{"id":896,"date":"2023-03-20T19:18:09","date_gmt":"2023-03-20T19:18:09","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-apply-it-1\/"},"modified":"2025-05-11T22:49:20","modified_gmt":"2025-05-11T22:49:20","slug":"z-score-and-the-empirical-rule-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-apply-it-1\/","title":{"raw":"Z-Score and the Empirical Rule: Apply It 1","rendered":"Z-Score and the Empirical Rule: Apply It 1"},"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;Calculate z-scores to explain the location of data points&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate [latex]z[\/latex]-scores to explain the location of data points.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Compare observations using z-scores and the Empirical Rule&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Compare observations using [latex]z[\/latex]-scores and the Empirical Rule.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>What is unusual?<\/h2>\r\n<p>In a medical study, many observations are made in an effort to obtain a data sample representative of a population. In this activity, you'll see how standardized scores and the Empirical Rule can be used to determine if an observation is usual or unusual.<\/p>\r\n<p>Around the world, pharmaceutical companies conduct clinical trials to evaluate the safety and efficacy of their drugs. Clinical trials are research studies performed on people and are aimed at evaluating whether a new drug is safe and effective. People who participate in clinical trials are volunteers.<\/p>\r\n\r\n[caption id=\"attachment_1138\" align=\"aligncenter\" width=\"651\"]<img class=\"wp-image-1138\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/03\/20191808\/pexels-thirdman-7659570.jpg\" alt=\"Two women speaking with a doctor who is taking notes, blood pressure cuff on table\" width=\"651\" height=\"434\" \/> Figure 1. Volunteers are essential in clinical trials, helping scientists gather data to decide whether a new drug behaves as expected\u2014or shows unusual results.[\/caption]\r\n\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2156[\/ohm2_question]<\/section>\r\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">Mice are often used for evaluation before testing chemicals and pharmaceuticals on humans in medical studies. One reason for this is that scientists know a lot about the genome <\/span><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">of a mouse. They are bred in labs to be identical, so the only thing different between them is the treatment. Mice also have short lifespans, which allows scientists to model the effects of a drug over their entire lifespan (about\u00a0[latex]800[\/latex] days). It is much more difficult to understand the effects of a drug over the lifetime of a human.<\/span><\/p>\r\n<p>Consider a study concerned with learning how a drug or a treatment affects the body. The toxicity of a chemical and its impact on vital organs are of interest when assessing the effects of a chemical treatment. A standard method used to measure the level of toxicity in an organ is to use the organ\u2019s weight.[footnote] Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., &amp; Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for toxicology studies. <em>Toxicologic Pathology.<\/em> 35(5), 751-755. https:\/\/doi.org\/10.1080\/01926230701595300[\/footnote]<\/p>\r\n<p>[reveal-answer q=\"283496\"]What is a genome?[footnote]<em>What is a genome?<\/em> (2017, January 6). Yourgenome. Retrieved from\u00a0<a href=\"https:\/\/www.yourgenome.org\/facts\/what-is-a-genome\">https:\/\/www.yourgenome.org\/facts\/what-is-a-genome<\/a>[\/footnote][\/reveal-answer]<br \/>\r\n[hidden-answer a=\"283496\"]A genome is an organism\u2019s complete set of genetic instructions. Each genome contains all of the information needed to build that organism and allow it to grow and develop. Our bodies are made up of millions of cells, each with its own complete set of instructions for making us, like a recipe book for the body. This set of instructions is known as our genome and is made up of DNA. For more information on genomes, visit <a href=\"https:\/\/www.yourgenome.org\/facts\/what-is-a-genome\">https:\/\/www.yourgenome.org\/facts\/what-is-a-genome<\/a>.[\/hidden-answer]<\/p>\r\n<p>[reveal-answer q=\"233331\"]What is toxicity?[footnote]<em>Definition of toxicity<\/em>. (2021, March 29). RxList. Retrieved from<br \/>\r\n<a href=\"https:\/\/www.rxlist.com\/toxicity\/definition.htm\">https:\/\/www.rxlist.com\/toxicity\/definition.htm<\/a>[\/footnote][\/reveal-answer]<br \/>\r\n[hidden-answer a=\"233331\"]The degree to which a substance (a toxin or poison) can harm humans or animals.[\/hidden-answer]<\/p>\r\n<p>[reveal-answer q=\"128123\"]Why is organ weight used to measure toxicity?[footnote]Lazic, S. E., Semenova, E., &amp; Williams, D. P. (2020, April 20). <em>Determining organ weight toxicity with Bayesian causal models: Improving on the analysis of relative organ weights<\/em>. National Center for Biotechnology Information. <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC7170916\/\">https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC7170916\/<\/a>[\/footnote][\/reveal-answer]<br \/>\r\n[hidden-answer a=\"128123\"]Organ weight changes are indicators of chemically-induced organ damage. Hence, changes in organ weight are often associated with treatment-related effects.[\/hidden-answer]<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate z-scores to explain the location of data points&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate [latex]z[\/latex]-scores to explain the location of data points.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Compare observations using z-scores and the Empirical Rule&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Compare observations using [latex]z[\/latex]-scores and the Empirical Rule.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>What is unusual?<\/h2>\n<p>In a medical study, many observations are made in an effort to obtain a data sample representative of a population. In this activity, you&#8217;ll see how standardized scores and the Empirical Rule can be used to determine if an observation is usual or unusual.<\/p>\n<p>Around the world, pharmaceutical companies conduct clinical trials to evaluate the safety and efficacy of their drugs. Clinical trials are research studies performed on people and are aimed at evaluating whether a new drug is safe and effective. People who participate in clinical trials are volunteers.