{"id":1377,"date":"2023-06-22T02:20:42","date_gmt":"2023-06-22T02:20:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/pair-wise-comparisons-for-anova-learn-it-2\/"},"modified":"2025-05-16T22:59:32","modified_gmt":"2025-05-16T22:59:32","slug":"pair-wise-comparisons-for-anova-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/pair-wise-comparisons-for-anova-learn-it-2\/","title":{"raw":"Pair-wise Comparisons for ANOVA \u2013 Learn It 2","rendered":"Pair-wise Comparisons for ANOVA \u2013 Learn It 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete an ANOVA hypothesis test for pair-wise comparisons&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Complete pair-wise comparisons for ANOVA<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13057,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Pair-wise Comparisons<\/h2>\r\n<p>Previously, we explored a one-way ANOVA hypothesis test that allowed us to compare means from two or more groups\/populations. More specifically, we performed calculations to determine if there was evidence that the means associated with the populations were statistically different from one another. However, because we are comparing two or more means, which means are different? We can perform multiple comparisons to identify the differences.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>pair-wise comparison<\/h3>\r\n<p>The <strong>pair-wise comparison for ANOVA<\/strong> is a process of analyzing groups\/populations by comparing them against each other in pairs.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>When conducting pair-wise comparisons for ANOVA, we will be conducting multiple two-sample tests in order to find the significant difference(s) among the means.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2243[\/ohm2_question]<\/section>\r\n<p>[reveal-answer q=\"630785\"]<strong>Hypothesis Testing Steps for Comparing Two Population Means.<\/strong>[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"630785\"]<\/p>\r\n<ol>\r\n\t<li>Write out the null and alternative hypotheses.<\/li>\r\n\t<li>Check the conditions for the hypothesis test - independent samples.<\/li>\r\n\t<li>Calculate a [latex]t[\/latex]-statistic.<\/li>\r\n\t<li>Calculate a P-value.<\/li>\r\n\t<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<\/li>\r\n\t<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<section class=\"textbox recall\"><strong>The null hypothesis ([latex]H_0[\/latex]):<\/strong>\u00a0It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.\r\n\r\n<ul>\r\n\t<li>Null hypothesis: [latex]H_0: \\mu_1=\\mu_2[\/latex] or [latex]H_0: \\mu_1-\\mu_2=0[\/latex]<\/li>\r\n<\/ul>\r\n<p><strong>The alternative hypothesis ([latex]H_A[\/latex])<\/strong><strong>:<\/strong> It is a claim about the population that is contradictory to [latex]H_0[\/latex] and what we conclude when we reject [latex]H_0[\/latex].<\/p>\r\n<ul>\r\n\t<li>Alternative hypothesis:\r\n\r\n<ul>\r\n\t<li>[latex]H_A: \\mu_1\\lt \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\lt 0[\/latex]<\/li>\r\n\t<li>[latex]H_A: \\mu_1&gt;\\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2&gt;0[\/latex]<\/li>\r\n\t<li>[latex]H_A: \\mu_1\\ne \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\ne0[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2244[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete an ANOVA hypothesis test for pair-wise comparisons&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Complete pair-wise comparisons for ANOVA<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13057,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Pair-wise Comparisons<\/h2>\n<p>Previously, we explored a one-way ANOVA hypothesis test that allowed us to compare means from two or more groups\/populations. More specifically, we performed calculations to determine if there was evidence that the means associated with the populations were statistically different from one another. However, because we are comparing two or more means, which means are different? We can perform multiple comparisons to identify the differences.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>pair-wise comparison<\/h3>\n<p>The <strong>pair-wise comparison for ANOVA<\/strong> is a process of analyzing groups\/populations by comparing them against each other in pairs.<\/p>\n<p>&nbsp;<\/p>\n<p>When conducting pair-wise comparisons for ANOVA, we will be conducting multiple two-sample tests in order to find the significant difference(s) among the means.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2243\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2243&theme=lumen&iframe_resize_id=ohm2243&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q630785\"><strong>Hypothesis Testing Steps for Comparing Two Population Means.<\/strong><\/button><\/p>\n<div id=\"q630785\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Write out the null and alternative hypotheses.<\/li>\n<li>Check the conditions for the hypothesis test &#8211; independent samples.<\/li>\n<li>Calculate a [latex]t[\/latex]-statistic.<\/li>\n<li>Calculate a P-value.<\/li>\n<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<\/li>\n<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<section class=\"textbox recall\"><strong>The null hypothesis ([latex]H_0[\/latex]):<\/strong>\u00a0It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.<\/p>\n<ul>\n<li>Null hypothesis: [latex]H_0: \\mu_1=\\mu_2[\/latex] or [latex]H_0: \\mu_1-\\mu_2=0[\/latex]<\/li>\n<\/ul>\n<p><strong>The alternative hypothesis ([latex]H_A[\/latex])<\/strong><strong>:<\/strong> It is a claim about the population that is contradictory to [latex]H_0[\/latex] and what we conclude when we reject [latex]H_0[\/latex].<\/p>\n<ul>\n<li>Alternative hypothesis:\n<ul>\n<li>[latex]H_A: \\mu_1\\lt \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\lt 0[\/latex]<\/li>\n<li>[latex]H_A: \\mu_1>\\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2>0[\/latex]<\/li>\n<li>[latex]H_A: \\mu_1\\ne \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\ne0[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2244\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2244&theme=lumen&iframe_resize_id=ohm2244&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":28,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1348,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1377"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1377\/revisions"}],"predecessor-version":[{"id":6851,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1377\/revisions\/6851"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1348"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1377\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1377"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1377"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1377"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}