{"id":52,"date":"2022-05-20T16:59:05","date_gmt":"2022-05-20T16:59:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/z-score-and-the-empirical-rule-forming-connections\/"},"modified":"2022-07-11T19:48:48","modified_gmt":"2022-07-11T19:48:48","slug":"z-score-and-the-empirical-rule-forming-connections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/z-score-and-the-empirical-rule-forming-connections\/","title":{"raw":"Z-Score and the Empirical Rule: Apply It 1","rendered":"Z-Score and the Empirical Rule: Apply It 1"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\nDuring this activity, you will:\r\n<ul>\r\n \t<li><a href=\"#useEmp\">Utilize standardized scores and the Empirical Rule to determine if an observation is unusual.<\/a><\/li>\r\n \t<li><a href=\"#CompUseZ\">Compare two observations by calculating and comparing z-scores.<\/a><\/li>\r\n<\/ul>\r\nClick on a skill above to jump to its location in this activity.\r\n\r\n<\/div>\r\n<h2>What Is Unusual?<\/h2>\r\nIn a medical study, many observations are made in an effort to obtain a data sample representative of the population from which it was taken.\u00a0In this activity, you'll see how standardized scores and the Empirical Rule can be used to determine if an observation is usual or unusual.\r\n\r\nAround 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 if a new drug is safe and effective. People who participate in clinical trials are volunteers.\r\n\r\n<strong><img class=\"aligncenter wp-image-1034\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11224131\/Picture60-300x201.jpg\" alt=\"Two people in a room with a doctor who is writing something on a clipboard. Everyone is wearing face masks.\" width=\"523\" height=\"350\" \/><\/strong>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]241229[\/ohm_question]\r\n\r\n[reveal-answer q=\"253038\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"253038\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>video placement<\/h3>\r\n<span style=\"background-color: #e6daf7;\">[Intro video: In this activity, we'll use the landscape of a medical study to learn how the Empirical Rule can help us identify unusual observations of a quantitative variable. We'll also compare two observations by calculating and comparing their standardized scores. Data collected during medical studies tends to form a bell-shaped, unimodal distribution, with a large number of observations located near the mean and equal numbers of values further from the mean falling off to either side. [voice over the empirical rule image from What to Know 4E]. Under these conditions, we know that almost all the observations in the distribution fall within three standard deviations from the mean. This lets us set an exact threshold for how far away from the mean an observation can be located for us to consider it unusual. But human clinical trials require people willing to participate. They are costly and take a great deal of time to gather the appropriate data, even decades to study the effects of a drug over an entire lifespan. Can you think of a good alternative to having human volunteers participate in clinical trials? How about using mice instead? In this activity, we'll explore a medical study involving mice as we learn to apply the Empirical Rule and standardized scores.]<\/span>\r\n\r\n<\/div>\r\nMice are often used in medical studies to evaluate the effects of chemicals and pharmaceuticals. One reason for this is that scientists know a lot about the <span style=\"background-color: #ffff99;\">genome<\/span> 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.\r\n\r\nConsider a study concerned with learning how a drug or a treatment affects the body. The <span style=\"background-color: #ffff99;\">toxicity<\/span> of a chemical and its impact on vital organs is 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 <span style=\"background-color: #ffff99;\">use the organ\u2019s weight<\/span>.[footnote] Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., &amp;\u00a0Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for\u00a0toxicology studies. <em>Toxicologic Pathology.<\/em> 35(5), 751-755. https:\/\/doi.org\/10.1080\/01926230701595300[\/footnote]\r\n\r\n[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]\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 their 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.\u00a0 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>.\r\n\r\n<hr \/>\r\n\r\n[\/hidden-answer]\r\n\r\n[reveal-answer q=\"233331\"]What is toxicity?[footnote]<em>Definition of toxicity<\/em>. (2021, March 29). RxList. Retrieved from\r\n<a href=\"https:\/\/www.rxlist.com\/toxicity\/definition.htm\">https:\/\/www.rxlist.com\/toxicity\/definition.htm<\/a>[\/footnote][\/reveal-answer]\r\n[hidden-answer a=\"233331\"]The degree to which a substance (a toxin or poison) can harm humans or animals.\r\n\r\n<hr \/>\r\n\r\n[\/hidden-answer]\r\n\r\n[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]\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.\r\n\r\n<hr \/>\r\n\r\n[\/hidden-answer]","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<p>During this activity, you will:<\/p>\n<ul>\n<li><a href=\"#useEmp\">Utilize standardized scores and the Empirical Rule to determine if an observation is unusual.<\/a><\/li>\n<li><a href=\"#CompUseZ\">Compare two observations by calculating and comparing z-scores.<\/a><\/li>\n<\/ul>\n<p>Click on a skill above to jump to its location in this activity.<\/p>\n<\/div>\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 the population from which it was taken.