<\/p>\n<figure id=\"attachment_1138\" aria-describedby=\"caption-attachment-1138\" style=\"width: 651px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1138\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/03\/20191808\/pexels-thirdman-7659570.jpg\" alt=\"Two women speaking with a doctor who is taking notes, blood pressure cuff on table\" width=\"651\" height=\"434\" \/><figcaption id=\"caption-attachment-1138\" class=\"wp-caption-text\">Figure 1. Volunteers are essential in clinical trials, helping scientists gather data to decide whether a new drug behaves as expected\u2014or shows unusual results.<\/figcaption><\/figure>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2156\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2156&theme=lumen&iframe_resize_id=ohm2156&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">Mice are often used for evaluation before testing chemicals and pharmaceuticals on humans in medical studies. One reason for this is that scientists know a lot about the genome <\/span><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">of a mouse. They are bred in labs to be identical, so the only thing different between them is the treatment. Mice also have short lifespans, which allows scientists to model the effects of a drug over their entire lifespan (about\u00a0[latex]800[\/latex] days). It is much more difficult to understand the effects of a drug over the lifetime of a human.<\/span><\/p>\n<p>Consider a study concerned with learning how a drug or a treatment affects the body. The toxicity of a chemical and its impact on vital organs are of interest when assessing the effects of a chemical treatment. A standard method used to measure the level of toxicity in an organ is to use the organ\u2019s weight.<a class=\"footnote\" title=\"Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., &amp; Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for toxicology studies. Toxicologic Pathology. 35(5), 751-755. https:\/\/doi.org\/10.1080\/01926230701595300\" id=\"return-footnote-896-1\" href=\"#footnote-896-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q283496\">What is a genome?<a class=\"footnote\" title=\"What is a genome? (2017, January 6). Yourgenome. Retrieved from\u00a0https:\/\/www.yourgenome.org\/facts\/what-is-a-genome\" id=\"return-footnote-896-2\" href=\"#footnote-896-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/button><\/p>\n<div id=\"q283496\" class=\"hidden-answer\" style=\"display: none\">A genome is an organism\u2019s complete set of genetic instructions. Each genome contains all of the information needed to build that organism and allow it to grow and develop. Our bodies are made up of millions of cells, each with its own complete set of instructions for making us, like a recipe book for the body. This set of instructions is known as our genome and is made up of DNA. For more information on genomes, visit <a href=\"https:\/\/www.yourgenome.org\/facts\/what-is-a-genome\">https:\/\/www.yourgenome.org\/facts\/what-is-a-genome<\/a>.<\/div>\n<\/div>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q233331\">What is toxicity?<a class=\"footnote\" title=\"Definition of toxicity. (2021, March 29). RxList. Retrieved from\nhttps:\/\/www.rxlist.com\/toxicity\/definition.htm\" id=\"return-footnote-896-3\" href=\"#footnote-896-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a><\/button><\/p>\n<div id=\"q233331\" class=\"hidden-answer\" style=\"display: none\">The degree to which a substance (a toxin or poison) can harm humans or animals.<\/div>\n<\/div>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q128123\">Why is organ weight used to measure toxicity?<a class=\"footnote\" title=\"Lazic, S. E., Semenova, E., &amp; Williams, D. P. (2020, April 20). Determining organ weight toxicity with Bayesian causal models: Improving on the analysis of relative organ weights. National Center for Biotechnology Information. https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC7170916\/\" id=\"return-footnote-896-4\" href=\"#footnote-896-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a><\/button><\/p>\n<div id=\"q128123\" class=\"hidden-answer\" style=\"display: none\">Organ weight changes are indicators of chemically-induced organ damage. Hence, changes in organ weight are often associated with treatment-related effects.<\/div>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-896-1\"> Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., &amp; Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for toxicology studies. <em>Toxicologic Pathology.<\/em> 35(5), 751-755. https:\/\/doi.org\/10.1080\/01926230701595300 <a href=\"#return-footnote-896-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-896-2\"><em>What is a genome?<\/em> (2017, January 6). Yourgenome. Retrieved from\u00a0<a href=\"https:\/\/www.yourgenome.org\/facts\/what-is-a-genome\">https:\/\/www.yourgenome.org\/facts\/what-is-a-genome<\/a> <a href=\"#return-footnote-896-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-896-3\"><em>Definition of toxicity<\/em>. (2021, March 29). RxList. Retrieved from<br \/>\r\n<a href=\"https:\/\/www.rxlist.com\/toxicity\/definition.htm\">https:\/\/www.rxlist.com\/toxicity\/definition.htm<\/a> <a href=\"#return-footnote-896-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><li id=\"footnote-896-4\">Lazic, S. E., Semenova, E., &amp; Williams, D. P. (2020, April 20). <em>Determining organ weight toxicity with Bayesian causal models: Improving on the analysis of relative organ weights<\/em>. National Center for Biotechnology Information. <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC7170916\/\">https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC7170916\/<\/a> <a href=\"#return-footnote-896-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":13,"menu_order":44,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Women with doctor image\",\"author\":\"Thirdman\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/women-having-a-conversation-7659570\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":834,"module-header":"apply_it","content_attributions":[{"type":"cc","description":"Women with doctor image","author":"Thirdman","organization":"Pexels","url":"https:\/\/www.pexels.com\/photo\/women-having-a-conversation-7659570\/","project":"","license":"cc0","license_terms":""}],"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\/896"}],"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\/13"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/896\/revisions"}],"predecessor-version":[{"id":6639,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/896\/revisions\/6639"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/834"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/896\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=896"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=896"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=896"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}