{"id":2840,"date":"2024-07-25T23:03:16","date_gmt":"2024-07-26T03:03:16","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=2840"},"modified":"2024-07-26T02:21:31","modified_gmt":"2024-07-26T06:21:31","slug":"example-of-a-matched-pair-differences-test","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/example-of-a-matched-pair-differences-test\/","title":{"raw":"Matched-Pair Differences Example","rendered":"Matched-Pair Differences Example"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThis section review the following learning objectives.\r\n<ul>\r\n \t<li>Set up a Matched-Pair t-Test<\/li>\r\n \t<li>Use Excel's Data Analysis Toolpak to calculate values in the test<\/li>\r\n \t<li>Draw conclusions based off of your test results<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\nLet us first recap what types of scenarios where testing for differences in two population means uses a matched-pair test:\r\n<ul>\r\n \t<li>One twin of sibling from one group is matched with the other twin or sibling from the second group<\/li>\r\n \t<li>One spouse from one group is matched with their spouse in the second group<\/li>\r\n \t<li>People with similar traits are matched between the two groups<\/li>\r\n \t<li>The same individuals or items are sampled before and after some change<\/li>\r\n<\/ul>\r\n<h1>Setting up a Matched-Pair Test<\/h1>\r\nLet us look at an example of cholesterol medication. A drug company has developed a new drug to treat high cholesterol. How do they go about testing its effectiveness?\r\n<h2>Example 63.1.1<\/h2>\r\n<strong><span style=\"color: #003366\">Problem Setup<\/span><\/strong>: One hundred suitable individuals were selected at random. Their baseline cholesterol levels were recorded at the start of the study. They were then instructed to take a new cholesterol-reducing medication for six months. Their cholesterol levels were re-tested. <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/Example63-1_Data.xlsx\">Click here<\/a> to download their before and after levels. The key metrics for each sample are shown in the table below:\r\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 65%;height: 188px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 17px\">\r\n<th style=\"width: 33.3333%;text-align: center;height: 17px\">Statistic<\/th>\r\n<th style=\"width: 33.3333%;text-align: center;height: 17px\">Before<\/th>\r\n<th style=\"width: 33.3333%;text-align: center;height: 17px\">After<\/th>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Mean<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">181.44<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">151.54<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Median<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">149<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">154<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Mode<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">86<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">154<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Standard Deviation<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">119.25<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">48.04<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Variance<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">14219.99<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">2307.60<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Skewness<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">2.39<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">1.53<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Minimum<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">77<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">78<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Maximum<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">633<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">366<\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px\">\r\n<td style=\"width: 33.3333%;height: 19px\">Count<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">100<\/td>\r\n<td style=\"width: 33.3333%;height: 19px\">100<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<span style=\"color: #003366\"><strong>Question<\/strong><\/span>: Is there enough evidence, at the 1% level of significance to conclude that the medication reduced the individual's cholesterol levels? Define the problem by setting up your null and alternate hypotheses for this problem.\r\n\r\n<span style=\"color: #003366\"><strong>Solution<\/strong><\/span>:\u00a0Let us assume that there is no difference in cholesterol levels before and after taking the medication. This is what We define this as our null hypothesis (H<sub>0<\/sub>):\r\n<ul>\r\n \t<li>H<sub style=\"text-align: initial\">0<\/sub><span style=\"text-align: initial\">: \u03bc<\/span><sub style=\"text-align: initial\">before<\/sub><span style=\"text-align: initial\"> = \u03bc<\/span><sub style=\"text-align: initial\">after<\/sub><span style=\"text-align: initial\"> or\u00a0 <\/span><span style=\"text-align: initial\">\u03bc<\/span><sub style=\"text-align: initial\">before <\/sub><span style=\"text-align: initial\">\u2212 \u03bc<\/span><sub style=\"text-align: initial\">after <\/sub><span style=\"text-align: initial\">= 0<\/span><\/li>\r\n \t<li>In other words, our hypothesized difference between the two groups equals zero.