{"id":250588,"date":"2024-04-03T04:23:48","date_gmt":"2024-04-03T04:23:48","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=250588"},"modified":"2024-04-03T04:23:48","modified_gmt":"2024-04-03T04:23:48","slug":"what-p-value-rejects-the-null-hypothesis-2","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/","title":{"rendered":"What P value rejects the null hypothesis?"},"content":{"rendered":"<p>When conducting hypothesis testing, the p-value is a fundamental statistical concept used to determine the strength of evidence against the null hypothesis. It quantifies the probability of obtaining results as extreme as the observed data, assuming the null hypothesis is true. In hypothesis testing, the smaller the p-value, the stronger the evidence against the null hypothesis. But what p-value determines if we reject or fail to reject the null hypothesis? Let&#8217;s explore this question in detail.<\/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-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#Rejecting_the_Null_Hypothesis\" title=\"Rejecting the Null Hypothesis\">Rejecting the Null Hypothesis<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#What_P_value_rejects_the_null_hypothesis\" title=\"What P value rejects the null hypothesis?\">What P value rejects the null hypothesis?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#Frequently_Asked_Questions_FAQs\" title=\"Frequently Asked Questions (FAQs)\">Frequently Asked Questions (FAQs)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#1_Does_a_p-value_smaller_than_the_significance_level_always_lead_to_the_rejection_of_the_null_hypothesis\" title=\"1. Does a p-value smaller than the significance level always lead to the rejection of the null hypothesis?\">1. Does a p-value smaller than the significance level always lead to the rejection of the null hypothesis?<\/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-p-value-rejects-the-null-hypothesis-2\/#2_Can_the_significance_level_alpha_be_something_other_than_005_or_001\" title=\"2. Can the significance level ((alpha)) be something other than 0.05 or 0.01?\">2. Can the significance level ((alpha)) be something other than 0.05 or 0.01?<\/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-p-value-rejects-the-null-hypothesis-2\/#3_What_happens_if_the_p-value_is_greater_than_the_significance_level\" title=\"3. What happens if the p-value is greater than the significance level?\">3. What happens if the p-value is greater than the significance level?<\/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-p-value-rejects-the-null-hypothesis-2\/#4_Can_a_p-value_be_negative\" title=\"4. Can a p-value be negative?\">4. Can a p-value be negative?<\/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-p-value-rejects-the-null-hypothesis-2\/#5_Does_a_smaller_p-value_indicate_a_larger_effect_size\" title=\"5. Does a smaller p-value indicate a larger effect size?\">5. Does a smaller p-value indicate a larger 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-p-value-rejects-the-null-hypothesis-2\/#6_Can_we_ever_accept_the_null_hypothesis\" title=\"6. Can we ever accept the null hypothesis?\">6. Can we ever accept 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-p-value-rejects-the-null-hypothesis-2\/#7_What_if_the_p-value_is_exactly_equal_to_the_significance_level\" title=\"7. What if the p-value is exactly equal to the significance level?\">7. What if the p-value is exactly equal to the significance level?<\/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-p-value-rejects-the-null-hypothesis-2\/#8_How_is_the_p-value_calculated\" title=\"8. How is the p-value calculated?\">8. How is the p-value calculated?<\/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-p-value-rejects-the-null-hypothesis-2\/#9_Is_the_p-value_the_probability_that_the_null_hypothesis_is_true\" title=\"9. Is the p-value the probability that the null hypothesis is true?\">9. Is the p-value the probability that the null hypothesis is true?<\/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-p-value-rejects-the-null-hypothesis-2\/#10_What_happens_if_we_reject_the_null_hypothesis_when_it_is_true\" title=\"10. What happens if we reject the null hypothesis when it is true?\">10. What happens if we reject the null hypothesis when it is true?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#11_Can_we_conclude_that_the_alternative_hypothesis_is_true_if_we_reject_the_null_hypothesis\" title=\"11. Can we conclude that the alternative hypothesis is true if we reject the null hypothesis?\">11. Can we conclude that the alternative hypothesis is true if we reject the null hypothesis?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#12_Is_the_p-value_a_measure_of_practical_significance\" title=\"12. Is the p-value a measure of practical significance?\">12. Is the p-value a measure of practical significance?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Rejecting_the_Null_Hypothesis\"><\/span>Rejecting the Null Hypothesis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In hypothesis testing, the null hypothesis ((H_0)) represents the possibility that there is no significant difference or relationship between variables. On the contrary, the alternative hypothesis ((H_1) or (H_a)) assumes there is a significant difference or relationship.<\/p>\n<p>The primary purpose of hypothesis testing is to test whether the observed data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This decision is made by comparing the calculated p-value with a predetermined significance level ((alpha)), usually set at 0.05 (5%) or 0.01 (1%).<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_P_value_rejects_the_null_hypothesis\"><\/span><b>What P value rejects the null hypothesis?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The p-value that rejects the null hypothesis is any p-value that is smaller than the predetermined significance level ((alpha)). If the calculated p-value is less than or equal to (alpha), we reject the null hypothesis and conclude that there is enough evidence to support the alternative hypothesis.<\/p>\n<p><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_FAQs\"><\/span>Frequently Asked Questions (FAQs)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"1_Does_a_p-value_smaller_than_the_significance_level_always_lead_to_the_rejection_of_the_null_hypothesis\"><\/span>1. Does a p-value smaller than the significance level always lead to the rejection of the null hypothesis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, the p-value must be smaller than the predetermined significance level ((alpha)) to reject the null hypothesis. Otherwise, it fails to reject the null hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_Can_the_significance_level_alpha_be_something_other_than_005_or_001\"><\/span>2. Can the significance level ((alpha)) be something other than 0.05 or 0.01?