <= 0.01", ylim = c(0, 0.01))
abline(0, 1 / m, col = "blue")
points(pj[1:fd.bh[j]], col = "green", pch = 19)
abline(0, 0.05 / m, col = "red")
legend("top", lty = 1, col = c("blue", "red"), c("Uniform", "BH, FDR = 0.05"))
plot(pj[pj <= 0.05], xlab = "Order", ylab = "Ordered p value", main = "Zoom-in to p values <= 0.05", ylim = c(0, 0.05))
abline(0, 1 / m, col = "blue")
points(pj[1:fd.bh[j]], col = "green", pch = 19)
abline(0, 0.05 / m, col = "red")
legend("top", lty = 1, col = c("blue", "red"), c("Uniform", "BH, FDR = 0.05"))
k = k + 1
}</code></pre>
<pre><code>N0. 1 : Data Set 724 ; pihat0 = 0.01606004 ; Number of False Discoveries: 79</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-2.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-4.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 2 : Data Set 33 ; pihat0 = 0.01680632 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-7.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-8.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-9.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-10.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-11.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 3 : Data Set 537 ; pihat0 = 0.01681555 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-13.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-14.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-15.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-16.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-17.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 4 : Data Set 522 ; pihat0 = 0.02083846 ; Number of False Discoveries: 4</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-19.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-20.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-21.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-22.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-23.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 5 : Data Set 693 ; pihat0 = 0.02122591 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-25.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-26.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-27.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-28.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-29.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-30.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 6 : Data Set 840 ; pihat0 = 0.02316832 ; Number of False Discoveries: 28</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-31.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-32.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-33.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-34.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-35.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-36.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 7 : Data Set 749 ; pihat0 = 0.02583276 ; Number of False Discoveries: 114</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-37.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-38.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-39.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-40.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-41.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-42.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 8 : Data Set 269 ; pihat0 = 0.02787007 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-43.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-44.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-45.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-46.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-47.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-48.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 9 : Data Set 360 ; pihat0 = 0.0308234 ; Number of False Discoveries: 6</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-49.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-50.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-51.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-52.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-53.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-54.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 10 : Data Set 23 ; pihat0 = 0.03139009 ; Number of False Discoveries: 408</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-55.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-56.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-57.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-58.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-59.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-60.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 11 : Data Set 389 ; pihat0 = 0.03156173 ; Number of False Discoveries: 11</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-61.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-62.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-63.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-64.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-65.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-66.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 12 : Data Set 923 ; pihat0 = 0.03239883 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-67.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-68.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-69.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-70.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-71.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-72.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 13 : Data Set 22 ; pihat0 = 0.03271534 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-73.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-74.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-75.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-76.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-77.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-78.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 14 : Data Set 885 ; pihat0 = 0.03413736 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-79.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-80.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-81.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-82.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-83.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-84.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 15 : Data Set 705 ; pihat0 = 0.03438913 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-85.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-86.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-87.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-88.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-89.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-90.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 16 : Data Set 40 ; pihat0 = 0.03668824 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-91.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-92.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-93.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-94.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-95.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-96.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 17 : Data Set 338 ; pihat0 = 0.0393062 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-97.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-98.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-99.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-100.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-101.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-102.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 18 : Data Set 379 ; pihat0 = 0.03958053 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-103.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-104.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-105.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-106.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-107.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-108.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 19 : Data Set 649 ; pihat0 = 0.04041784 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-109.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-110.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-111.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-112.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-113.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-114.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 20 : Data Set 627 ; pihat0 = 0.04041922 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-115.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-116.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-117.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-118.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-119.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-120.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 21 : Data Set 133 ; pihat0 = 0.04064386 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-121.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-122.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-123.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-124.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-125.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-126.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 22 : Data Set 915 ; pihat0 = 0.04083527 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-127.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-128.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-129.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-130.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-131.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-132.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 23 : Data Set 999 ; pihat0 = 0.04218153 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-133.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-134.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-135.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-136.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-137.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-138.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 24 : Data Set 182 ; pihat0 = 0.04223457 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-139.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-140.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-141.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-142.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-143.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-144.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 25 : Data Set 511 ; pihat0 = 0.04232901 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-145.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-146.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-147.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-148.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-149.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-150.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 26 : Data Set 122 ; pihat0 = 0.04301549 ; Number of False Discoveries: 331</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-151.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-152.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-153.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-154.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-155.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-156.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 27 : Data Set 937 ; pihat0 = 0.04305909 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-157.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-158.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-159.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-160.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-161.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-162.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 28 : Data Set 771 ; pihat0 = 0.04316169 ; Number of False Discoveries: 12</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-163.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-164.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-165.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-166.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-167.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-168.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 29 : Data Set 495 ; pihat0 = 0.04395344 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-169.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-170.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-171.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-172.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-173.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-174.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 30 : Data Set 41 ; pihat0 = 0.04491135 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-175.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-176.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-177.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-178.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-179.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-180.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 31 : Data Set 984 ; pihat0 = 0.04567195 ; Number of False Discoveries: 7</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-181.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-182.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-183.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-184.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-185.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-186.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 32 : Data Set 3 ; pihat0 = 0.0465218 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-187.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-188.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-189.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-190.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-191.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-192.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 33 : Data Set 907 ; pihat0 = 0.04653847 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-193.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-194.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-195.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-196.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-197.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-198.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 34 : Data Set 355 ; pihat0 = 0.04750946 ; Number of False Discoveries: 639</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-199.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-200.