[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-564196-105":3,"detail-sidebar-cat-1-en-105":74,"doc-detail-564196-en":120},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":67,"head_meta":69,"extra_data":71,"updated_unix":73},105,"en","p-values-simplified-explanation-of-p-values-in-hypothesis-testing","P-VALUES - Simplified - Explanation of p-values in hypothesis testing","","A clear, tutorial-style explanation of p-values in the setting of hypothesis testing. It emphasizes that hypothesis tests cannot prove a null hypothesis and instead assess evidence for rejecting it under the assumption that the null is correct. The text contrasts formal definitions with a more intuitive view: the probability level to which data support the null. Examples with p=0.836 and p=0.022 illustrate how large p-values support failing to reject, while small p-values provide weak support for the null and favor the alternative.",{"@graph":14,"@context":66},[15,34,49],{"@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/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/forms/","Forms",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/p-values-simplified-explanation-of-p-values-in-hypothesis-testing/564196/",4,{"url":32,"name":10,"@type":35,"author":36,"headline":10,"publisher":39,"fileFormat":42,"inLanguage":8,"description":12,"dateModified":43,"datePublished":43,"encodingFormat":42,"isAccessibleForFree":44,"interactionStatistic":45},"DigitalDocument",{"name":37,"@type":38},"Rizky","Person",{"url":19,"name":40,"@type":41},"DocShare","Organization","application/pdf","2026-10-12",true,{"@type":46,"interactionType":47,"userInteractionCount":4},"InteractionCounter",{"@type":48},"ViewAction",{"@type":50,"mainEntity":51},"FAQPage",[52,58,62],{"name":53,"@type":54,"acceptedAnswer":55},"Can a hypothesis test prove that the null hypothesis is true?","Question",{"text":56,"@type":57},"No. The discussion states that one can never prove the null hypothesis is true; instead, the test is conducted assuming the null and checking whether there is acceptable evidence to reject it.","Answer",{"name":59,"@type":54,"acceptedAnswer":60},"What does a p-value measure in intuitive terms?",{"text":61,"@type":57},"A p-value is defined as the probability to which the data support the null hypothesis, answering how likely the null would be given the sample data under the assumption the null is true.",{"name":63,"@type":54,"acceptedAnswer":64},"How should p-values be interpreted for rejecting or failing to reject the null?",{"text":65,"@type":57},"Large p-values lend support to the null, leading to failure to reject it, while small p-values indicate the data provide lesser support for the null, making rejection of the null more likely.","https://schema.org",{"og:url":32,"og:type":68,"og:title":10,"og:site_name":40,"og:description":12},"article",{"robots":70,"canonical":32},"index,follow",{"doc_id":72,"site_id":7},564196,1791840788,{"code":4,"msg":75,"data":76},"success",[77,82,87,92,97,102,106,111,116],{"id":78,"doc_module":22,"doc_module_name":25,"category_name":79,"show_sort_weight":80,"slug":81},11,"Presentations",90,"presentations",{"id":83,"doc_module":22,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},12,"Resumes",80,"resumes",{"id":88,"doc_module":22,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},14,"Invoices",70,"invoices",{"id":93,"doc_module":22,"doc_module_name":25,"category_name":94,"show_sort_weight":95,"slug":96},15,"Posters",60,"posters",{"id":98,"doc_module":22,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},16,"Social Media",50,"social-media",{"id":103,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":104,"slug":105},17,40,"forms",{"id":107,"doc_module":22,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},18,"Letters",30,"letters",{"id":112,"doc_module":22,"doc_module_name":25,"category_name":113,"show_sort_weight":114,"slug":115},21,"Paper Templates",5,"papers-templates",{"id":117,"doc_module":22,"doc_module_name":25,"category_name":118,"show_sort_weight":4,"slug":119},158,"General","general-158",{"code":4,"msg":75,"data":121},{"doc_id":72,"user_id":122,"nickname":37,"user_avatar":123,"doc_module":22,"category_id":103,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":124,"file_id":125,"file_url":126,"file_type":127,"file_size":128,"view_count":4,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":129,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":130,"faqs":131,"seo_title":132,"seo_description":12,"update_tm":73,"read_time":22},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","P-VALUES SIMPLIFIED  \nPreface  \nThis discussion of p-values is viewed in the context of a hypothesis test. While the concepts can be extended to more complex models, this simple test is employed for the sake of clarity and ease of comprehension.  \nIn the realm of hypothesis testing one can never prove that a null hypothesis is true; rather, we conduct a test under the assumption that the null hypothesis is correct and endeavor to see if there is an acceptable level of probability to reject it.  \nStrictly speaking, if we don’t find evidence to reject, we cannot say that we “accept the null”. The aim of hypothesis testing is not to verify the null hypothesis; but, rather to examine (test) some  \nclaim/condition delineated via an alternative hypothesis.  \nIn the following discussion we sometimes refer to the null hypothesis as being true, when in fact, we do not know and are not testing if it is true.  \nQuick Definitions  \nThe term p-value is an abbreviation for Probability Value.  \nHence, the concept of a p-value concerns the notion of probability.  \nProbability is defined as:  \nThe branch of mathematics concerning events and numerical descriptions of how likely they are to occur.  \nThe probability of an event is a number between 0 and 1 (inclusive) . The larger the probability, the more likely an event is to occur.  \nIn mathematical terms, the probability value domain is -- [ 0 ≤ p-value ≤ 1 ]  \nFORMAL DEFINITIONS  \nThe formal definition often proffered defines a p-value as:  \nThe probability of obtaining test results at least as extreme as the result actually observed, under the  \nassumption that the null hypothesis is correct.  \nSimilarly, it is often postulated:  \nWe are assuming the null hypothesis is true and trying to see if there is evidence against it.  \nConfused yet?... Hang it there!  \nThis “evidence against it” wording could be more precisely delineated as“evidence of statistical significance against the null”.  \nFollowing this line of reasoning, smaller p-values provide greater evidence for rejecting the null hypothesis.  \nHowever, the idea (and wording) of a smaller p-value providing greater evidence against the null hypothesis  \nis counterintuitive.  \nFor many people not versed is the field of statistics, such formal definitions may contribute to high levels of confusion and frustration.  \nA MORE UNDERSTANDABLE DEFINITION  \nA clearer and more intuitive definition of a p-value answers the question: Assuming the null hypothesis is true, what do the sample data say about how likely the null hypothesis is to be true?  \nWhen viewed in the context of this question, a p-value is more simply defined as:  \nTHE PROBABILITY TO WHICH THE DATA SUPPORT THE NULL HYPOTHESIS  \nAccordingly, a large p-value lends support to the assertion of a correct null hypothesis.  \nHence, larger p-values result in failure to reject the null hypothesis.  \n*****************************************************  \nConversely, a small p-value means that there is a lesser chance that the data support the null hypothesis.  \nThereby lending acceptance of the alternative hypothesis.  \nRemember, a p-value doesn’t tell you if the null hypothesis is true or false. It just tells you how likely it would be to obtain a particular result (from sample data) if the null hypothesis were true.  \nA p-value is a piece of evidence, not a definitive proof.  \nExamples to Help Solidify this Discussion.  \n● A result of p = 0.836 shows an 86.3% probability that the data support the null. This is strong evidence supporting the null hypothesis. (And weak evidence to reject it) .  \n● A result of p = 0.022 shows a 2.2% probability that the data support the null. This is weak evidence supporting the null. Accordingly, this would most likely lead to rejecting the null and accepting the alternative hypothesis.","cbCaifX6dFVDxsZl","https://ap.wps.com/l/cbCaifX6dFVDxsZl","pdf",153763,"English","# Preface\n# Quick Definitions\n# Formal Definitions\n# A More Understandable Definition\n# Examples to Help Solidify this Discussion","[{\"question\":\"Can a hypothesis test prove that the null hypothesis is true?\",\"answer\":\"No. The discussion states that one can never prove the null hypothesis is true; instead, the test is conducted assuming the null and checking whether there is acceptable evidence to reject it.\"},{\"question\":\"What does a p-value measure in intuitive terms?\",\"answer\":\"A p-value is defined as the probability to which the data support the null hypothesis, answering how likely the null would be given the sample data under the assumption the null is true.\"},{\"question\":\"How should p-values be interpreted for rejecting or failing to reject the null?\",\"answer\":\"Large p-values lend support to the null, leading to failure to reject it, while small p-values indicate the data provide lesser support for the null, making rejection of the null more likely.\"}]","P-VALUES - Simplified - Explanation of p-values in hypothesis testing | PDF"]