{"id":213256,"date":"2023-12-12T11:37:33","date_gmt":"2023-12-12T11:37:33","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/"},"modified":"2023-12-12T11:37:33","modified_gmt":"2023-12-12T11:37:33","slug":"how-do-you-estimate-the-p-value","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/","title":{"rendered":"How do you estimate the p-value?"},"content":{"rendered":"<p>When conducting statistical hypothesis tests, the p-value plays a crucial role in determining the strength of evidence against the null hypothesis. It measures the probability of obtaining test results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence for rejecting the null hypothesis. But how do you estimate the p-value? Let&#8217;s dive into the process.<\/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\/how-do-you-estimate-the-p-value\/#Process_to_estimate_the_p-value\" title=\"Process to estimate the p-value\">Process to estimate the p-value<\/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\/how-do-you-estimate-the-p-value\/#Formulate_the_null_and_alternative_hypotheses\" title=\"Formulate the null and alternative hypotheses\">Formulate the null and alternative hypotheses<\/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\/how-do-you-estimate-the-p-value\/#Select_an_appropriate_statistical_test\" title=\"Select an appropriate statistical test\">Select an appropriate statistical test<\/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\/how-do-you-estimate-the-p-value\/#Collect_and_analyze_data\" title=\"Collect and analyze data\">Collect and analyze data<\/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\/how-do-you-estimate-the-p-value\/#Calculate_the_test_statistic\" title=\"Calculate the test statistic\">Calculate the test statistic<\/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\/how-do-you-estimate-the-p-value\/#Determine_the_significance_level_%CE%B1\" title=\"Determine the significance level (\u03b1)\">Determine the significance level (\u03b1)<\/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\/how-do-you-estimate-the-p-value\/#Find_the_critical_region_or_critical_value\" title=\"Find the critical region or critical value\">Find the critical region or critical value<\/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\/how-do-you-estimate-the-p-value\/#Compare_the_test_statistic_with_the_critical_value\" title=\"Compare the test statistic with the critical value\">Compare the test statistic with the critical value<\/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\/how-do-you-estimate-the-p-value\/#Estimate_the_p-value\" title=\"Estimate the p-value\">Estimate the p-value<\/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\/how-do-you-estimate-the-p-value\/#Interpret_the_p-value\" title=\"Interpret the p-value\">Interpret the p-value<\/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\/how-do-you-estimate-the-p-value\/#Consider_the_significance_level\" title=\"Consider the significance level\">Consider the significance level<\/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\/how-do-you-estimate-the-p-value\/#Draw_conclusions\" title=\"Draw conclusions\">Draw conclusions<\/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\/how-do-you-estimate-the-p-value\/#Beware_of_Type_I_and_Type_II_errors\" title=\"Beware of Type I and Type II errors\">Beware of Type I and Type II errors<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#Related_FAQs\" title=\"Related FAQs\">Related FAQs<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#1_What_if_the_p-value_is_greater_than_the_significance_level\" title=\"1. What if the p-value is greater than the significance level?\">1. What 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-16\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#2_Can_the_p-value_be_negative\" title=\"2. Can the p-value be negative?\">2. Can the 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-17\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#3_How_does_the_sample_size_influence_the_p-value\" title=\"3. How does the sample size influence the p-value?\">3. How does the sample size influence the p-value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#4_What_if_the_p-value_is_exactly_equal_to_the_significance_level\" title=\"4. What if the p-value is exactly equal to the significance level?\">4. 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-19\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#5_Can_the_p-value_prove_causation\" title=\"5. Can the p-value prove causation?\">5. Can the p-value prove causation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#6_Is_a_smaller_p-value_always_better\" title=\"6. Is a smaller p-value always better?\">6. Is a smaller p-value always better?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#7_Can_p-values_be_used_for_non-inferiority_or_equivalence_testing\" title=\"7. Can p-values be used for non-inferiority or equivalence testing?\">7. Can p-values be used for non-inferiority or equivalence testing?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#8_What_happens_if_I_change_the_significance_level_%CE%B1\" title=\"8. What happens if I change the significance level (\u03b1)?\">8. What happens if I change the significance level (\u03b1)?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#9_How_does_the_choice_of_statistical_test_affect_the_p-value\" title=\"9. How does the choice of statistical test affect the p-value?\">9. How does the choice of statistical test affect the p-value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#10_Is_the_p-value_affected_by_the_direction_of_the_test\" title=\"10. Is the p-value affected by the direction of the test?\">10. Is the p-value affected by the direction of the test?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#11_Can_the_p-value_be_used_as_a_measure_of_effect_size\" title=\"11. Can the p-value be used as a measure of effect size?