{"id":229020,"date":"2024-03-30T11:06:32","date_gmt":"2024-03-30T11:06:32","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=229020"},"modified":"2024-03-30T11:06:32","modified_gmt":"2024-03-30T11:06:32","slug":"what-happens-when-the-p-value-is-less-than-alpha","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/","title":{"rendered":"What happens when the p-value is less than alpha?"},"content":{"rendered":"<p>When conducting statistical hypothesis testing, it is essential to compare the p-value of a test with a predetermined significance level known as alpha (\u03b1). Alpha is typically set at values such as 0.05 or 0.01, representing the acceptable level of error or the probability of observing a result as extreme as the one obtained, assuming the null hypothesis is true. If the calculated p-value is less than alpha, it indicates that the evidence against the null hypothesis is strong enough to reject it. In simpler terms, it suggests that the observed data is unlikely to occur by chance alone, supporting the alternative hypothesis instead.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_62 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_happens_when_the_p-value_is_less_than_alpha\" title=\"What happens when the p-value is less than alpha?\">What happens when the p-value is less than alpha?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_are_the_consequences_of_rejecting_the_null_hypothesis\" title=\"What are the consequences of rejecting the null hypothesis?\">What are the consequences of rejecting the null hypothesis?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_if_the_p-value_is_greater_than_alpha\" title=\"What if the p-value is greater than alpha?\">What if the p-value is greater than alpha?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#Is_it_always_appropriate_to_reject_the_null_hypothesis_when_the_p-value_is_less_than_alpha\" title=\"Is it always appropriate to reject the null hypothesis when the p-value is less than alpha?\">Is it always appropriate to reject the null hypothesis when the p-value is less than alpha?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_is_Type_I_error\" title=\"What is Type I error?\">What is Type I error?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_is_Type_II_error\" title=\"What is Type II error?\">What is Type II error?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_is_the_relationship_between_alpha_and_the_risk_of_Type_I_error\" title=\"What is the relationship between alpha and the risk of Type I error?\">What is the relationship between alpha and the risk of Type I error?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#Does_a_small_p-value_imply_a_large_effect_size\" title=\"Does a small p-value imply a large effect size?\">Does a small p-value imply a large effect size?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#Can_we_conclude_that_the_alternative_hypothesis_is_absolutely_true_when_rejecting_the_null_hypothesis\" title=\"Can we conclude that the alternative hypothesis is absolutely true when rejecting the null hypothesis?\">Can we conclude that the alternative hypothesis is absolutely true when rejecting the null hypothesis?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_if_the_p-value_is_very_close_to_alpha\" title=\"What if the p-value is very close to alpha?\">What if the p-value is very close to alpha?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#Can_we_compare_p-values_from_different_studies_or_experiments\" title=\"Can we compare p-values from different studies or experiments?\">Can we compare p-values from different studies or experiments?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#What_does_it_mean_when_p-value_is_greater_than_alpha_but_still_significant\" title=\"What does it mean when p-value is greater than alpha but still significant?\">What does it mean when p-value is greater than alpha but still significant?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#Can_a_study_be_accurate_or_valid_if_the_p-value_is_greater_than_alpha\" title=\"Can a study be accurate or valid if the p-value is greater than alpha?\">Can a study be accurate or valid if the p-value is greater than alpha?<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"What_happens_when_the_p-value_is_less_than_alpha\"><\/span>What happens when the p-value is less than alpha?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>**When the p-value is less than alpha, we reject the null hypothesis in favor of the alternative hypothesis.** This implies that there is enough evidence to conclude that the effect or relationship being tested is statistically significant and not due to random chance.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_are_the_consequences_of_rejecting_the_null_hypothesis\"><\/span>What are the consequences of rejecting the null hypothesis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>By rejecting the null hypothesis, we are essentially stating that the observed difference or relationship found in the sample is likely to exist in the population. This may lead to practical implications such as supporting the effectiveness of a new treatment, demonstrating the impact of a marketing campaign, or validating a scientific theory.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_if_the_p-value_is_greater_than_alpha\"><\/span>What if the p-value is greater than alpha?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If the p-value is greater than alpha, it suggests that the evidence against the null hypothesis is not strong enough. In such cases, we fail to reject the null hypothesis, meaning we do not have sufficient evidence to support the alternative hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Is_it_always_appropriate_to_reject_the_null_hypothesis_when_the_p-value_is_less_than_alpha\"><\/span>Is it always appropriate to reject the null hypothesis when the p-value is less than alpha?