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<h1 id="test-stats-aggregators">Test Stats Aggregators</h1>
<p>This Apache Druid (incubating) extension incorporates test statistics related aggregators, including z-score and p-value. Please refer to <a href="https://www.paypal-engineering.com/2017/06/29/democratizing-experimentation-data-for-product-innovations/">https://www.paypal-engineering.com/2017/06/29/democratizing-experimentation-data-for-product-innovations/</a> for math background and details.</p>
<p>Make sure to include <code>druid-stats</code> extension in order to use these aggregrators.</p>
<h2 id="z-score-for-two-sample-ztests-post-aggregator">Z-Score for two sample ztests post aggregator</h2>
<p>Please refer to <a href="https://www.isixsigma.com/tools-templates/hypothesis-testing/making-sense-two-proportions-test/">https://www.isixsigma.com/tools-templates/hypothesis-testing/making-sense-two-proportions-test/</a> and <a href="http://www.ucs.louisiana.edu/%7Ejcb0773/Berry_statbook/Berry_statbook_chpt6.pdf">http://www.ucs.louisiana.edu/~jcb0773/Berry_statbook/Berry_statbook_chpt6.pdf</a> for more details.</p>
<p>z = (p1 - p2) / S.E. (assuming null hypothesis is true)</p>
<p>Please see below for p1 and p2.
Please note S.E. stands for standard error where </p>
<p>S.E. = sqrt{ p1 * ( 1 - p1 )/n1 + p2 * (1 - p2)/n2) }</p>
<p>(p1 – p2) is the observed difference between two sample proportions.</p>
<h3 id="zscore2sample-post-aggregator">zscore2sample post aggregator</h3>
<ul>
<li><strong><code>zscore2sample</code></strong>: calculate the z-score using two-sample z-test while converting binary variables (<strong><em>e.g.</em></strong> success or not) to continuous variables (<strong><em>e.g.</em></strong> conversion rate).</li>
</ul>
<div class="highlight"><pre><code class="language-json" data-lang="json"><span></span><span class="p">{</span>
<span class="nt">&quot;type&quot;</span><span class="p">:</span> <span class="s2">&quot;zscore2sample&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span><span class="p">:</span> <span class="s2">&quot;&lt;output_name&gt;&quot;</span><span class="p">,</span>
<span class="nt">&quot;successCount1&quot;</span><span class="p">:</span> <span class="err">&lt;post_aggregator&gt;</span> <span class="err">success</span> <span class="err">count</span> <span class="err">of</span> <span class="err">sample</span> <span class="mi">1</span><span class="p">,</span>
<span class="nt">&quot;sample1Size&quot;</span><span class="p">:</span> <span class="err">&lt;post_aggregaror&gt;</span> <span class="err">sample</span> <span class="mi">1</span> <span class="err">size</span><span class="p">,</span>
<span class="nt">&quot;successCount2&quot;</span><span class="p">:</span> <span class="err">&lt;post_aggregator&gt;</span> <span class="err">success</span> <span class="err">count</span> <span class="err">of</span> <span class="err">sample</span> <span class="mi">2</span><span class="p">,</span>
<span class="nt">&quot;sample2Size&quot;</span> <span class="p">:</span> <span class="err">&lt;post_aggregator&gt;</span> <span class="err">sample</span> <span class="mi">2</span> <span class="err">size</span>
<span class="p">}</span>
</code></pre></div>
<p>Please note the post aggregator will be converting binary variables to continuous variables for two population proportions. Specifically</p>
<p>p1 = (successCount1) / (sample size 1)</p>
<p>p2 = (successCount2) / (sample size 2)</p>
<h3 id="pvalue2tailedztest-post-aggregator">pvalue2tailedZtest post aggregator</h3>
<ul>
<li><strong><code>pvalue2tailedZtest</code></strong>: calculate p-value of two-sided z-test from zscore
<ul>
<li><strong><em>pvalue2tailedZtest(zscore)</em></strong> - the input is a z-score which can be calculated using the zscore2sample post aggregator</li>