\u00a0In 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 if a new drug is safe and effective. People who participate in clinical trials are volunteers.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1034\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11224131\/Picture60-300x201.jpg\" alt=\"Two people in a room with a doctor who is writing something on a clipboard. Everyone is wearing face masks.\" width=\"523\" height=\"350\" \/><\/strong><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241229\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241229&theme=oea&iframe_resize_id=ohm241229\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q253038\">Hint<\/span><\/p>\n<div id=\"q253038\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[Intro video: In this activity, we&#8217;ll use the landscape of a medical study to learn how the Empirical Rule can help us identify unusual observations of a quantitative variable. We&#8217;ll also compare two observations by calculating and comparing their standardized scores. Data collected during medical studies tends to form a bell-shaped, unimodal distribution, with a large number of observations located near the mean and equal numbers of values further from the mean falling off to either side. [voice over the empirical rule image from What to Know 4E]. Under these conditions, we know that almost all the observations in the distribution fall within three standard deviations from the mean. This lets us set an exact threshold for how far away from the mean an observation can be located for us to consider it unusual. But human clinical trials require people willing to participate. They are costly and take a great deal of time to gather the appropriate data, even decades to study the effects of a drug over an entire lifespan. Can you think of a good alternative to having human volunteers participate in clinical trials? How about using mice instead? In this activity, we&#8217;ll explore a medical study involving mice as we learn to apply the Empirical Rule and standardized scores.]<\/span><\/p>\n<\/div>\n<p>Mice are often used in medical studies to evaluate the effects of chemicals and pharmaceuticals. One reason for this is that scientists know a lot about the <span style=\"background-color: #ffff99;\">genome<\/span> 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.<\/p>\n<p>Consider a study concerned with learning how a drug or a treatment affects the body. The <span style=\"background-color: #ffff99;\">toxicity<\/span> of a chemical and its impact on vital organs is 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 <span style=\"background-color: #ffff99;\">use the organ\u2019s weight<\/span>.<a class=\"footnote\" title=\"Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., &amp;\u00a0Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for\u00a0toxicology studies. Toxicologic Pathology. 35(5), 751-755. https:\/\/doi.org\/10.1080\/01926230701595300\" id=\"return-footnote-52-1\" href=\"#footnote-52-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" 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-52-2\" href=\"#footnote-52-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/span><\/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 their 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.\u00a0 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>.<\/p>\n<hr \/>\n<\/div>\n<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" 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-52-3\" href=\"#footnote-52-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a><\/span><\/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.<\/p>\n<hr \/>\n<\/div>\n<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" 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-52-4\" href=\"#footnote-52-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a><\/span><\/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.<\/p>\n<hr \/>\n<\/div>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-52-1\"> Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., &amp;\u00a0Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for\u00a0toxicology studies. <em>Toxicologic Pathology.<\/em> 35(5), 751-755. https:\/\/doi.org\/10.1080\/01926230701595300 <a href=\"#return-footnote-52-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-52-2\"><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-52-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-52-3\"><em>Definition of toxicity<\/em>. (2021, March 29). RxList. Retrieved from\r\n<a href=\"https:\/\/www.rxlist.com\/toxicity\/definition.htm\">https:\/\/www.rxlist.com\/toxicity\/definition.htm<\/a> <a href=\"#return-footnote-52-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><li id=\"footnote-52-4\">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-52-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":17533,"menu_order":53,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-52","chapter","type-chapter","status-publish","hentry"],"part":20,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/52\/revisions"}],"predecessor-version":[{"id":521,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/52\/revisions\/521"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/52\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=52"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=52"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=52"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}