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Yes, the choice of significance level is subjective and varies depending on the field of study or the researcher&#8217;s preferences. However, 0.05 and 0.01 are commonly used due to their conventionality.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_What_happens_if_the_p-value_is_greater_than_the_significance_level\"><\/span>3. What happens if the p-value is greater than the significance level?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If the p-value is greater than the significance level ((alpha)), we fail to reject the null hypothesis. This means that there is not enough evidence to support the alternative hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Can_a_p-value_be_negative\"><\/span>4. Can a p-value be negative?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, a p-value cannot be negative. It is always a value between 0 and 1, inclusive.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_Does_a_smaller_p-value_indicate_a_larger_effect_size\"><\/span>5. Does a smaller p-value indicate a larger effect size?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, the p-value and effect size are different measures of statistical significance. A smaller p-value indicates stronger evidence against the null hypothesis but does not directly relate to the magnitude of the effect.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_Can_we_ever_accept_the_null_hypothesis\"><\/span>6. Can we ever accept the null hypothesis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In hypothesis testing, we do not directly accept the null hypothesis; rather, we either reject it or fail to reject it. However, failing to reject the null hypothesis does not necessarily imply that it is true or valid.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_What_if_the_p-value_is_exactly_equal_to_the_significance_level\"><\/span>7. What if the p-value is exactly equal to the significance level?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If the p-value is exactly equal to the significance level ((alpha)), it is generally considered borderline or marginal. In such cases, researchers may decide to interpret the results with caution, taking into account other relevant factors.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_How_is_the_p-value_calculated\"><\/span>8. How is the p-value calculated?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The calculation of the p-value involves determining the probability of obtaining observed data as extreme or more extreme than the collected sample, given that the null hypothesis is true. The specific calculation method depends on the statistical test used.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_Is_the_p-value_the_probability_that_the_null_hypothesis_is_true\"><\/span>9. Is the p-value the probability that the null hypothesis is true?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, the p-value is not the probability that the null hypothesis is true. It represents the probability of obtaining the observed data when the null hypothesis is true. It measures the strength of evidence against the null hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_What_happens_if_we_reject_the_null_hypothesis_when_it_is_true\"><\/span>10. What happens if we reject the null hypothesis when it is true?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Making a Type I error occurs when we mistakenly reject the null hypothesis when it is actually true, which is known as a false positive. This indicates that the decision to reject the null hypothesis is incorrect.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_Can_we_conclude_that_the_alternative_hypothesis_is_true_if_we_reject_the_null_hypothesis\"><\/span>11. Can we conclude that the alternative hypothesis is true if we reject the null hypothesis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, rejecting the null hypothesis does not necessarily imply that the alternative hypothesis is true. It suggests that there is sufficient evidence to support the alternative hypothesis, but other factors and additional research should be considered for a more comprehensive conclusion.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_Is_the_p-value_a_measure_of_practical_significance\"><\/span>12. Is the p-value a measure of practical significance?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>No, the p-value is not a measure of practical significance. It only provides a measure of the statistical significance of the observed results. The interpretation of practical or real-world significance depends on the context and should consider other relevant factors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When conducting hypothesis testing, the p-value is a fundamental statistical concept used to determine the strength of evidence against the null hypothesis. It quantifies the probability of obtaining results as extreme as the observed data, assuming the null hypothesis is true. In hypothesis testing, the smaller the p-value, the stronger the evidence against the null &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"What P value rejects the null hypothesis?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/#more-250588\">Read more<span class=\"screen-reader-text\">What P value rejects the null hypothesis?<\/span><\/a><\/p>\n","protected":false},"author":63,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-250588","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 P value rejects the null hypothesis?<\/title>\n<meta name=\"description\" content=\"When conducting hypothesis testing, the p-value is a fundamental statistical concept used to determine the strength of evidence against the null\" \/>\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-p-value-rejects-the-null-hypothesis-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What P value rejects the null hypothesis?\" \/>\n<meta property=\"og:description\" content=\"When conducting hypothesis testing, the p-value is a fundamental statistical concept used to determine the strength of evidence against the null\" \/>\n<meta property=\"og:url\" content=\"https:\/\/namso-gen.co\/blog\/what-p-value-rejects-the-null-hypothesis-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Namso Gen Blog - 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