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The material reviews common core expectations for randomized experiments, compares approaches using normal assumptions (z-test) versus permutation tests without distribution requirements, and applies P-tests through null/alternative hypotheses, simulation randomization, and interpretation of p-values to decide significance.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/significance-of-experimental-results-using-a-permutation-test-p-test/267683/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/significance-of-experimental-results-using-a-permutation-test-p-test/267683.png","ImageObject",300,407,{"name":42,"@type":43},"\tWilliam","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"When is a difference between the control group and treatment group likely caused by the treatment?","Question",{"text":63,"@type":64},"A difference is likely caused by the treatment when the observed gap between group means is statistically significant under an appropriate null hypothesis for randomization.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why can permutation tests be used without assuming the data are normally distributed?",{"text":68,"@type":64},"Permutation tests rely on resampling by randomly reassigning observations to groups, building the reference distribution from simulations rather than from a normal model.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you decide significance using a permutation test p-value?",{"text":72,"@type":64},"Use the p-value thresholds: p>0.10 means not significant (fail to reject the null), 0.05\u003Cp≤0.10 is marginally significant, 0.01\u003Cp≤0.05 is significant, and p≤0.01 is highly significant (reject the null).","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},267683,1790074363,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & 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Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123},5909887254083,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","# Significance of ExperimentalResults\n\nGoing Deeper  \nEssential question:In an experinent,ahenis the difvence betueen the controlgroup and trearnenr group likely to be caursed by he treatnenr?  \nEssential question:In an experiment,when is a difference between the control groupand treatment group likely to be caused by the treatment?  \nCOMMON Standards for  \nCORE Mathematical Content  \nCC.9-12.5.JC.5 Use data from a randomized  \nexperiment to compare twotreatments;usesimulationsto decide if differences between  \nparazneters are signiflcant.  \n## Using a Permutation Test(P-Test)\n\n\n|  | SAT Scores   |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Treatment Group   | 1440   | 1610   | 1430   | 1700   | 1690   |\n|  | 1570   | 1480   | 1620   | 1780   | 2010   |\n| Control Group   | 1150   | 1500   | 1050   | 1600   | 1460   |\n|  | 1860   | 1350   | 1750   | 1680   | 1330   |\n\n\n|  | SAT Scores   |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Treatment Group   | 1440   | 1610   | 1430   | 1700   | 1690   |\n|  | 1570   | 1480   | 1620   | 1780   | 2010   |\n| Control Group   | 1150   | 1500   | 1050   | 1600   | 1460   |\n|  | 1860   | 1350   | 1750   | 1680   | 1330   |\n\nDo students that take an SAT prep courseactually improve their SAT scores?  \nUsing a Permutation Test(P-Test)  \n\n|  | SAT Scores   |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Treatment Group   | 1440   | 1610   | 1430   | 1700   | 1690   |\n|  | 1570   | 1480   | 1620   | 1780   | 2010   |\n| Control Group   | 1150   | 1500   | 1050   | 1600   | 1460   |\n|  | 1860   | 1350   | 1750   | 1680   | 1330   |\n\nb.) Calculate the mean score for each group  \n3=1633  \n₅=1473  \n买--160  \n答5  \nWhen conducting a z-test,we are actually assuming thatthe data(or the random errors)follow a normaldistribution.  \nPermutation tests(randomization tests)can be used without the normalassumption for the distribution of data.  \n## Using a Permutation Test(P-Test)\n\na.)State the null and alternative hypothesis interms of the difference of the 2 group means.  \nH₀:The difference of the 2 group means is 0.  \nHa:The difference between the 2 groupmeans(treatment -control)is positive.  \nIf the PREP course has NO effect at all,then if werearrange the data in the two group,we shouldexpect the same results.  \nSIMULATION:  \nWe are going to randomize the data before putting theminto 2 groups.We then will find the difference in themeans between the 2 groups.  \n\n|  | SAT Scores   |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Treatment Group   | 1440   | 1610   | 1430   | 1700   | 1690   |\n|  | 1570   | 1480   | 1620   | 1780   | 2010   |\n| Control Group   | 1150   | 1500   | 1050   | 1600   | 1460   |\n|  | 1860   | 1350   | 1750   | 1680   | 1330   |\n\n\n|  | SATSCORES   |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| A   | 1490   |  |  |  |  |\n|  |  |  |  |  |  |\n| B   |  |  |  |  |  |\n|  |  |  |  |  |  |\n\n## Using a Permutation Test(P-Test)\n\nthatamstu  \n| Interval   | Frequency   |  |\n| --- | --- | --- |\n| Ax\u003C-240   | 2   |  |\n| -240≤x\u003C-160   | 生   |  |\n| -160≤x\u003C-80   |  |  |\n| -80≤x\u003C0   | 多4   |  |\n| 0sx\u003C80   |  |  |\n| 80sx\u003C160   | 5   |  |\n| 160sx\u003C240   |  |  |\n| 240sxyn   |  |  |\n\n\n| Interval   | Frequency   |\n| --- | --- |\n| -320≤x\u003C-240   | 1   |\n| -240≤x\u003C-160   | 7   |\n| -160≤x\u003C-80   | 19   |\n| -80≤x\u003C0   | 26   |\n| 0≤x\u003C80   | 23   |\n| 80≤x\u003C160   | 11   |\n| 160≤x\u003C240   |  |\n| 240≤x\u003C320   |  |\n\nUsing a Permutation Test(P-Test)  \nd.)Here is another way to represent the data.This is a DOTPLOT representing how manytimes our simulated value of 160 or morecould occur in90 simulations  \nRandom number generator on graphing calc to select10 data to be on groupA.The rest will be in group B.  \nMake sure you select 10 unique random numbers.Hit enter until you do.  \nA×A-B3Bx  \nUsing a Permutation Test(P-Test)  \ne.)Look at the histogram or frequency table tosee how many times our test statistic of 160or more occurred.(this is a sample of what thesimulations would also look like)  \np va","cbCairrtIyOP3pR4","https://ap.wps.com/l/cbCairrtIyOP3pR4","pdf",5441521,"English","# Significance of Experimental Results\n## Using a Permutation Test (P-Test)\n## Hypotheses and Simulation Randomization\n## Test Statistic, p-Value, and Significance","[{\"question\":\"When is a difference between the control group and treatment group likely caused by the treatment?\",\"answer\":\"A difference is likely caused by the treatment when the observed gap between group means is statistically significant under an appropriate null hypothesis for randomization.\"},{\"question\":\"Why can permutation tests be used without assuming the data are normally distributed?\",\"answer\":\"Permutation tests rely on resampling by randomly reassigning observations to groups, building the reference distribution from simulations rather than from a normal model.\"},{\"question\":\"How do you decide significance using a permutation test p-value?\",\"answer\":\"Use the p-value thresholds: p\\u003e0.10 means not significant (fail to reject the null), 0.05\\u003cp≤0.10 is marginally significant, 0.01\\u003cp≤0.05 is significant, and p≤0.01 is highly significant (reject the null).\"}]","Significance of ExperimentalResults - Using a Permutation Test (P-Test) | PDF",1789424017]