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-201.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-202.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-203.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-204.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 35 : Data Set 485 ; pihat0 = 0.04794909 ; Number of False Discoveries: 9</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-205.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-206.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-207.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-208.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-209.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-210.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 36 : Data Set 56 ; pihat0 = 0.04829662 ; Number of False Discoveries: 35</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-211.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-212.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-213.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-214.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-215.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-216.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 37 : Data Set 809 ; pihat0 = 0.04880257 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-217.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-218.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-219.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-220.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-221.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-222.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 38 : Data Set 404 ; pihat0 = 0.05059485 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-223.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-224.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-225.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-226.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-227.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-228.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 39 : Data Set 858 ; pihat0 = 0.05110069 ; Number of False Discoveries: 16</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-229.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-230.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-231.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-232.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-233.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-234.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 40 : Data Set 77 ; pihat0 = 0.05151585 ; Number of False Discoveries: 7</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-235.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-236.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-237.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-238.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-239.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-240.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 41 : Data Set 800 ; pihat0 = 0.05218407 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-241.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-242.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-243.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-244.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-245.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-246.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 42 : Data Set 562 ; pihat0 = 0.05247834 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-247.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-248.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-249.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-250.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-251.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-252.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 43 : Data Set 893 ; pihat0 = 0.05252202 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-253.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-254.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-255.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-256.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-257.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-258.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 44 : Data Set 403 ; pihat0 = 0.0531628 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-259.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-260.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-261.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-262.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-263.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-264.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 45 : Data Set 780 ; pihat0 = 0.05426134 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-265.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-266.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-267.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-268.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-269.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-270.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 46 : Data Set 538 ; pihat0 = 0.05493143 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-271.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-272.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-273.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-274.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-275.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-276.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 47 : Data Set 324 ; pihat0 = 0.05506971 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-277.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-278.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-279.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-280.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-281.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-282.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 48 : Data Set 176 ; pihat0 = 0.05513259 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-283.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-284.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-285.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-286.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-287.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-288.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 49 : Data Set 972 ; pihat0 = 0.05539611 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-289.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-290.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-291.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-292.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-293.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-294.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 50 : Data Set 644 ; pihat0 = 0.0557842 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-295.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-296.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-297.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-298.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-299.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-300.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 51 : Data Set 977 ; pihat0 = 0.0564768 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-301.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-302.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-303.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-304.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-305.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-306.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 52 : Data Set 467 ; pihat0 = 0.06112237 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-307.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-308.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-309.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-310.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-311.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-312.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 53 : Data Set 857 ; pihat0 = 0.06183555 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-313.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-314.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-315.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-316.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-317.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-318.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 54 : Data Set 783 ; pihat0 = 0.06208376 ; Number of False Discoveries: 170</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-319.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-320.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-321.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-322.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-323.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-324.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 55 : Data Set 976 ; pihat0 = 0.06343862 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-325.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-326.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-327.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-328.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-329.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-330.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 56 : Data Set 968 ; pihat0 = 0.06385437 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-331.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-332.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-333.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-334.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-335.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-336.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 57 : Data Set 942 ; pihat0 = 0.06399678 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-337.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-338.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-339.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-340.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-341.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-342.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 58 : Data Set 402 ; pihat0 = 0.06468693 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-343.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-344.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-345.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-346.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-347.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-348.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 59 : Data Set 341 ; pihat0 = 0.06681535 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-349.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-350.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-351.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-352.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-353.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-354.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 60 : Data Set 411 ; pihat0 = 0.06812445 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-355.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-356.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-357.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-358.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-359.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-360.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 61 : Data Set 484 ; pihat0 = 0.06857855 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-361.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-362.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-363.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-364.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-365.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-366.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 62 : Data Set 476 ; pihat0 = 0.06944478 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-367.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-368.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-369.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-370.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-371.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-372.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 63 : Data Set 407 ; pihat0 = 0.07139176 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-373.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-374.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-375.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-376.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-377.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-378.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 64 : Data Set 871 ; pihat0 = 0.07236197 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-379.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-380.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-381.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-382.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-383.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-384.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 65 : Data Set 638 ; pihat0 = 0.07281058 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-385.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-386.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-387.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-388.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-389.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-390.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 66 : Data Set 232 ; pihat0 = 0.07317683 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-391.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-392.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-393.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-394.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-395.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-396.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 67 : Data Set 778 ; pihat0 = 0.07619716 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-397.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-398.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-399.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-400.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-401.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-402.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 68 : Data Set 349 ; pihat0 = 0.07627442 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-403.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-404.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-405.