{"id":7264,"date":"2010-11-22T06:24:27","date_gmt":"2010-11-22T11:24:27","guid":{"rendered":"https:\/\/staging.opexlearning.com\/resources\/?p=7264"},"modified":"2013-08-23T13:50:53","modified_gmt":"2013-08-23T18:50:53","slug":"lean-six-sigma-hypothesis-testing-chi-square","status":"publish","type":"post","link":"https:\/\/staging.opexlearning.com\/resources\/lean-six-sigma-hypothesis-testing-chi-square\/7264\/","title":{"rendered":"Lean Six Sigma: Contingency Table and Chi Square Test"},"content":{"rendered":"<div class=\"a296a24fa2fc69ef5487857f02f111e8\" data-index=\"9\" style=\"float: none; margin:10px 0 10px 0; text-align:center;\">\n<script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\r\n<!-- Single Post readerboard -->\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:inline-block;width:728px;height:90px\"\r\n     data-ad-client=\"ca-pub-8207522353004717\"\r\n     data-ad-slot=\"1144967431\"><\/ins>\r\n<script>\r\n(adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\n<\/div>\n<p>Part of the Analyze Phase in the DMAIC <a title=\"6 sigmas, six sigmas\" href=\"https:\/\/staging.opexlearning.com\/resources\/lean-six-sigma-the-dmaic-framework\/2874\/\">Six Sigmas<\/a> Methodology is to verify the potential root causes with hypothesis testing. One common hypothesis test is an application of the Chi Square Test called a Contingency Table, also called a Present \/ Not Present Matrix.<\/p>\n<h2>What is a Contingency Table<\/h2>\n<p>For something to be a root cause, the defect rate must be higher when root cause is present and the defect must be lower when this root cause absent.\u00a0The easiest way to show this is to use 2&#215;2 grid and look for patterns.<\/p>\n<p>The data on the grid will make it very clear if what you are looking at is a root cause of the defect that you are after or not.\u00a0The grid is constructed so that you have a box containing four other boxes (2&#215;2).<\/p>\n<p>On the rows, you add labels root cause present\u009d and root cause absent\u009d and across the columns, you label the columns defect present\u009d and defect absent.\u009d\u00a0Then, you fill in the grid with data (numbers of observations).<\/p>\n<p>You will have to go and look at some non-defective parts and see if your potential root cause is present or absent (you may already have data for your potential root cause from MEASURE, if not, you have to measure that too).<\/p>\n<p>For a potential root cause to be considered verified by this tool, most of the data must be on the diagonal.\u009d\u00a0This means that it will fall in the defect present\/root cause present\u009d box and the defect absent\/root cause absent\u009d box.<\/p>\n<p>If it fits this pattern, then you can be confident that if you eliminate the root cause, then the defect will go away.\u00a0If it does not fit this pattern, you can use more advanced Statistical Tests to verify the root causes.<\/p>\n<p>As an example, let&#8217;s assume the following:<\/p>\n<p class=\"alert\"><strong>Defect<\/strong>: Packages in Order Fulfillment are rejected by the Packing Scanner<\/p>\n<p>And, during our data collection phase in Measure, we have data that shows the data below:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-7266 aligncenter\" title=\"dmaic-hypothesis-test-contingency-table\" alt=\"dmaic, contingency table, hypothesis testing\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/dmaic-hypothesis-test-contingency-table.jpg\" width=\"567\" height=\"229\" srcset=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/dmaic-hypothesis-test-contingency-table.jpg 709w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/dmaic-hypothesis-test-contingency-table-600x242.jpg 600w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/dmaic-hypothesis-test-contingency-table-300x121.jpg 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Typically, they hypothesis takes the form of:<\/p>\n<p class=\"alert\">H<sub>0<\/sub>: there is no relationship between dirty shipping labels and packing scanner rejections<br \/>\nH<sub>1<\/sub>: there is a relationship between dirty labels and packing scanner rejections<\/p>\n<p>Given the data above, we follow this intermediate equation:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-7268 aligncenter\" title=\"chi-square-equation\" alt=\"dmaic, chi square equation\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-equation.gif\" width=\"305\" height=\"51\" srcset=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-equation.gif 305w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-equation-300x50.gif 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Then, we follow the Chi-Square Equation:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-7269 aligncenter\" title=\"chi-square-equation-dmaic\" alt=\"chi square, dmaic, six sigmas, 6 sigmas\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-equation-dmaic.gif\" width=\"153\" height=\"65\" srcset=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-equation-dmaic.gif 153w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-equation-dmaic-150x65.gif 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><\/p>\n<p>Which gives us the results below:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-7270 aligncenter\" title=\"chi-square-six-sigmas-example\" alt=\"6 sigmas, six sigmas, chi square example\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-six-sigmas-example.jpg\" width=\"574\" height=\"386\" srcset=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-six-sigmas-example.jpg 717w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-six-sigmas-example-600x403.jpg 600w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2010\/11\/chi-square-six-sigmas-example-300x201.jpg 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Given the results above, we can conclude the following:<\/p>\n<p class=\"alert\">We Reject the Null Hypothesis<\/p>\n<p>There are many possible applications of the contingency table. Think about your business, the defects that you deal with, and perhaps there might be an opportunity to apply the Chi-Square or Contingency Table to your process.<\/p>\n<p style=\"text-align: center;\"><strong>Click Here to download a <a title=\"download chi square template\" href=\"https:\/\/staging.opexlearning.com\/resources\/six-sigma-chi-square-analysis-example-template\/\">Chi Square Calculator<\/a>.<\/strong><\/p>\n<!--CusAds0-->\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Part of the Analyze Phase in the DMAIC Six Sigmas Methodology is to verify the potential root causes with hypothesis testing. One common hypothesis test is an application of the Chi Square Test called a Contingency Table, also called a Present \/ Not Present Matrix. What is a Contingency Table For something to be a [&hellip;]<\/p>\n","protected":false},"author":12327,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[670],"tags":[662],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Six Sigma | DMAIC | Contingency Table | Hypothesis Testing | Chi Square<\/title>\n<meta name=\"description\" content=\"An example of how to apply the contingency table to a six sigma project\" \/>\n<meta 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