{"id":261503,"date":"2024-05-06T23:19:17","date_gmt":"2024-05-06T23:19:17","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=261503"},"modified":"2024-05-06T23:19:17","modified_gmt":"2024-05-06T23:19:17","slug":"how-to-find-p-value-from-four-by-four-graph","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/","title":{"rendered":"How to find p value from four by four graph?"},"content":{"rendered":"<p>A 4&#215;4 graph, also known as a contingency table or a cross-tabulation table, is a helpful tool used in statistical analysis to study the relationship between two categorical variables. It allows you to observe the frequency distribution of the variables and determine if there is a significant association between them. One common method to assess the significance of this association is by calculating the p-value. In this article, we will explore how to find the p-value from a 4&#215;4 graph and provide answers to some related frequently asked questions.<\/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-to-find-p-value-from-four-by-four-graph\/#Understanding_the_4%C3%974_Graph\" title=\"Understanding the 4&#215;4 Graph\">Understanding the 4&#215;4 Graph<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/#How_to_Find_P-Value_from_a_4%C3%974_Graph\" title=\"How to Find P-Value from a 4&#215;4 Graph?\">How to Find P-Value from a 4&#215;4 Graph?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/#Step_1_Define_Hypotheses\" title=\"Step 1: Define Hypotheses\">Step 1: Define Hypotheses<\/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-to-find-p-value-from-four-by-four-graph\/#Step_2_Calculate_the_Expected_Frequencies\" title=\"Step 2: Calculate the Expected Frequencies\">Step 2: Calculate the Expected Frequencies<\/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-to-find-p-value-from-four-by-four-graph\/#Step_3_Calculate_the_Chi-Square_Test_Statistic\" title=\"Step 3: Calculate the Chi-Square Test Statistic\">Step 3: Calculate the Chi-Square 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-to-find-p-value-from-four-by-four-graph\/#Step_4_Determine_the_Degrees_of_Freedom\" title=\"Step 4: Determine the Degrees of Freedom\">Step 4: Determine the Degrees of Freedom<\/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-to-find-p-value-from-four-by-four-graph\/#Step_5_Find_the_Critical_Value\" title=\"Step 5: Find the Critical Value\">Step 5: Find the 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-to-find-p-value-from-four-by-four-graph\/#Step_6_Compare_the_Test_Statistic_with_the_Critical_Value\" title=\"Step 6: Compare the Test Statistic with the Critical Value\">Step 6: 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-to-find-p-value-from-four-by-four-graph\/#Step_7_Calculate_the_P-Value\" title=\"Step 7: Calculate the P-Value\">Step 7: Calculate 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-to-find-p-value-from-four-by-four-graph\/#How_to_find_p-value_from_a_4%C3%974_graph\" title=\"How to find p-value from a 4&#215;4 graph?\">How to find p-value from a 4&#215;4 graph?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/#Frequently_Asked_Questions\" title=\"Frequently Asked Questions\">Frequently Asked Questions<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/#1_What_is_a_4%C3%974_graph\" title=\"1. What is a 4&#215;4 graph?\">1. What is a 4&#215;4 graph?<\/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-to-find-p-value-from-four-by-four-graph\/#2_What_is_a_p-value\" title=\"2. What is a p-value?\">2. What is a p-value?<\/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\/how-to-find-p-value-from-four-by-four-graph\/#3_What_does_the_p-value_indicate\" title=\"3. What does the p-value indicate?\">3. What does the p-value indicate?<\/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\/how-to-find-p-value-from-four-by-four-graph\/#4_What_is_the_chi-square_test_of_independence\" title=\"4. What is the chi-square test of independence?\">4. What is the chi-square test of independence?<\/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-to-find-p-value-from-four-by-four-graph\/#5_How_is_the_null_hypothesis_defined_in_the_chi-square_test\" title=\"5. How is the null hypothesis defined in the chi-square test?\">5. How is the null hypothesis defined in the chi-square test?<\/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-to-find-p-value-from-four-by-four-graph\/#6_What_are_expected_frequencies\" title=\"6. What are expected frequencies?\">6. What are expected frequencies?<\/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-to-find-p-value-from-four-by-four-graph\/#7_What_are_degrees_of_freedom\" title=\"7. What are degrees of freedom?\">7. What are degrees of freedom?<\/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-to-find-p-value-from-four-by-four-graph\/#8_How_do_we_define_the_critical_value_for_the_chi-square_test\" title=\"8. How do we define the critical value for the chi-square test?\">8. How do we define the critical value for the chi-square test?<\/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-to-find-p-value-from-four-by-four-graph\/#9_What_happens_if_the_test_statistic_is_larger_than_the_critical_value\" title=\"9. What happens if the test statistic is larger than the critical value?\">9. What happens if the test statistic is larger than the critical value?<\/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-to-find-p-value-from-four-by-four-graph\/#10_What_if_the_test_statistic_is_smaller_than_the_critical_value\" title=\"10. What if the test statistic is smaller than the critical value?