<\/li>\r\n \t<li>Later, the p-value gives a likelihood of this hypothesis being true given our sample results.<\/li>\r\n<\/ul>\r\nThe alternative (which we hope to be left with after rejecting H<sub>0<\/sub>) is that cholesterol levels are lower in the individuals after six months of taking the medication. In other words:\r\n<ul>\r\n \t<li>The average level before taking the medication is higher than the average levels after taking the medical<\/li>\r\n \t<li>H<sub style=\"text-align: initial\">A<\/sub><span style=\"text-align: initial\">: \u03bc<\/span><sub style=\"text-align: initial\">before<\/sub><span style=\"text-align: initial\"> &gt; \u03bc<\/span><sub style=\"text-align: initial\">after<\/sub><span style=\"text-align: initial\"> or\u00a0 <\/span><span style=\"text-align: initial\">\u03bc<\/span><sub style=\"text-align: initial\">before <\/sub><span style=\"text-align: initial\">\u2212 \u03bc<\/span><sub style=\"text-align: initial\">after <\/sub><span style=\"text-align: initial\">&gt; 0<\/span><\/li>\r\n<\/ul>\r\nIf we define the 'before' levels as sample 1 the 'after' levels as sample 2, we have a right-tailed test.\r\n<h1>Using Excel's Data Analysis Toolpak<\/h1>\r\nLet us continue with Example 63.1. In this section, we will step through how to use Excel's <a href=\"https:\/\/support.microsoft.com\/en-us\/office\/use-the-analysis-toolpak-to-perform-complex-data-analysis-6c67ccf0-f4a9-487c-8dec-bdb5a2cefab6\">Data Analysis Toolpak<\/a> to calculate the required metrics for this question.\r\n<h2>Example 63.2<\/h2>\r\n<strong><span style=\"color: #003366\">Problem Setup<\/span><\/strong>: Continue with Example 63.1. In this example, pick the correct test within the Data Analysis Toolpak and then run this test to determine the following metrics:\r\n<ul>\r\n \t<li>The test statistic (t<sub>test<\/sub>)<\/li>\r\n \t<li>The p-value for correct tail<\/li>\r\n \t<li>The critical value (t<sub>crit<\/sub>)<\/li>\r\n<\/ul>\r\n<strong>Solutions<\/strong>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/Example63-1_Solutions.xlsx\">Click here<\/a> to download the solutions shown in the video or click to reveal the step-by-step instructions below.\r\n\r\nhttps:\/\/youtu.be\/zVGUgWtMYKI\r\n<div>\r\n<h1>Step-by-Step Solutions<\/h1>\r\n<ol>\r\n \t<li>Click on the 'Data' tab and select 'Data Analysis'\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis.jpg\"><img class=\"alignnone wp-image-2854\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis.jpg\" alt=\"Image of 'Data Analysis' highlighted in the Data Tab in Excel\" width=\"620\" height=\"150\" \/><\/a><\/li>\r\n \t<li>Select 't-test: Paired Two Sample for Means' and click 'OK'\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means.jpg\"><img class=\"alignnone size-full wp-image-2855\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means.jpg\" alt=\"Image of drop-down menu with t-test Paired Two Sample for Means selected\" width=\"650\" height=\"312\" \/><\/a><\/li>\r\n \t<li>Put the following inputs in the t-test dialogue box:\r\n<ol>\r\n \t<li>Select the 'Before' column as Variable <span style=\"text-decoration: underline\">1<\/span>.<\/li>\r\n \t<li>Select the 'After' column as Variable <span style=\"text-decoration: underline\">2<\/span>.<\/li>\r\n \t<li>Set the Hypoth<span style=\"text-decoration: underline\">e<\/span>sized Mean Difference to 0.<\/li>\r\n \t<li>Check off <span style=\"text-decoration: underline\">L<\/span>abels.<\/li>\r\n \t<li>Enter 0.01 for <span style=\"text-decoration: underline\">A<\/span>lpha (this is the level of significance)<\/li>\r\n \t<li>Select an '<span style=\"text-decoration: underline\">O<\/span>utput Range' (either somewhere in the worksheet or a new worksheet)<\/li>\r\n \t<li>Click 'OK'\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1.jpg\"><img class=\"alignnone wp-image-2867 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1.jpg\" alt=\"Image with Paired t-test dialogue box and inputs included. These inputs are also given in the Excel solutions.\" width=\"695\" height=\"447\" \/><\/a><\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\nThe following outputs should be given:\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\"><img class=\"size-full wp-image-2858 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\" alt=\"Screenshot of paired t-test outputs that are also given in the excel file provided\" width=\"393\" height=\"416\" \/><\/a>\r\n\r\n<\/div>\r\n<h1>The Decision and Conclusion<\/h1>\r\nSo how do we interpret the output given by the Data Analysis Toolpak? Let us form a conclusion based off the output given in the previous section.\r\n<h2>Example 63.3<\/h2>\r\n<strong><span style=\"color: #003366\">Problem Setup<\/span><\/strong>: Continue with Example 63.2. Interpret the Excel output given in that example (see below).