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href="/docs/0.17.1/comparisons/druid-vs-kudu.html">Apache Druid vs Kudu</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/comparisons/druid-vs-redshift.html">Apache Druid vs Redshift</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/comparisons/druid-vs-spark.html">Apache Druid vs Spark</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/comparisons/druid-vs-sql-on-hadoop.html">Apache Druid vs SQL-on-Hadoop</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/design/auth.html">Authentication and Authorization</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/design/broker.html">Broker</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/design/coordinator.html">Coordinator Process</a></li><li class="navListItem"><a class="navItem" href="/docs/0.17.1/design/historical.html">Historical Process</a></li><li class="navListItem"><a class="navItem" 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<p>This Apache Druid 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 aggregators.</p>
<h2><a class="anchor" aria-hidden="true" id="z-score-for-two-sample-ztests-post-aggregator"></a><a href="#z-score-for-two-sample-ztests-post-aggregator" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>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/~jcb0773/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><a class="anchor" aria-hidden="true" id="zscore2sample-post-aggregator"></a><a href="#zscore2sample-post-aggregator" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>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>
<pre><code class="hljs css language-json">{
  <span class="hljs-attr">"type"</span>: <span class="hljs-string">"zscore2sample"</span>,
  <span class="hljs-attr">"name"</span>: <span class="hljs-string">"&lt;output_name&gt;"</span>,
  <span class="hljs-attr">"successCount1"</span>: &lt;post_aggregator&gt; success count of sample <span class="hljs-number">1</span>,
  <span class="hljs-attr">"sample1Size"</span>: &lt;post_aggregaror&gt; sample <span class="hljs-number">1</span> size,
  <span class="hljs-attr">"successCount2"</span>: &lt;post_aggregator&gt; success count of sample <span class="hljs-number">2</span>,
  <span class="hljs-attr">"sample2Size"</span> : &lt;post_aggregator&gt; sample <span class="hljs-number">2</span> size
}
</code></pre>
<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><a class="anchor" aria-hidden="true" id="pvalue2tailedztest-post-aggregator"></a><a href="#pvalue2tailedztest-post-aggregator" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>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>
<pre><code class="hljs css language-json">{
  <span class="hljs-attr">"type"</span>: <span class="hljs-string">"pvalue2tailedZtest"</span>,
  <span class="hljs-attr">"name"</span>: <span class="hljs-string">"&lt;output_name&gt;"</span>,
  <span class="hljs-attr">"zScore"</span>: &lt;zscore post_aggregator&gt;
}
</code></pre>
<h2><a class="anchor" aria-hidden="true" id="example-usage"></a><a href="#example-usage" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>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>
<pre><code class="hljs css language-json">{
  ...
    "postAggregations" : {
    "type"   : "pvalue2tailedZtest",
    "name"   : "pvalue",
    "zScore" :
    {
     "type"   : "zscore2sample",
     "name"   : "zscore",
     "successCount1" :
       { "type"   : "constant",
         "name"   : "successCountFromPopulation1Sample",
         "value"  : 300
       },
     "sample1Size" :
       { "type"   : "constant",
         "name"   : "sampleSizeOfPopulation1",
         "value"  : 500
       },
     "successCount2":
       { "type"   : "constant",
         "name"   : "successCountFromPopulation2Sample",
         "value"  : 450
       },
     "sample2Size" :
       { "type"   : "constant",
         "name"   : "sampleSizeOfPopulation2",
         "value"  : 600
       }
     }
    }
}

</code></pre>
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