\">11. Can the p-value be used as a measure of effect size?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#12_Can_multiple_p-values_be_adjusted_for_multiple_comparisons\" title=\"12. Can multiple p-values be adjusted for multiple comparisons?\">12. Can multiple p-values be adjusted for multiple comparisons?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Process_to_estimate_the_p-value\"><\/span>Process to estimate the p-value<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Formulate_the_null_and_alternative_hypotheses\"><\/span>Formulate the null and alternative hypotheses<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Before estimating the p-value, it is essential to clearly define the null hypothesis (H0) and the alternative hypothesis (H1) based on the research question.<\/p>\n<p>2. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Select_an_appropriate_statistical_test\"><\/span>Select an appropriate statistical test<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Choose a statistical test based on the nature of the data and the research question. Common tests include t-tests, chi-square tests, ANOVA, regression analysis, etc.<\/p>\n<p>3. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Collect_and_analyze_data\"><\/span>Collect and analyze data<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Gather relevant data through experiments, surveys, or observations. Analyze the data using the chosen statistical test to obtain the test statistic.<\/p>\n<p>4. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Calculate_the_test_statistic\"><\/span>Calculate the test statistic<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Compute the test statistic that is relevant to the selected statistical test. The test statistic measures how far the observed data deviates from the null hypothesis.<\/p>\n<p>5. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Determine_the_significance_level_%CE%B1\"><\/span>Determine the significance level (\u03b1)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Set the significance level, also known as alpha (\u03b1), which defines the threshold for rejecting the null hypothesis. Common choices for \u03b1 are 0.05 or 0.01, but it depends on the study&#8217;s context and the level of confidence desired.<\/p>\n<p>6. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Find_the_critical_region_or_critical_value\"><\/span>Find the critical region or critical value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Locate the critical region or critical value associated with the chosen significance level and the selected statistical test. The critical region is the range of values that will lead to the rejection of the null hypothesis.<\/p>\n<p>7. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Compare_the_test_statistic_with_the_critical_value\"><\/span>Compare the test statistic with the critical value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   Compare the test statistic obtained from the data analysis with the critical value or range. If the test statistic falls within the critical region, the null hypothesis is rejected, and the alternative hypothesis is supported.<\/p>\n<p>8. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Estimate_the_p-value\"><\/span>Estimate the p-value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   **Finally, to estimate the p-value, determine the probability of observing a test statistic as extreme or more extreme than the one calculated from the data, assuming the null hypothesis is true.**<\/p>\n<p>9. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Interpret_the_p-value\"><\/span>Interpret the p-value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n   The p-value obtained through estimation provides a quantitative measure of the strength of evidence against the null hypothesis. A small p-value indicates strong evidence against the null hypothesis, suggesting that the observed data is unlikely to occur by chance under the null hypothesis.<\/p>\n<p>10. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Consider_the_significance_level\"><\/span>Consider the significance level<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n    Compare the estimated p-value with the chosen significance level (\u03b1). If the p-value is smaller than \u03b1, it suggests the observed data is statistically significant, supporting the alternative hypothesis.<\/p>\n<p>11. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Draw_conclusions\"><\/span>Draw conclusions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n    Based on the estimated p-value and the chosen significance level, draw conclusions regarding the research question. Reject the null hypothesis if the p-value is smaller than \u03b1 and accept it otherwise.<\/p>\n<p>12. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"Beware_of_Type_I_and_Type_II_errors\"><\/span>Beware of Type I and Type II errors<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\n    Remember that the p-value is not a measure of the truth or importance of an effect, but rather the probability of observing the data assuming the null hypothesis is true. While small p-values are associated with rejecting the null hypothesis, there is still a possibility of committing Type I errors (false positives) or Type II errors (false negatives).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Related_FAQs\"><\/span>Related FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"1_What_if_the_p-value_is_greater_than_the_significance_level\"><\/span>1. What if the p-value is greater than the significance level?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the calculated p-value is greater than the chosen significance level (\u03b1), it suggests that the observed data is reasonably likely to occur under the null hypothesis. In such cases, we do not reject the null hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_Can_the_p-value_be_negative\"><\/span>2. Can the p-value be negative?