</ul></li>
</ul>
<div class="highlight"><pre><code class="language-json" data-lang="json"><span></span><span class="p">{</span>
<span class="nt">&quot;type&quot;</span><span class="p">:</span> <span class="s2">&quot;pvalue2tailedZtest&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span><span class="p">:</span> <span class="s2">&quot;&lt;output_name&gt;&quot;</span><span class="p">,</span>
<span class="nt">&quot;zScore&quot;</span><span class="p">:</span> <span class="err">&lt;zscore</span> <span class="err">post_aggregator&gt;</span>
<span class="p">}</span>
</code></pre></div>
<h2 id="example-usage">Example Usage</h2>
<p>In this example, we use zscore2sample post aggregator to calculate z-score, and then feed the z-score to pvalue2tailedZtest post aggregator to calculate p-value.</p>
<p>A JSON query example can be as follows:</p>
<div class="highlight"><pre><code class="language-json" data-lang="json"><span></span><span class="p">{</span>
<span class="err">...</span>
<span class="nt">&quot;postAggregations&quot;</span> <span class="p">:</span> <span class="p">{</span>
<span class="nt">&quot;type&quot;</span> <span class="p">:</span> <span class="s2">&quot;pvalue2tailedZtest&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span> <span class="p">:</span> <span class="s2">&quot;pvalue&quot;</span><span class="p">,</span>
<span class="nt">&quot;zScore&quot;</span> <span class="p">:</span>
<span class="p">{</span>
<span class="nt">&quot;type&quot;</span> <span class="p">:</span> <span class="s2">&quot;zscore2sample&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span> <span class="p">:</span> <span class="s2">&quot;zscore&quot;</span><span class="p">,</span>
<span class="nt">&quot;successCount1&quot;</span> <span class="p">:</span>
<span class="p">{</span> <span class="nt">&quot;type&quot;</span> <span class="p">:</span> <span class="s2">&quot;constant&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span> <span class="p">:</span> <span class="s2">&quot;successCountFromPopulation1Sample&quot;</span><span class="p">,</span>
<span class="nt">&quot;value&quot;</span> <span class="p">:</span> <span class="mi">300</span>
<span class="p">},</span>
<span class="nt">&quot;sample1Size&quot;</span> <span class="p">:</span>
<span class="p">{</span> <span class="nt">&quot;type&quot;</span> <span class="p">:</span> <span class="s2">&quot;constant&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span> <span class="p">:</span> <span class="s2">&quot;sampleSizeOfPopulation1&quot;</span><span class="p">,</span>
<span class="nt">&quot;value&quot;</span> <span class="p">:</span> <span class="mi">500</span>
<span class="p">},</span>
<span class="nt">&quot;successCount2&quot;</span><span class="p">:</span>
<span class="p">{</span> <span class="nt">&quot;type&quot;</span> <span class="p">:</span> <span class="s2">&quot;constant&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span> <span class="p">:</span> <span class="s2">&quot;successCountFromPopulation2Sample&quot;</span><span class="p">,</span>
<span class="nt">&quot;value&quot;</span> <span class="p">:</span> <span class="mi">450</span>
<span class="p">},</span>
<span class="nt">&quot;sample2Size&quot;</span> <span class="p">:</span>
<span class="p">{</span> <span class="nt">&quot;type&quot;</span> <span class="p">:</span> <span class="s2">&quot;constant&quot;</span><span class="p">,</span>
<span class="nt">&quot;name&quot;</span> <span class="p">:</span> <span class="s2">&quot;sampleSizeOfPopulation2&quot;</span><span class="p">,</span>
<span class="nt">&quot;value&quot;</span> <span class="p">:</span> <span class="mi">600</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="p">}</span>
</code></pre></div>
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