{"id":1197,"date":"2014-04-25T11:40:01","date_gmt":"2014-04-25T15:40:01","guid":{"rendered":"https:\/\/keyknowledge.com\/?p=1197"},"modified":"2014-04-25T11:40:01","modified_gmt":"2014-04-25T15:40:01","slug":"hypothesis-testing-some-basic-concepts-and-issues","status":"publish","type":"post","link":"https:\/\/keyknowledge.com\/de_ch\/2014\/04\/hypothesis-testing-some-basic-concepts-and-issues\/","title":{"rendered":"Hypothesentests \u2013 Einige grundlegende Konzepte und Probleme"},"content":{"rendered":"

Our Six Sigma courses include a number of lessons on hypothesis testing.\u00a0 The most common problems that I see with submissions for these assignments are related to how the null and alternate hypotheses are stated and how the results of the hypothesis test are expressed.
\nThe null and alternate hypotheses must be mutually exclusive, and must contain all of the possibilities. \u00a0The null hypothesis should include a null statement such as no difference, no change, or no improvement.\u00a0 The alternate hypothesis should state that there was a difference, a change or an improvement.
\nThe example that most students can relate to is that of a courtroom trial.\u00a0 In a criminal trial, the burden of proof is on the prosecution to prove that a crime was committed.\u00a0 There is no such burden for the defendant to prove that they did not commit a crime.\u00a0 The null hypothesis in the courtroom is that the defendant is not guilty of the crime that they are charged with committing, i.e. the null condition.\u00a0 The alternate hypothesis is that the defendant is guilty of the crime as charged.
\nFor a process improvement project, the burden of proof is on the project team to show that improvement was really achieved.\u00a0 We might state the null and alternate hypotheses as follows:
\nNull hypothesis:\u00a0 There was no improvement to the output of the process.
\nAlternate hypothesis:\u00a0 There was improvement in the output of the process.
\nWe test by formulating the null and the alternate hypotheses, collecting data (or evidence) and then calculating how probable it is that the data would be collected if the null hypothesis were true.\u00a0 If the data or evidence appears improbable then the null hypothesis is probably not true and it is rejected.\u00a0 Otherwise, we must fail to reject the null hypothesis.\u00a0 The correct way to state the outcome of a hypothesis test is that we either reject the null hypothesis, or we fail to reject the null hypothesis.\u00a0 We do not accept the null hypothesis, nor do we accept the alternate hypothesis.
\nIn the courtroom, the null hypothesis is not guilty.\u00a0 We weigh the evidence in the case and then ask ourselves how likely it is that the defendant is not guilty.\u00a0 If not guilty seems unlikely then we return a verdict of guilty.\u00a0 In other words, if we feel that there is guilt beyond a reasonable doubt, we reject the null hypothesis of not guilty and return a verdict of guilty.
\nIf we feel that there is some probability that the null hypothesis of not guilty is true then we fail to reject the null hypothesis due to insufficient evidence and the conclusion is not guilty.\u00a0 Please note that the verdict is never returned as innocent, as we do not know for certain that the defendant is innocent.\u00a0 The verdict of not guilty is based on the fact that there was not enough proof, i.e. proof beyond a reasonable doubt, to declare the defendant guilty.
\nThere are two types of errors that we can make in hypothesis testing.\u00a0 The first is to reject the null hypotheses when it is true.\u00a0 In the courtroom the null hypothesis is not guilty.\u00a0 If the defendant is truly not guilty and we reject the null hypothesis of not guilty, we return a guilty verdict.\u00a0 The result is that an innocent person is convicted.\u00a0 This is a grievous error, and one that we want to avoid.\u00a0 In practice we want the reasonable doubt that we are making the correct decision to be small.\u00a0 A level of five percent doubt, or 95% confidence that we are making the correct decision, is a common standard in hypothesis testing.\u00a0 The more confident we want to be in our decision, the more facts or evidence that we need to support our conclusion.
\nThe second type of error that we can make is to fail to reject the null hypothesis when it is false.\u00a0 Again in the courtroom the null hypothesis is not guilty.\u00a0 If the null is in truth false and the defendant is really guilty, and we fail to reject the null hypothesis, we return a verdict of not guilty.\u00a0 The result is that a guilty defendant goes free.
\nIn the example of the process improvement project, to test the null hypothesis we collect data about the output of the process before and after improvement and we calculate the probability that the data after improvement is the same as before improvement using confidence intervals.\u00a0 If this probability turns out to be small, i.e. smaller than the level of reasonable doubt we are willing to accept (usually five percent) then we reject the null hypothesis of no improvement and conclude that there was statistically significant improvement.\u00a0 Otherwise, we fail to reject the null hypothesis and conclude that there was no statistically significant improvement.
\nAs a final note on the process improvement example, improvement must be of practical significance as well as of statistical significance.\u00a0 It is possible for improvement to be statistically significant but small enough that it is of no practical value.
\nIhre Kommentare und Fragen zu diesem Artikel sowie Anregungen f\u00fcr zuk\u00fcnftige Artikel sind herzlich willkommen. Sie k\u00f6nnen mich gerne per E-Mail kontaktieren unter roger@keyperformance.com<\/a>.
\n\u00dcber den Autor: Roger C. Ellis ist studierter und praktizierender Wirtschaftsingenieur. Er ist Six Sigma Master Black Belt und verf\u00fcgt \u00fcber mehr als 45 Jahre Berufserfahrung in verschiedenen Branchen. Herr Ellis entwickelt und leitet Six-Sigma-Zertifizierungskurse f\u00fcr Key Performance LLC. Eine ausf\u00fchrlichere Biografie finden Sie hier: www.keyperformance.com<\/a>.
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Our Six Sigma courses include a number of lessons on hypothesis testing.\u00a0 The most common problems that I see with submissions for these assignments are related to how the null and alternate hypotheses are stated and how the results of the hypothesis test are expressed. The null and alternate hypotheses must be mutually exclusive, and […]\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"cybocfi_hide_featured_image":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1197","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/posts\/1197","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/comments?post=1197"}],"version-history":[{"count":0,"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/posts\/1197\/revisions"}],"wp:attachment":[{"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/media?parent=1197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/categories?post=1197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/keyknowledge.com\/de_ch\/wp-json\/wp\/v2\/tags?post=1197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}