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the p-value cannot be negative. It is always a value between 0 and 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_How_does_the_sample_size_influence_the_p-value\"><\/span>3. How does the sample size influence the p-value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nA larger sample size tends to yield a more precise estimate of the p-value. With a larger sample, even small effects can be detected, leading to smaller p-values.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_What_if_the_p-value_is_exactly_equal_to_the_significance_level\"><\/span>4. What if the p-value is exactly equal to the significance level?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the p-value is exactly equal to the chosen significance level (\u03b1), it is considered borderline. In such cases, the decision whether to reject or accept the null hypothesis should consider other factors such as the study&#8217;s context and potential consequences of making an error.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_Can_the_p-value_prove_causation\"><\/span>5. Can the p-value prove causation?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the p-value alone cannot establish causation. It only measures the likelihood of observing the data assuming the null hypothesis is true. Establishing causation requires additional evidence and study designs.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_Is_a_smaller_p-value_always_better\"><\/span>6. Is a smaller p-value always better?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nA smaller p-value indicates stronger evidence against the null hypothesis. However, the interpretation of &#8220;better&#8221; depends on the research question and context. It is essential to consider effect size and practical significance alongside the p-value.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_Can_p-values_be_used_for_non-inferiority_or_equivalence_testing\"><\/span>7. Can p-values be used for non-inferiority or equivalence testing?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, p-values can be used in non-inferiority or equivalence testing, but the interpretation and methodology may differ from traditional hypothesis testing.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_What_happens_if_I_change_the_significance_level_%CE%B1\"><\/span>8. What happens if I change the significance level (\u03b1)?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nBy changing the significance level (\u03b1), you alter the threshold for rejecting the null hypothesis. A lower \u03b1 makes it harder to reject the null hypothesis, whereas a higher \u03b1 makes it easier. However, it is crucial to select \u03b1 before analyzing the data and stick to it to avoid data-driven decisions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_How_does_the_choice_of_statistical_test_affect_the_p-value\"><\/span>9. How does the choice of statistical test affect the p-value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nDifferent statistical tests yield different test statistics and, consequently, different p-values. Choosing an appropriate statistical test for the research question ensures accurate estimation of the p-value.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_Is_the_p-value_affected_by_the_direction_of_the_test\"><\/span>10. Is the p-value affected by the direction of the test?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, the direction of the test, whether one-tailed or two-tailed, influences the p-value. One-tailed tests focus on one specific direction (e.g., greater than or less than), while two-tailed tests consider both directions. The p-value calculated differs accordingly.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_Can_the_p-value_be_used_as_a_measure_of_effect_size\"><\/span>11. Can the p-value be used as a measure of effect size?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the p-value does not provide information about the magnitude or size of the effect. To measure effect size, specific statistics like Cohen&#8217;s d, odds ratios, or correlation coefficients should be used.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_Can_multiple_p-values_be_adjusted_for_multiple_comparisons\"><\/span>12. Can multiple p-values be adjusted for multiple comparisons?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, when conducting multiple hypothesis tests or making multiple comparisons, it is crucial to adjust the p-values to control the family-wise error rate (FWER) or false discovery rate (FDR). Adjustments like the Bonferroni correction or the Benjamini-Hochberg procedure can be applied to address this issue.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When conducting statistical hypothesis tests, the p-value plays a crucial role in determining the strength of evidence against the null hypothesis. It measures the probability of obtaining test results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence for rejecting the null hypothesis. &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How do you estimate the p-value?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-do-you-estimate-the-p-value\/#more-213256\">Read more<span class=\"screen-reader-text\">How do you estimate the p-value?<\/span><\/a><\/p>\n","protected":false},"author":54,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-213256","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>How do you estimate the p-value?<\/title>\n<meta name=\"description\" content=\"When conducting statistical hypothesis tests, the p-value plays a crucial role in determining the strength of evidence against the null hypothesis. 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