\r\n\r\n[caption id=\"attachment_2858\" align=\"aligncenter\" width=\"393\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\"><img class=\"wp-image-2858 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\" alt=\"Screenshot of paired t-test outputs that are also given in the excel file provided\" width=\"393\" height=\"416\" \/><\/a> Figure 63.1 The t-test output from Example 63.2[\/caption]\r\n\r\n<strong><span style=\"color: #003366\">Question<\/span><\/strong>: What are your decision and conclusion based on the above output?\r\n\r\n<span style=\"color: #003366\"><strong>Solutions<\/strong><\/span>: We are performing a right-tailed test. This is a one-tailed test. Therefore, read the P(T&lt;=t) one-tail line to determine the p-value.\r\n<ul>\r\n \t<li><span style=\"color: #003366\">Decision<\/span>: Reject H<sub>0<\/sub> at the 1% level of significance<\/li>\r\n \t<li><span style=\"color: #003366\">Reasoning<\/span>: The p-value = 0.000318 is less than (&lt;) the level of significance (0.01)<\/li>\r\n \t<li><span style=\"color: #003366\">Conclusion<\/span>: There is sufficient evidence to conclude that the subjects' average cholesterol level is lower after six months of taking the medication than before taking the medication (baseline level).<\/li>\r\n<\/ul>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>This section review the following learning objectives.<\/p>\n<ul>\n<li>Set up a Matched-Pair t-Test<\/li>\n<li>Use Excel&#8217;s Data Analysis Toolpak to calculate values in the test<\/li>\n<li>Draw conclusions based off of your test results<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>Let us first recap what types of scenarios where testing for differences in two population means uses a matched-pair test:<\/p>\n<ul>\n<li>One twin of sibling from one group is matched with the other twin or sibling from the second group<\/li>\n<li>One spouse from one group is matched with their spouse in the second group<\/li>\n<li>People with similar traits are matched between the two groups<\/li>\n<li>The same individuals or items are sampled before and after some change<\/li>\n<\/ul>\n<h1>Setting up a Matched-Pair Test<\/h1>\n<p>Let us look at an example of cholesterol medication. A drug company has developed a new drug to treat high cholesterol. How do they go about testing its effectiveness?<\/p>\n<h2>Example 63.1.1<\/h2>\n<p><strong><span style=\"color: #003366\">Problem Setup<\/span><\/strong>: One hundred suitable individuals were selected at random. Their baseline cholesterol levels were recorded at the start of the study. They were then instructed to take a new cholesterol-reducing medication for six months. Their cholesterol levels were re-tested. <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/Example63-1_Data.xlsx\">Click here<\/a> to download their before and after levels. The key metrics for each sample are shown in the table below:<\/p>\n<table class=\"lines aligncenter\" style=\"border-collapse: collapse;width: 65%;height: 188px\">\n<tbody>\n<tr style=\"height: 17px\">\n<th style=\"width: 33.3333%;text-align: center;height: 17px\">Statistic<\/th>\n<th style=\"width: 33.3333%;text-align: center;height: 17px\">Before<\/th>\n<th style=\"width: 33.3333%;text-align: center;height: 17px\">After<\/th>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Mean<\/td>\n<td style=\"width: 33.3333%;height: 19px\">181.44<\/td>\n<td style=\"width: 33.3333%;height: 19px\">151.54<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Median<\/td>\n<td style=\"width: 33.3333%;height: 19px\">149<\/td>\n<td style=\"width: 33.3333%;height: 19px\">154<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Mode<\/td>\n<td style=\"width: 33.3333%;height: 19px\">86<\/td>\n<td style=\"width: 33.3333%;height: 19px\">154<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Standard Deviation<\/td>\n<td style=\"width: 33.3333%;height: 19px\">119.25<\/td>\n<td style=\"width: 33.3333%;height: 19px\">48.04<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Variance<\/td>\n<td style=\"width: 33.3333%;height: 19px\">14219.99<\/td>\n<td style=\"width: 33.3333%;height: 19px\">2307.60<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Skewness<\/td>\n<td style=\"width: 33.3333%;height: 19px\">2.39<\/td>\n<td style=\"width: 33.3333%;height: 19px\">1.53<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Minimum<\/td>\n<td style=\"width: 33.3333%;height: 19px\">77<\/td>\n<td style=\"width: 33.3333%;height: 19px\">78<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Maximum<\/td>\n<td style=\"width: 33.3333%;height: 19px\">633<\/td>\n<td style=\"width: 33.3333%;height: 19px\">366<\/td>\n<\/tr>\n<tr style=\"height: 19px\">\n<td style=\"width: 33.3333%;height: 19px\">Count<\/td>\n<td style=\"width: 33.3333%;height: 19px\">100<\/td>\n<td style=\"width: 33.3333%;height: 19px\">100<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #003366\"><strong>Question<\/strong><\/span>: Is there enough evidence, at the 1% level of significance to conclude that the medication reduced the individual&#8217;s cholesterol levels? Define the problem by setting up your null and alternate hypotheses for this problem.