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-406.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-407.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-408.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 69 : Data Set 985 ; pihat0 = 0.07865805 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-409.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-410.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-411.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-412.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-413.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-414.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 70 : Data Set 259 ; pihat0 = 0.0794454 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-415.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-416.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-417.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-418.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-419.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-420.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 71 : Data Set 452 ; pihat0 = 0.079703 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-421.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-422.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-423.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-424.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-425.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-426.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 72 : Data Set 268 ; pihat0 = 0.08182634 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-427.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-428.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-429.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-430.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-431.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-432.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 73 : Data Set 526 ; pihat0 = 0.08340671 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-433.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-434.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-435.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-436.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-437.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-438.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 74 : Data Set 274 ; pihat0 = 0.08580661 ; Number of False Discoveries: 2</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-439.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-440.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-441.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-442.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-443.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-444.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 75 : Data Set 685 ; pihat0 = 0.08592309 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-445.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-446.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-447.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-448.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-449.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-450.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 76 : Data Set 499 ; pihat0 = 0.08826948 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-451.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-452.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-453.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-454.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-455.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-456.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 77 : Data Set 982 ; pihat0 = 0.08854547 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-457.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-458.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-459.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-460.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-461.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-462.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 78 : Data Set 582 ; pihat0 = 0.08899861 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-463.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-464.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-465.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-466.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-467.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-468.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 79 : Data Set 953 ; pihat0 = 0.08900989 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-469.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-470.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-471.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-472.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-473.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-474.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 80 : Data Set 811 ; pihat0 = 0.08962902 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-475.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-476.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-477.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-478.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-479.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-480.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 81 : Data Set 575 ; pihat0 = 0.0946117 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-481.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-482.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-483.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-484.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-485.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-486.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 82 : Data Set 997 ; pihat0 = 0.09560788 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-487.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-488.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-489.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-490.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-491.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-492.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 83 : Data Set 231 ; pihat0 = 0.09686204 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-493.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-494.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-495.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-496.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-497.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-498.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 84 : Data Set 781 ; pihat0 = 0.09690435 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-499.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-500.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-501.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-502.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-503.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-504.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 85 : Data Set 853 ; pihat0 = 0.09889116 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-505.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-506.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-507.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-508.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-509.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-510.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 86 : Data Set 868 ; pihat0 = 0.09918104 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-511.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-512.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-513.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-514.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-515.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-516.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 87 : Data Set 502 ; pihat0 = 0.1001788 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-517.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-518.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-519.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-520.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-521.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-522.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 88 : Data Set 606 ; pihat0 = 0.1033893 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-523.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-524.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-525.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-526.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-527.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-528.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 89 : Data Set 912 ; pihat0 = 0.106048 ; Number of False Discoveries: 2</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-529.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-530.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-531.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-532.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-533.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-534.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 90 : Data Set 659 ; pihat0 = 0.1065714 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-535.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-536.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-537.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-538.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-539.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-540.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 91 : Data Set 501 ; pihat0 = 0.1090034 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-541.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-542.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-543.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-544.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-545.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-546.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 92 : Data Set 296 ; pihat0 = 0.1115216 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-547.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-548.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-549.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-550.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-551.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-552.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 93 : Data Set 895 ; pihat0 = 0.1119629 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-553.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-554.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-555.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-556.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-557.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-558.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 94 : Data Set 153 ; pihat0 = 0.1148195 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-559.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-560.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-561.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-562.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-563.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-564.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 95 : Data Set 477 ; pihat0 = 0.1172838 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-565.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-566.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-567.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-568.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-569.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-570.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 96 : Data Set 769 ; pihat0 = 0.1187511 ; Number of False Discoveries: 1</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-571.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-572.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-573.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-574.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-575.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-576.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 97 : Data Set 555 ; pihat0 = 0.1210902 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-577.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-578.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-579.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-580.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-581.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-582.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 98 : Data Set 475 ; pihat0 = 0.1273824 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-583.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-584.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-585.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-586.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-587.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-588.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 99 : Data Set 584 ; pihat0 = 0.1291777 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-589.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-590.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-591.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-592.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-593.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-594.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>N0. 100 : Data Set 949 ; pihat0 = 0.1308901 ; Number of False Discoveries: 0</code></pre>
<p><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-595.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-596.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-597.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-598.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-599.png" width="672" style="display: block; margin: auto;" /><img src="figure/correlated_z_2.Rmd/unnamed-chunk-6-600.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>write.table(pihat0, file = "../output/pihat0_z_null_liver_777.txt", quote = FALSE, col.names = FALSE, row.names = FALSE)</code></pre>
</div>
<div id="session-information" class="section level2">
<h2>Session Information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.3
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] backports_1.0.5 magrittr_1.5 rprojroot_1.2 tools_3.3.2
[5] htmltools_0.3.5 yaml_2.1.14 Rcpp_0.12.9 stringi_1.1.2
[9] rmarkdown_1.3 knitr_1.15.1 git2r_0.18.0 stringr_1.1.0
[13] digest_0.6.9 workflowr_0.3.0 evaluate_0.10 </code></pre>
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