{"id":247,"date":"2017-04-15T03:20:07","date_gmt":"2017-04-15T03:20:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/introduction-5\/"},"modified":"2017-05-30T23:36:34","modified_gmt":"2017-05-30T23:36:34","slug":"introduction-5","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/chapter\/introduction-5\/","title":{"raw":"Why It Matters: Relationships in Categorical Data with Intro to Probability","rendered":"Why It Matters: Relationships in Categorical Data with Intro to Probability"},"content":{"raw":"&nbsp;\r\n\r\nBefore we begin <em>Relationships in Categorical Data with Intro to Probability<\/em>, it is helpful to consider how it relates to the work we have already done in previous modules.\r\n\r\nAt the start of <em>Summarizing Data Graphically and Numerically<\/em>, we stated the difference between quantitative and categorical variables:\r\n<ul>\r\n \t<li><strong>Quantitative variables<\/strong> have <em>numeric<\/em> values that can be averaged. A quantitative variable is frequently a measurement - for example, a person\u2019s height in inches.<\/li>\r\n \t<li><strong>Categorical variables<\/strong> are variables that can have one of a limited number of values, or labels. Values that can be represented by categorical variables include, for example, a person's eye color, gender, or home state; a vehicle's body style (sedan, SUV, minivan, etc.); a dog's breed (bulldog, greyhound, beagle, etc.).<\/li>\r\n<\/ul>\r\nThe remainder of <em>Summarizing Data Graphically and Numerically<\/em> focused on describing the overall pattern (shape, center, and spread) of the distribution of a quantitative variable.\r\n\r\nIn and <em>Examining Relationships: Quantitative Data<\/em> and <em>Nonlinear Models<\/em>, our goal was to identify and model the relationship between <em>two quantitative variables.<\/em>\r\n\r\nNow, in this module, we turn our full attention back to categorical variables. Our objective is to study the relationship between two categorical variables. Just as in <em>Examining Relationships: Quantitative Data<\/em> and <em>Nonlinear Models<\/em>, we will be looking for patterns in the data.\r\n\r\nAs we organize and analyze data from two categorical variables, we make extensive use of <strong>two-way tables<\/strong>. Two-way tables for two categorical variables are in some ways like scatterplots for two quantitative variables: they give us a useful snapshot of all of the data organized in terms of the two variables of interest. This will be helpful in finding and comparing patterns. This part of <em>Relationships in Categorical Data with Intro to Probability<\/em> is exploratory data analysis in the Big Picture of Statistics.\r\n\r\nA second important objective of this module is to introduce you to the concept of <strong>probability<\/strong>. Two-way tables give us a practical context for talking about probability. We also use two-way tables to help us visualize and solve real-world problems involving probability. This part of the module is part of probability in the Big Picture of Statistics.\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15032006\/m5_two_way_tables_topic_5_1_big_picture_mod5.gif\" alt=\"The Big Picture of Statistics. Shown on the diagram are Step 1: Producing Data, Step 2: Exploratory Data Analysis, Step 3: Probability, and Step 4: Inference. Highlighted in this diagram is Step 3: Probability\" width=\"868\" height=\"420\" \/>","rendered":"<p>&nbsp;<\/p>\n<p>Before we begin <em>Relationships in Categorical Data with Intro to Probability<\/em>, it is helpful to consider how it relates to the work we have already done in previous modules.<\/p>\n<p>At the start of <em>Summarizing Data Graphically and Numerically<\/em>, we stated the difference between quantitative and categorical variables:<\/p>\n<ul>\n<li><strong>Quantitative variables<\/strong> have <em>numeric<\/em> values that can be averaged. A quantitative variable is frequently a measurement &#8211; for example, a person\u2019s height in inches.<\/li>\n<li><strong>Categorical variables<\/strong> are variables that can have one of a limited number of values, or labels. Values that can be represented by categorical variables include, for example, a person&#8217;s eye color, gender, or home state; a vehicle&#8217;s body style (sedan, SUV, minivan, etc.); a dog&#8217;s breed (bulldog, greyhound, beagle, etc.).<\/li>\n<\/ul>\n<p>The remainder of <em>Summarizing Data Graphically and Numerically<\/em> focused on describing the overall pattern (shape, center, and spread) of the distribution of a quantitative variable.<\/p>\n<p>In and <em>Examining Relationships: Quantitative Data<\/em> and <em>Nonlinear Models<\/em>, our goal was to identify and model the relationship between <em>two quantitative variables.<\/em><\/p>\n<p>Now, in this module, we turn our full attention back to categorical variables. Our objective is to study the relationship between two categorical variables. Just as in <em>Examining Relationships: Quantitative Data<\/em> and <em>Nonlinear Models<\/em>, we will be looking for patterns in the data.<\/p>\n<p>As we organize and analyze data from two categorical variables, we make extensive use of <strong>two-way tables<\/strong>. Two-way tables for two categorical variables are in some ways like scatterplots for two quantitative variables: they give us a useful snapshot of all of the data organized in terms of the two variables of interest. This will be helpful in finding and comparing patterns. This part of <em>Relationships in Categorical Data with Intro to Probability<\/em> is exploratory data analysis in the Big Picture of Statistics.<\/p>\n<p>A second important objective of this module is to introduce you to the concept of <strong>probability<\/strong>. Two-way tables give us a practical context for talking about probability. We also use two-way tables to help us visualize and solve real-world problems involving probability. This part of the module is part of probability in the Big Picture of Statistics.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15032006\/m5_two_way_tables_topic_5_1_big_picture_mod5.gif\" alt=\"The Big Picture of Statistics. Shown on the diagram are Step 1: Producing Data, Step 2: Exploratory Data Analysis, Step 3: Probability, and Step 4: Inference. Highlighted in this diagram is Step 3: Probability\" width=\"868\" height=\"420\" \/><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-247\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"442ebb29-19e0-43f5-af47-2c76a4437334","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-247","chapter","type-chapter","status-publish","hentry"],"part":245,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/247\/revisions"}],"predecessor-version":[{"id":1392,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/247\/revisions\/1392"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/245"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/247\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/media?parent=247"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=247"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=247"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/license?post=247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}