[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-187769-en":3,"doc-seo-187769-105":31,"detail-sidebar-cat-1-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":11,"category_id":12,"category_name":13,"doc_title":14,"doc_description":15,"doc_content":16,"file_id":17,"file_url":18,"file_type":19,"file_size":20,"view_count":21,"is_deleted":4,"is_public":11,"is_downloadable":11,"audit_status":11,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":15,"update_tm":29,"read_time":30},187769,1374402739827,"Nguyễn Văn Học","https://ap-avatar.wpscdn.com/avatar/14000c97e7351f1a627?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787885694763230660",1,158,"General","Introduction - 1 - Assessing Significance in a Hypothesis Test","The text introduces hypothesis testing as a structured process for evaluating substantive theory through evidence against a null hypothesis. It explains the three essential ingredients: a hypothesis, a single-valued test statistic, and a method to generate the test statistic’s probability distribution under the null. The discussion emphasizes choosing test statistics for sensitivity to the theory’s direction, illustrates issues with conventional assumptions like Normality in the t test, and describes computing significance as a right-tail probability using density estimates or computer-intensive methods.","AN INTRODUCTION  \nEric W.Noreen  \nUniversity of Washington  \nA Wiley-Interscience PublicationJOHN WILEY&SONS  \nNew York  ·  Chichester  ·  Brisbane  \n# Introduction\n\nThe next few years are likely to bean exciting period for those involvedin testing hypotheses.Recentdramatic decreases in the costs ofcomputing now make revolutionarymethods for testing hypotheses avail-able to anyone with access to apersonal computer.These methodsare easy to understand,very general,and can often avoid troublesomeassumptions that are required withconventional methods.  \n# 2 Chapter 1 Introduction\n\n## 1.1 ASSESSING SIGNIFICANCE IN A HYPOTHESIS TEST\n\nThree ingredients are usually required for a hypothesis test:a hypothesis,atest statistic,and some means of generating the probability distribution of thetest statistic under the assumption that the hypothesis is true.The first ingre-dient,the hypothesis,should be suggested by substantive theory.For example,economists would predict that,all other things being equal,an increase in thesupply of corn should lead to a decrease in the price of corn.Because of thelogic of inference,the hypothesis is ordinarily stated negatively in the form of anull hypothesis which the researcher would like to reject.To take the aboveexample,the null hypothesis might be that there is no relationship between thesupply and the price of corn.The alternative hypothesis is that the price of cornis negatively related to its supply.  \nA test statistic is the second ingredient required for a hypothesis test.A teststatistic can be any single-valued function of the data.For example,the averagevalue of a variable across all cases is a single-valued function of the data.Thereare many possible test statistics in any given situation.Often test statistics areselected because they are familiar or because the distribution of the test statisticis known for a sufficiently structured nullhypothesis.¹However,a test statisticshould be chosen because its value is most sensitive to the veracity of the sub-stantive theory being tested.In other words,a test statistic should have the char-acteristic that the larger the value of the test statistic,the stronger the evidence ofdeparture from the null hypothesis in the direction indicated by the substantivetheory.²For example,economic theory suggests that as the supply of cornincreases,its price should fall;that is,supply and price should be negativelycorrelated.A natural test statistic would be the negative of the correlationbetween the two variables.If the relationship between the price and supply ofcorn is perfect,the correlation will be-1 and the value of the test statistic willbe  \n+1.In cases where the relationship is strong but not perfect,the value of the teststatistic will be positive,but less than+1.  \nThe third ingredient required for a hypothesis test is some means of generat-ing the probability distribution of the test statistic under the assumption that thenull hypothesis is true.In conventional statistics,this is ordinarily accomplishedby adding structure to the null hypothesis in such a way that it is possible to ana-lytically derive the probability distribution.For the example of research involv-ing the relationship between the price and the supply of corn,the simple null  \nAssessing Significance in a Hypothesis Test 3  \nhypothesis of interest is that the price of corn does not depend on the supply ofcorn.However,when the t test is used to assess the significance of the correla-tion,the null hypothesis is implicitly much more structured and complex thanthe researcher would like.Under the assumptions that the price of corn and thesupply of corn are independently and Normally distributed random variableswith constant means and variances,the probability distribution of the samplecorrelation can be analytically derived.Without this assumption (or some otherrestrictive assumption),the probability distribution of the correlation cannot bederived.  \nNote that the conventional t test is thus a tes","cbCaibUE6WYhj8cy","https://ap.wps.com/l/cbCaibUE6WYhj8cy","pdf",6591455,2,93,"English","en",105,"# Introduction\n## Assessing Significance in a Hypothesis Test","[{\"question\":\"What are the three ingredients required for a hypothesis test?\",\"answer\":\"A hypothesis, a test statistic, and a way to generate the probability distribution of the test statistic under the assumption that the null hypothesis is true.\"},{\"question\":\"Why is the null hypothesis often stated negatively?\",\"answer\":\"The logic of inference typically frames the hypothesis to be tested in negative form as a null hypothesis, which researchers aim to reject.\"},{\"question\":\"How does conventional t testing relate to assumptions like Normality?\",\"answer\":\"The conventional t test effectively tests a joint hypothesis including independence and Normality; rejecting it may reflect dependence or violations of Normality rather than only the relationship of interest.\"}]","Introduction - 1 - Assessing Significance in a Hypothesis Test | 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are the three ingredients required for a hypothesis test?","Question",{"text":76,"@type":77},"A hypothesis, a test statistic, and a way to generate the probability distribution of the test statistic under the assumption that the null hypothesis is true.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Why is the null hypothesis often stated negatively?",{"text":81,"@type":77},"The logic of inference typically frames the hypothesis to be tested in negative form as a null hypothesis, which researchers aim to reject.",{"name":83,"@type":74,"acceptedAnswer":84},"How does conventional t testing relate to assumptions like Normality?",{"text":85,"@type":77},"The conventional t test effectively tests a joint hypothesis including independence and Normality; rejecting it may reflect dependence or violations of Normality rather than only the relationship of 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