<\/p>\n<p><span style=\"color: #003366\"><strong>Solution<\/strong><\/span>:\u00a0Let us assume that there is no difference in cholesterol levels before and after taking the medication. This is what We define this as our null hypothesis (H<sub>0<\/sub>):<\/p>\n<ul>\n<li>H<sub style=\"text-align: initial\">0<\/sub><span style=\"text-align: initial\">: \u03bc<\/span><sub style=\"text-align: initial\">before<\/sub><span style=\"text-align: initial\"> = \u03bc<\/span><sub style=\"text-align: initial\">after<\/sub><span style=\"text-align: initial\"> or\u00a0 <\/span><span style=\"text-align: initial\">\u03bc<\/span><sub style=\"text-align: initial\">before <\/sub><span style=\"text-align: initial\">\u2212 \u03bc<\/span><sub style=\"text-align: initial\">after <\/sub><span style=\"text-align: initial\">= 0<\/span><\/li>\n<li>In other words, our hypothesized difference between the two groups equals zero.<\/li>\n<li>Later, the p-value gives a likelihood of this hypothesis being true given our sample results.<\/li>\n<\/ul>\n<p>The alternative (which we hope to be left with after rejecting H<sub>0<\/sub>) is that cholesterol levels are lower in the individuals after six months of taking the medication. In other words:<\/p>\n<ul>\n<li>The average level before taking the medication is higher than the average levels after taking the medical<\/li>\n<li>H<sub style=\"text-align: initial\">A<\/sub><span style=\"text-align: initial\">: \u03bc<\/span><sub style=\"text-align: initial\">before<\/sub><span style=\"text-align: initial\"> &gt; \u03bc<\/span><sub style=\"text-align: initial\">after<\/sub><span style=\"text-align: initial\"> or\u00a0 <\/span><span style=\"text-align: initial\">\u03bc<\/span><sub style=\"text-align: initial\">before <\/sub><span style=\"text-align: initial\">\u2212 \u03bc<\/span><sub style=\"text-align: initial\">after <\/sub><span style=\"text-align: initial\">&gt; 0<\/span><\/li>\n<\/ul>\n<p>If we define the &#8216;before&#8217; levels as sample 1 the &#8216;after&#8217; levels as sample 2, we have a right-tailed test.<\/p>\n<h1>Using Excel&#8217;s Data Analysis Toolpak<\/h1>\n<p>Let us continue with Example 63.1. In this section, we will step through how to use Excel&#8217;s <a href=\"https:\/\/support.microsoft.com\/en-us\/office\/use-the-analysis-toolpak-to-perform-complex-data-analysis-6c67ccf0-f4a9-487c-8dec-bdb5a2cefab6\">Data Analysis Toolpak<\/a> to calculate the required metrics for this question.<\/p>\n<h2>Example 63.2<\/h2>\n<p><strong><span style=\"color: #003366\">Problem Setup<\/span><\/strong>: Continue with Example 63.1. In this example, pick the correct test within the Data Analysis Toolpak and then run this test to determine the following metrics:<\/p>\n<ul>\n<li>The test statistic (t<sub>test<\/sub>)<\/li>\n<li>The p-value for correct tail<\/li>\n<li>The critical value (t<sub>crit<\/sub>)<\/li>\n<\/ul>\n<p><strong>Solutions<\/strong>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/Example63-1_Solutions.xlsx\">Click here<\/a> to download the solutions shown in the video or click to reveal the step-by-step instructions below.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Test if a medication has improved patient outcomes (conducting a paired two sample for means test).\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zVGUgWtMYKI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div>\n<h1>Step-by-Step Solutions<\/h1>\n<ol>\n<li>Click on the &#8216;Data&#8217; tab and select &#8216;Data Analysis&#8217;<br \/>\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2854\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis.jpg\" alt=\"Image of 'Data Analysis' highlighted in the Data Tab in Excel\" width=\"620\" height=\"150\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis.jpg 1635w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-300x73.jpg 300w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-1024x248.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-768x186.jpg 768w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-1536x372.jpg 1536w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-65x16.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-225x54.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/DataAnalysis-350x85.jpg 350w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/a><\/li>\n<li>Select &#8216;t-test: Paired Two Sample for Means&#8217; and click &#8216;OK&#8217;<br \/>\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2855\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means.jpg\" alt=\"Image of drop-down menu with t-test Paired Two Sample for Means selected\" width=\"650\" height=\"312\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means.jpg 650w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means-300x144.jpg 300w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means-65x31.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means-225x108.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_Two_Sample_For_Means-350x168.jpg 350w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><\/li>\n<li>Put the following inputs in the t-test dialogue box:\n<ol>\n<li>Select the &#8216;Before&#8217; column as Variable <span style=\"text-decoration: underline\">1<\/span>.