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>While it is common practice to reject the null hypothesis when the p-value is less than alpha, it is essential to consider other factors such as study design, sample size, and the potential for Type I or Type II errors. Rejecting or failing to reject the null hypothesis should be interpreted within the broader context of the research question.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_Type_I_error\"><\/span>What is Type I error?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Type I error, also known as a false positive, occurs when we reject the null hypothesis when it is actually true. It represents the probability of mistakenly concluding that there is a significant effect or relationship when there isn&#8217;t one.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_Type_II_error\"><\/span>What is Type II error?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Type II error, also known as a false negative, occurs when we fail to reject the null hypothesis when it is actually false. It represents the probability of missing a significant effect or relationship that truly exists.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_the_relationship_between_alpha_and_the_risk_of_Type_I_error\"><\/span>What is the relationship between alpha and the risk of Type I error?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The alpha level directly determines the risk of committing a Type I error. By setting a lower alpha (e.g., 0.01 instead of 0.05), we reduce the chance of falsely rejecting the null hypothesis but increase the chance of a Type II error.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Does_a_small_p-value_imply_a_large_effect_size\"><\/span>Does a small p-value imply a large effect size?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, the p-value does not relate to the size or magnitude of the effect observed. It only provides information about the strength of evidence against the null hypothesis. Effect size is a separate measure that quantifies the practical significance of a relationship or an effect.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Can_we_conclude_that_the_alternative_hypothesis_is_absolutely_true_when_rejecting_the_null_hypothesis\"><\/span>Can we conclude that the alternative hypothesis is absolutely true when rejecting the null hypothesis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Rejecting the null hypothesis does not necessarily imply that the alternative hypothesis is absolutely true. It suggests that the evidence supports the alternative hypothesis, but there may still be other unexplored factors or limitations within the study that prevent us from making definitive conclusions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_if_the_p-value_is_very_close_to_alpha\"><\/span>What if the p-value is very close to alpha?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If the p-value is very close to alpha, it indicates a marginal result. In such cases, it is advisable to exercise caution and critically evaluate the methodology, sample size, and potential sources of bias before drawing firm conclusions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Can_we_compare_p-values_from_different_studies_or_experiments\"><\/span>Can we compare p-values from different studies or experiments?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Yes, p-values can be compared across studies or experiments to assess the generalizability or consistency of the results. However, multiple factors, such as sample size, study design, and context, must be taken into account to make meaningful comparisons.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_does_it_mean_when_p-value_is_greater_than_alpha_but_still_significant\"><\/span>What does it mean when p-value is greater than alpha but still significant?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This could be due to a language misinterpretation, as a p-value greater than alpha cannot be considered statistically significant. Statistical significance implies that the p-value is smaller than or equal to alpha.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Can_a_study_be_accurate_or_valid_if_the_p-value_is_greater_than_alpha\"><\/span>Can a study be accurate or valid if the p-value is greater than alpha?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Yes, a study can still be accurate and valid even if the p-value is greater than alpha. Statistical significance is not the sole determinant of a study&#8217;s quality or reliability. It is crucial to consider the study design, sample size, effect size, and other contextual factors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When conducting statistical hypothesis testing, it is essential to compare the p-value of a test with a predetermined significance level known as alpha (\u03b1). Alpha is typically set at values such as 0.05 or 0.01, representing the acceptable level of error or the probability of observing a result as extreme as the one obtained, assuming &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"What happens when the p-value is less than alpha?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/#more-229020\">Read more<span class=\"screen-reader-text\">What happens when the p-value is less than alpha?<\/span><\/a><\/p>\n","protected":false},"author":57,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-229020","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What happens when the p-value is less than alpha?<\/title>\n<meta name=\"description\" content=\"When conducting statistical hypothesis testing, it is essential to compare the p-value of a test with a predetermined significance level known as alpha\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What happens when the p-value is less than alpha?\" \/>\n<meta property=\"og:description\" content=\"When conducting statistical hypothesis testing, it is essential to compare the p-value of a test with a predetermined significance level known as alpha\" \/>\n<meta property=\"og:url\" content=\"https:\/\/namso-gen.co\/blog\/what-happens-when-the-p-value-is-less-than-alpha\/\" \/>\n<meta property=\"og:site_name\" content=\"Namso Gen Blog - 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