{"id":42545,"date":"2014-03-15T08:18:48","date_gmt":"2014-03-15T02:48:48","guid":{"rendered":"http:\/\/vskills.in\/certification\/tutorial\/?p=42545"},"modified":"2024-04-12T14:19:43","modified_gmt":"2024-04-12T08:49:43","slug":"analysis-of-variance-anova","status":"publish","type":"page","link":"https:\/\/www.vskills.in\/certification\/tutorial\/analysis-of-variance-anova\/","title":{"rendered":"Analysis of Variance (ANOVA)"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><a ref=\"magnificPopup\" href=\"https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/Cisco-Business-Architecture-Specialist-820-445-DTBAS-10-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"400\" src=\"https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/Cisco-Business-Architecture-Specialist-820-445-DTBAS-10-1.png\" alt=\"Analysis of Variance (ANOVA)\" class=\"wp-image-94305\" srcset=\"https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/Cisco-Business-Architecture-Specialist-820-445-DTBAS-10-1.png 750w, https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/Cisco-Business-Architecture-Specialist-820-445-DTBAS-10-1-300x160.png 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><\/a><\/figure><\/div>\n\n\n<p>\u00a0<\/p>\n<h4><strong>Analysis of Variance<\/strong><\/h4>\n<p>ANOVA is used to determine if the average of a group of data is different than the average of other (multiple) groups of data. This tool is used in the\u00a0&#8216;Analysis&#8217;\u00a0phase of a DMAIC Six Sigma project.<\/p>\n<p>The statistical method is applied to test hypotheses among means from several populations. It assumes the sampled populations are normally distributed.<\/p>\n<p>The Y-data is variable type of data (such as time).<\/p>\n<p>The X-data is attribute data (such as appraiser name).<\/p>\n<p>ANOVA is a hypothesis test for means (not median or mode) and usually is applied for testing &gt;2 means. Use 1 sample t or 2 sample t test for one or two means-testing respectively.<\/p>\n<p>It uses two components of variance and the F test to test the two components:<\/p>\n<ul>\n<li>BETWEEN sample variance<\/li>\n<li>WITHIN sample varianceBETWEEN sample variance is a study of the variation among all the samples usually due to process difference or factor changesWITHIN sample variance explains the variation within each sample itself (look at a Box Plot of one data set to graphically comprehend this &#8211; the tip of one whisker to another)ANOVA shows the right results if the means of several populations are statistically different or equal. It also computes a lot of other valuable insight that can help steer a GB\/BB in clearer direction. A statistical difference is found when the difference BETWEEN samples is large enough &#8220;relative to the difference WITHIN the samples.<\/li>\n<\/ul>\n<h5><strong>ANOVA Jargon<\/strong><\/h5>\n<ul>\n<li>Factor (Process Input Variable &#8211; PIV, x): A controlled or uncontrolled variable whose influence is being evaluated.<\/li>\n<li>Factor Level (+1,-1,Hi,Low,+,-,A,B,): Factor setting.<\/li>\n<li>Response(Process Output Variable &#8211; POV, y): The output of the process.<\/li>\n<li>Inference Space: Range of the factors being evaluated.<\/li>\n<li>Fit: Predicted value of the POV (y) with a specified setting of factors.<\/li>\n<li>Residual: Difference from a FIT (predicted output) from the actual experimental output.<\/li>\n<\/ul>\n<h5><strong>One-Way ANOVA Example<\/strong><\/h5>\n<ul>\n<li>Determine if there is a significant difference in two or more appraisers. The results of a mock study where four appraisers were timed to make an inspection decision on 13 widgets.<\/li>\n<li>All other criteria are equal.<\/li>\n<li>Since TIME is the only factor, this is a One-Factor or One-Way ANOVA. There are four levels that are controlled in the experiment, one being each appraiser.<\/li>\n<li>The first step is to create the test. In general, if the P-value is lower than the alpha-risk then the alternate hypothesis is inferred (reject the null).<\/li>\n<\/ul>\n<p><strong><span style=\"text-decoration: underline;\">Hypothesis Test:<\/span><\/strong><\/p>\n<p><strong>Null Hypothesis:<\/strong> Population means of the different appraisers are equal.<br \/><strong>Alternate Hypothesis:<\/strong> One of the means is not the same<\/p>\n<ul>\n<li>There are 51 Degrees of Freedom computed from (13*4)-1.<\/li>\n<li>Using a One-Way test with alpha at 0.05,the P-value is well above 0.05 at 0.847,\u00a0f-statistic, and heavily overlapping confidence intervals are all evidence that there is no difference among any pairs or combinations of them.<\/li>\n<li>It is concluded that there is not a statistical difference\u00a0between\u00a0any of the appraisers.