\">10. What if the test statistic is smaller than the critical value?<\/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-to-find-p-value-from-four-by-four-graph\/#11_How_is_the_p-value_interpreted\" title=\"11. How is the p-value interpreted?\">11. How is the p-value interpreted?<\/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-to-find-p-value-from-four-by-four-graph\/#12_Can_the_p-value_ever_be_larger_than_1_or_negative\" title=\"12. Can the p-value ever be larger than 1 or negative?\">12. Can the p-value ever be larger than 1 or negative?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Understanding_the_4%C3%974_Graph\"><\/span>Understanding the 4&#215;4 Graph<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Before delving into finding the p-value, let&#8217;s have a quick overview of how a 4&#215;4 graph is structured. A 4&#215;4 graph consists of two categorical variables, each having four possible outcomes. These outcomes are arranged in rows and columns of the table, forming a grid. The intersections of rows and columns represent the observed frequencies or counts of instances.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Find_P-Value_from_a_4%C3%974_Graph\"><\/span>How to Find P-Value from a 4&#215;4 Graph?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To find the p-value from a 4&#215;4 graph, we need to perform a statistical test, such as the chi-square test of independence. Here&#8217;s a step-by-step guide on how to obtain the p-value:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_1_Define_Hypotheses\"><\/span>Step 1: Define Hypotheses<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nFormulate the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis usually assumes there is no association between the two variables, while the alternative hypothesis suggests that an association exists.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_2_Calculate_the_Expected_Frequencies\"><\/span>Step 2: Calculate the Expected Frequencies<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nCompute the expected frequencies for each cell of the 4&#215;4 graph under the assumption of independence between the variables.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_3_Calculate_the_Chi-Square_Test_Statistic\"><\/span>Step 3: Calculate the Chi-Square Test Statistic<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nCompute the chi-square test statistic by comparing the observed frequencies from the 4&#215;4 graph with the expected frequencies.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_4_Determine_the_Degrees_of_Freedom\"><\/span>Step 4: Determine the Degrees of Freedom<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe degrees of freedom for a 4&#215;4 graph are calculated as (r &#8211; 1) x (c &#8211; 1), where &#8216;r&#8217; represents the number of rows and &#8216;c&#8217; represents the number of columns in the table.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_5_Find_the_Critical_Value\"><\/span>Step 5: Find the Critical Value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nUse a chi-square distribution table or a statistical software to find the critical value corresponding to the chosen significance level (usually 0.05 or 0.01) and the degrees of freedom.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_6_Compare_the_Test_Statistic_with_the_Critical_Value\"><\/span>Step 6: Compare the Test Statistic with the Critical Value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the test statistic is larger than the critical value, we reject the null hypothesis. If it is smaller, we fail to reject the null hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Step_7_Calculate_the_P-Value\"><\/span>Step 7: Calculate the P-Value<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nCalculate the p-value associated with the test statistic. The p-value represents the probability of observing a chi-square test statistic at least as extreme as the one calculated under the null hypothesis.<\/p>\n<p>**<\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_to_find_p-value_from_a_4%C3%974_graph\"><\/span>How to find p-value from a 4&#215;4 graph?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>**<br \/>\nTo find the p-value from a 4&#215;4 graph, perform a chi-square test of independence and calculate the probability of observing a test statistic as extreme or more extreme than the one obtained under the null hypothesis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span>Frequently Asked Questions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"1_What_is_a_4%C3%974_graph\"><\/span>1. What is a 4&#215;4 graph?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nA 4&#215;4 graph, also known as a contingency table or a cross-tabulation table, is a table that displays the distribution of two categorical variables.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_What_is_a_p-value\"><\/span>2. What is a p-value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nA p-value is a probability value that measures the strength of evidence against the null hypothesis. It quantifies the likelihood of obtaining the observed data if the null hypothesis were true.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_What_does_the_p-value_indicate\"><\/span>3. What does the p-value indicate?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe p-value indicates the statistical significance of the relationship between the variables. If the p-value is small (typically less than 0.05), it suggests a significant association exists between the variables.