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class="search-icon" tabindex="0"></span><input type="search" id="search_input_react" placeholder="Loading..." aria-label="Search" class="navbar__search-input search-bar" disabled=""></div></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div></nav><div id="__docusaurus_skipToContent_fallback" class="main-wrapper mainWrapper_z2l0 docsWrapper_BCFX"><button aria-label="Scroll back to top" class="clean-btn theme-back-to-top-button backToTopButton_sjWU" type="button"></button><div class="docPage__5DB"><main class="docMainContainer_gTbr docMainContainerEnhanced_Uz_u"><div class="container padding-top--md padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Test Stats Aggregators</h1></header><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/" target="_blank" rel="noopener noreferrer">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 class="anchor anchorWithStickyNavbar_LWe7" id="z-score-for-two-sample-ztests-post-aggregator">Z-Score for two sample ztests post aggregator<a href="#z-score-for-two-sample-ztests-post-aggregator" class="hash-link" aria-label="Direct link to Z-Score for two sample ztests post aggregator" title="Direct link to Z-Score for two sample ztests post aggregator"></a></h2><p>Please refer to <a href="https://www.isixsigma.com/tools-templates/hypothesis-testing/making-sense-two-proportions-test/" target="_blank" rel="noopener noreferrer">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" target="_blank" rel="noopener noreferrer">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 <em> ( 1 - p1 )/n1 + p2 </em> (1 - p2)/n2) }</p><p>(p1 – p2) is the observed difference between two sample proportions.</p><h3 class="anchor anchorWithStickyNavbar_LWe7" id="zscore2sample-post-aggregator">zscore2sample post aggregator<a href="#zscore2sample-post-aggregator" class="hash-link" aria-label="Direct link to zscore2sample post aggregator" title="Direct link to zscore2sample post aggregator"></a></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="language-json codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#bfc7d5;--prism-background-color:#292d3e"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-json codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#bfc7d5"><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;type&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;zscore2sample&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;name&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;&lt;output_name&gt;&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;successCount1&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> &lt;post_aggregator&gt; success count of sample </span><span class="token number" style="color:rgb(247, 140, 108)">1</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;sample1Size&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> &lt;post_aggregaror&gt; sample </span><span class="token number" style="color:rgb(247, 140, 108)">1</span><span class="token plain"> size</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;successCount2&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> &lt;post_aggregator&gt; success count of sample </span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;sample2Size&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> &lt;post_aggregator&gt; sample </span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> size</span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain"></span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></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 class="anchor anchorWithStickyNavbar_LWe7" id="pvalue2tailedztest-post-aggregator">pvalue2tailedZtest post aggregator<a href="#pvalue2tailedztest-post-aggregator" class="hash-link" aria-label="Direct link to pvalue2tailedZtest post aggregator" title="Direct link to pvalue2tailedZtest post aggregator"></a></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="language-json codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#bfc7d5;--prism-background-color:#292d3e"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-json codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#bfc7d5"><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;type&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;pvalue2tailedZtest&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;name&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;&lt;output_name&gt;&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  </span><span class="token property">&quot;zScore&quot;</span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> &lt;zscore post_aggregator&gt;</span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain"></span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h2 class="anchor anchorWithStickyNavbar_LWe7" id="example-usage">Example Usage<a href="#example-usage" class="hash-link" aria-label="Direct link to Example Usage" title="Direct link to Example Usage"></a></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="language-json codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#bfc7d5;--prism-background-color:#292d3e"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-json codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#bfc7d5"><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">  ...</span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">    </span><span class="token property">&quot;postAggregations&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">    </span><span class="token property">&quot;type&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;pvalue2tailedZtest&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">    </span><span class="token property">&quot;name&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;pvalue&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">    </span><span class="token property">&quot;zScore&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">    </span><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">     </span><span class="token property">&quot;type&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;zscore2sample&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">     </span><span class="token property">&quot;name&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;zscore&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">     </span><span class="token property">&quot;successCount1&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"> </span><span class="token property">&quot;type&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;constant&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">         </span><span class="token property">&quot;name&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;successCountFromPopulation1Sample&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">         </span><span class="token property">&quot;value&quot;</span><span class="token plain">  </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">300</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">     </span><span class="token property">&quot;sample1Size&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">{</span><span class="token plain"> </span><span class="token property">&quot;type&quot;</span><span class="token plain">   </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;constant&quot;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">         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</span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">     </span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain">    </span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain"></span><span class="token punctuation" style="color:rgb(199, 146, 234)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#bfc7d5"><span class="token plain" style="display:inline-block"></span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span 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aggregator</a></li><li><a href="#pvalue2tailedztest-post-aggregator" class="table-of-contents__link toc-highlight">pvalue2tailedZtest post aggregator</a></li></ul></li><li><a href="#example-usage" class="table-of-contents__link toc-highlight">Example Usage</a></li></ul></div></div></div></div></main></div></div><footer class="footer"><div class="container container-fluid"><div class="footer__bottom text--center"><div class="margin-bottom--sm"><img src="/img/favicon.png" class="themedImage_ToTc themedImage--light_HNdA footer__logo"><img src="/img/favicon.png" class="themedImage_ToTc themedImage--dark_i4oU footer__logo"></div><div class="footer__copyright">Copyright © 2023 Apache Software Foundation. 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