<\/li>\n<li>Select the &#8216;After&#8217; column as Variable <span style=\"text-decoration: underline\">2<\/span>.<\/li>\n<li>Set the Hypoth<span style=\"text-decoration: underline\">e<\/span>sized Mean Difference to 0.<\/li>\n<li>Check off <span style=\"text-decoration: underline\">L<\/span>abels.<\/li>\n<li>Enter 0.01 for <span style=\"text-decoration: underline\">A<\/span>lpha (this is the level of significance)<\/li>\n<li>Select an &#8216;<span style=\"text-decoration: underline\">O<\/span>utput Range&#8217; (either somewhere in the worksheet or a new worksheet)<\/li>\n<li>Click &#8216;OK&#8217;<br \/>\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2867 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1.jpg\" alt=\"Image with Paired t-test dialogue box and inputs included. These inputs are also given in the Excel solutions.\" width=\"695\" height=\"447\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1.jpg 695w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1-300x193.jpg 300w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1-65x42.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1-225x145.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_dialogue_box-1-350x225.jpg 350w\" sizes=\"auto, (max-width: 695px) 100vw, 695px\" \/><\/a><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>The following outputs should be given:<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2858 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\" alt=\"Screenshot of paired t-test outputs that are also given in the excel file provided\" width=\"393\" height=\"416\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg 393w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-283x300.jpg 283w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-65x69.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-225x238.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-350x370.jpg 350w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/a><\/p>\n<\/div>\n<h1>The Decision and Conclusion<\/h1>\n<p>So how do we interpret the output given by the Data Analysis Toolpak? Let us form a conclusion based off the output given in the previous section.<\/p>\n<h2>Example 63.3<\/h2>\n<p><strong><span style=\"color: #003366\">Problem Setup<\/span><\/strong>: Continue with Example 63.2. Interpret the Excel output given in that example (see below).<\/p>\n<figure id=\"attachment_2858\" aria-describedby=\"caption-attachment-2858\" style=\"width: 393px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2858 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg\" alt=\"Screenshot of paired t-test outputs that are also given in the excel file provided\" width=\"393\" height=\"416\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output.jpg 393w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-283x300.jpg 283w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-65x69.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-225x238.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/07\/t-test_Paired_output-350x370.jpg 350w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/a><figcaption id=\"caption-attachment-2858\" class=\"wp-caption-text\">Figure 63.1 The t-test output from Example 63.2<\/figcaption><\/figure>\n<p><strong><span style=\"color: #003366\">Question<\/span><\/strong>: What are your decision and conclusion based on the above output?<\/p>\n<p><span style=\"color: #003366\"><strong>Solutions<\/strong><\/span>: We are performing a right-tailed test. This is a one-tailed test. Therefore, read the P(T&lt;=t) one-tail line to determine the p-value.<\/p>\n<ul>\n<li><span style=\"color: #003366\">Decision<\/span>: Reject H<sub>0<\/sub> at the 1% level of significance<\/li>\n<li><span style=\"color: #003366\">Reasoning<\/span>: The p-value = 0.000318 is less than (&lt;) the level of significance (0.01)<\/li>\n<li><span style=\"color: #003366\">Conclusion<\/span>: There is sufficient evidence to conclude that the subjects&#8217; average cholesterol level is lower after six months of taking the medication than before taking the medication (baseline level).<\/li>\n<\/ul>\n","protected":false},"author":865,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2840","chapter","type-chapter","status-publish","hentry"],"part":2690,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/2840","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":15,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/2840\/revisions"}],"predecessor-version":[{"id":2875,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/2840\/revisions\/2875"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/2690"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/2840\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=2840"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=2840"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=2840"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=2840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}