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_What_is_the_chi-square_test_of_independence\"><\/span>4. What is the chi-square test of independence?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe chi-square test of independence is a statistical test used to determine if there is a significant association between two categorical variables. It assesses whether the observed frequencies differ significantly from the expected frequencies under the assumption of independence.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_How_is_the_null_hypothesis_defined_in_the_chi-square_test\"><\/span>5. How is the null hypothesis defined in the chi-square test?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe null hypothesis (H0) in the chi-square test assumes that there is no association between the variables. It suggests that any observed relationship is due to chance alone.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_What_are_expected_frequencies\"><\/span>6. What are expected frequencies?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nExpected frequencies are the frequencies that would be expected in each cell of the 4&#215;4 graph if the variables were independent. They are calculated under the assumption of no association between the variables.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_What_are_degrees_of_freedom\"><\/span>7. What are degrees of freedom?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nDegrees of freedom represent the number of values that are free to vary in the calculation of a statistic. In the case of a 4&#215;4 graph, it is calculated as (r &#8211; 1) x (c &#8211; 1), where &#8216;r&#8217; is the number of rows and &#8216;c&#8217; is the number of columns in the table.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_How_do_we_define_the_critical_value_for_the_chi-square_test\"><\/span>8. How do we define the critical value for the chi-square test?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe critical value for the chi-square test is determined based on the chosen significance level (such as 0.05 or 0.01) and the degrees of freedom. It represents the test statistic value beyond which we reject the null hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_What_happens_if_the_test_statistic_is_larger_than_the_critical_value\"><\/span>9. What happens if the test statistic is larger than the critical value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the test statistic is larger than the critical value, we reject the null hypothesis. It suggests that the observed association between the variables is unlikely to have occurred by chance.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_What_if_the_test_statistic_is_smaller_than_the_critical_value\"><\/span>10. What if the test statistic is smaller than the critical value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nIf the test statistic is smaller than the critical value, we fail to reject the null hypothesis. It implies that the observed association between the variables could reasonably be attributed to chance.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_How_is_the_p-value_interpreted\"><\/span>11. How is the p-value interpreted?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe p-value is interpreted as the probability of observing a test statistic as extreme or more extreme than the one calculated under the null hypothesis. A small p-value suggests strong evidence against the null hypothesis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_Can_the_p-value_ever_be_larger_than_1_or_negative\"><\/span>12. Can the p-value ever be larger than 1 or negative?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the p-value cannot be larger than 1 or negative. It represents a probability, which ranges from 0 to 1. A p-value larger than 1 or negative indicates an improper calculation or misinterpretation of the test statistic.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A 4&#215;4 graph, also known as a contingency table or a cross-tabulation table, is a helpful tool used in statistical analysis to study the relationship between two categorical variables. It allows you to observe the frequency distribution of the variables and determine if there is a significant association between them. One common method to assess &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"How to find p value from four by four graph?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/#more-261503\">Read more<span class=\"screen-reader-text\">How to find p value from four by four graph?<\/span><\/a><\/p>\n","protected":false},"author":66,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-261503","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 to find p value from four by four graph?<\/title>\n<meta name=\"description\" content=\"A 4x4 graph, also known as a contingency table or a cross-tabulation table, is a helpful tool used in statistical analysis to study the relationship\" \/>\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\/how-to-find-p-value-from-four-by-four-graph\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to find p value from four by four graph?\" \/>\n<meta property=\"og:description\" content=\"A 4x4 graph, also known as a contingency table or a cross-tabulation table, is a helpful tool used in statistical analysis to study the relationship\" \/>\n<meta property=\"og:url\" content=\"https:\/\/namso-gen.co\/blog\/how-to-find-p-value-from-four-by-four-graph\/\" \/>\n<meta property=\"og:site_name\" content=\"Namso Gen Blog - 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