{"id":572,"date":"2017-04-15T03:27:43","date_gmt":"2017-04-15T03:27:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/introduction-10\/"},"modified":"2017-05-31T04:19:26","modified_gmt":"2017-05-31T04:19:26","slug":"introduction-10","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/chapter\/introduction-10\/","title":{"raw":"Why It Matters: Chi-Square Tests","rendered":"Why It Matters: Chi-Square Tests"},"content":{"raw":"&nbsp;\r\n\r\nIn this module, <em>Chi-Square Tests<\/em>, we again focus on inference with categorical variables. We learn three new hypothesis tests, two of which are an extension of hypothesis tests about proportions that we learned in the modules <em>Inference for One Proportion<\/em> and <em>Inference for Two Proportions<\/em>. This module does not focus on estimating a parameter, so there is nothing about confidence intervals in this module.\r\n\r\nHere is the Big Picture of Statistics with the new material for <em>Chi-Square Tests<\/em> highlighted in purple.\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15032741\/m11_chi_square_tests_topic_11_1_m11_intro_1_image1.png\" 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 4: Inference. Introduced to this module: A new curve called the chi-square\" width=\"871\" height=\"699\" \/>&nbsp;\r\n\r\nFollowing are examples of research questions that procedures in this module can address:\r\n\r\n<strong>Goodness-of-Fit Test: <\/strong>Test a claim about the distribution of a categorical variable in a population.\r\n<ul>\r\n \t<li>During the presidential election of 2008, the Pew Research Center collected survey data that suggested that 24% of registered voters were liberal, 38% were moderate, and 38% were conservative. Is the distribution of political views different this year?<\/li>\r\n \t<li>The distribution of blood types for whites in the United States is 45% type O, 41% type A, 10% type B, and 4% type AB. Is the distribution of blood types different for Asian Americans?<\/li>\r\n<\/ul>\r\n<strong>Test of Independence: <\/strong>Test a claim about the relationship between two categorical variables in a population.\r\n<ul>\r\n \t<li>For young adults in the United States, is gender related to body image?<\/li>\r\n \t<li>Is alcohol abuse by New York firefighters dependent on participation in the 9\/11 rescue operation?<\/li>\r\n \t<li>In the United States, is race associated with political views (conservative, moderate, liberal)?<\/li>\r\n<\/ul>\r\n<strong>Test of Homogeneity: <\/strong>Test a claim about the distribution of a categorical variable in several populations.\r\n<ul>\r\n \t<li>Does the use of steroids in collegiate athletics differ across the three NCAA divisions?<\/li>\r\n \t<li>Was the distribution of political views (liberal, moderate, conservative) different for the last three presidential elections in the United States?<\/li>\r\n<\/ul>\r\n&nbsp;","rendered":"<p>&nbsp;<\/p>\n<p>In this module, <em>Chi-Square Tests<\/em>, we again focus on inference with categorical variables. We learn three new hypothesis tests, two of which are an extension of hypothesis tests about proportions that we learned in the modules <em>Inference for One Proportion<\/em> and <em>Inference for Two Proportions<\/em>. This module does not focus on estimating a parameter, so there is nothing about confidence intervals in this module.<\/p>\n<p>Here is the Big Picture of Statistics with the new material for <em>Chi-Square Tests<\/em> highlighted in purple.<\/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\/15032741\/m11_chi_square_tests_topic_11_1_m11_intro_1_image1.png\" 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 4: Inference. Introduced to this module: A new curve called the chi-square\" width=\"871\" height=\"699\" \/>&nbsp;<\/p>\n<p>Following are examples of research questions that procedures in this module can address:<\/p>\n<p><strong>Goodness-of-Fit Test: <\/strong>Test a claim about the distribution of a categorical variable in a population.<\/p>\n<ul>\n<li>During the presidential election of 2008, the Pew Research Center collected survey data that suggested that 24% of registered voters were liberal, 38% were moderate, and 38% were conservative. Is the distribution of political views different this year?<\/li>\n<li>The distribution of blood types for whites in the United States is 45% type O, 41% type A, 10% type B, and 4% type AB. Is the distribution of blood types different for Asian Americans?<\/li>\n<\/ul>\n<p><strong>Test of Independence: <\/strong>Test a claim about the relationship between two categorical variables in a population.<\/p>\n<ul>\n<li>For young adults in the United States, is gender related to body image?<\/li>\n<li>Is alcohol abuse by New York firefighters dependent on participation in the 9\/11 rescue operation?<\/li>\n<li>In the United States, is race associated with political views (conservative, moderate, liberal)?<\/li>\n<\/ul>\n<p><strong>Test of Homogeneity: <\/strong>Test a claim about the distribution of a categorical variable in several populations.<\/p>\n<ul>\n<li>Does the use of steroids in collegiate athletics differ across the three NCAA divisions?<\/li>\n<li>Was the distribution of political views (liberal, moderate, conservative) different for the last three presidential elections in the United States?<\/li>\n<\/ul>\n<p>&nbsp;<\/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-572\">\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":"7e1615b3-4e1f-42a1-9c14-884dfc0ad181","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-572","chapter","type-chapter","status-web-only","hentry"],"part":570,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/chapters\/572","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/chapters\/572\/revisions"}],"predecessor-version":[{"id":1513,"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/chapters\/572\/revisions\/1513"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/parts\/570"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/chapters\/572\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/wp\/v2\/media?parent=572"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/pressbooks\/v2\/chapter-type?post=572"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/wp\/v2\/contributor?post=572"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-herkimer-statisticssocsci\/wp-json\/wp\/v2\/license?post=572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}