<\/li>\n<li>If the P was &lt;0.05, then at least one group of data is different than at least one other group.<\/li>\n<li>The low F-value of 0.27 says the variation\u00a0within\u00a0the appraisers is greater than the variation\u00a0between\u00a0them. The F-critical value is 2.81.<\/li>\n<li>It is advisable to a project manager to re-running (depending on cost and time) the trial with a larger sample size and additional appraiser training to reduce the variation within each one. The variation is fairly consistent among each of them so it appears there is a systemic issue.<\/li>\n<\/ul>\n<p align=\"center\"><img decoding=\"async\" title=\"Example of One-way ANOVA statistical results\" src=\"http:\/\/www.six-sigma-material.com\/images\/OneWayANOVAexample.JPG\" alt=\"Example of One-way ANOVA statistical results\" width=\"503\" \/><\/p>\n<h5><strong>Two-Way ANOVA<\/strong><\/h5>\n<p>Other factors can be added to this type of test and get more complicated but most statistical software programs can run Two-Way and Three-Way ANOVA.<\/p>\n<p><strong>Two-Way Hypothesis Tests:<\/strong><\/p>\n<p><strong>Null Hypothesis:<\/strong> There is no difference in the means of the 1st factor<br \/><strong>Null Hypothesis:<\/strong> There is no difference in means of the 2nd factor<br \/><strong>Null Hypothesis:<\/strong> There is no interaction between the two factors<\/p>\n<p><strong>Alternate Hypothesis:<\/strong> Means are not equal among the levels of the 1st factor<br \/><strong>Alternate Hypothesis:<\/strong> Means are not equal among the levels of the 2nd factor<br \/><strong>Alternate Hypothesis:<\/strong> There is an interaction between the two factors<\/p>\n<div class=\"apply\">\n<p>Test Your Six Sigma Black Belt Skills By Taking Our Practice Tests on This <a href=\"http:\/\/www.vskills.in\/practice\/quiz\/Six-Sigma-Black-Belt\">Link<\/a><\/p>\n<h5>Apply for Six Sigma Black Belt Certification Now!!<\/h5>\n<p><a href=\"http:\/\/www.vskills.in\/certification\/Certified-Six-Sigma-Black-Belt-Professional\">http:\/\/www.vskills.in\/certification\/Certified-Six-Sigma-Black-Belt-Professional<\/a><\/p>\n<\/div>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><a ref=\"magnificPopup\" href=\"https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/1Z0-1050-20-Oracle-Payroll-Cloud-2020-Implementation-Essentials-1-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"961\" height=\"150\" src=\"https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/1Z0-1050-20-Oracle-Payroll-Cloud-2020-Implementation-Essentials-1-1.png\" alt=\"\" class=\"wp-image-94260\" srcset=\"https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/1Z0-1050-20-Oracle-Payroll-Cloud-2020-Implementation-Essentials-1-1.png 961w, https:\/\/www.vskills.in\/certification\/tutorial\/wp-content\/uploads\/2020\/12\/1Z0-1050-20-Oracle-Payroll-Cloud-2020-Implementation-Essentials-1-1-300x47.png 300w\" sizes=\"auto, (max-width: 961px) 100vw, 961px\" \/><\/a><\/figure><\/div>\n\n\n\n<p><a href=\"https:\/\/www.vskills.in\/certification\/tutorial\/six-sigma-black-belt-certification\/\" target=\"_blank\" rel=\"noreferrer noopener\">Go back to Tutorial<\/a>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <a href=\"https:\/\/www.vskills.in\/certification\/Certified-Six-Sigma-Black-Belt-Professional\" target=\"_blank\" rel=\"noreferrer noopener\">Go to Home Page<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0 Analysis of Variance ANOVA is used to determine if the average of a group of data is different than the average of other (multiple) groups of data. This tool is used in the\u00a0&#8216;Analysis&#8217;\u00a0phase of a DMAIC Six Sigma project. The statistical method is applied to test hypotheses among means from several populations. It assumes&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[3897,6280],"tags":[6920,6921,9750,9747,9749,9751,9748,9752,6848,6871],"class_list":["post-42545","page","type-page","status-publish","hentry","category-quality","category-six-sigma-black-belt-quality","tag-analysis-of-variance","tag-anova","tag-certified-six-sigma-black-belt-professional-course-outline","tag-certified-six-sigma-black-belt-professional-exam-details","tag-certified-six-sigma-black-belt-professional-free-practice-test","tag-certified-six-sigma-black-belt-professional-online-tutorial","tag-certified-six-sigma-black-belt-professional-preparatory-guide","tag-certified-six-sigma-black-belt-professional","tag-quality","tag-tutorials"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Six Sigma Black Belt Tutorial | Analysis of Variance (ANOVA)<\/title>\n<meta name=\"description\" content=\"ANOVA is used to determine if the average of a group of data is different than the average of other (multiple) groups of data. 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