{"id":233,"date":"2022-02-18T23:35:52","date_gmt":"2022-02-18T23:35:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=233"},"modified":"2022-03-29T22:06:17","modified_gmt":"2022-03-29T22:06:17","slug":"applications-of-bar-graphs-what-to-know","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/applications-of-bar-graphs-what-to-know\/","title":{"raw":"Applications of Bar Graphs: What to Know","rendered":"Applications of Bar Graphs: What to Know"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\nAfter completing this section, you should feel comfortable performing these skills.\r\n<ul>\r\n \t<li><a href=\"#Contingency Tables\">Read and interpret a two-way table.<\/a><\/li>\r\n \t<li><a href=\"#Side by Side Bar Graphs\">Make comparisons of different groups using side-by-side bar graphs.<\/a><\/li>\r\n \t<li><a href=\"#Stacked Bar Graphs\">Make comparisons of different groups using stacked bar graphs.<\/a><\/li>\r\n \t<li><a href=\"#DiffInGraphs\">Identify the differences between side-by-side and stacked bar graphs.<\/a><\/li>\r\n \t<li style=\"list-style-type: none;\"><\/li>\r\n<\/ul>\r\nClick on a skill above to jump to its location in this section.\r\n\r\n<\/div>\r\n<img class=\"alignnone wp-image-1720 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/20223832\/Screen-Shot-2022-01-20-at-5.37.07-PM-300x123.png\" alt=\"A generic contingency (or two-way) table between &quot;Snack of Choice&quot; (Pretzels, Skittles, Cookies, M&amp;Ms, Twizzlers) and &quot;Board Game of Choice&quot; (Monopoly, Clue, Life, Scrabble). \" width=\"300\" height=\"123\" \/>\u00a0 \u00a0 \u00a0<img class=\"alignnone wp-image-1743 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/21203826\/Screen-Shot-2022-01-21-at-3.37.51-PM-300x156.png\" alt=\"A generic stacked bar graph between &quot;Hours Studied&quot; (0-7 in increments of 1) and &quot;Course&quot; (Math, Science, History, English).\" width=\"300\" height=\"156\" \/>\u00a0 \u00a0 \u00a0<img class=\"alignnone wp-image-1745 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/21205442\/Screen-Shot-2022-01-21-at-3.54.28-PM-300x158.png\" alt=\"A generic side-by-side bar graph of &quot;Handedness&quot; (Left or right) amongst Faculty and students, and &quot;Frequency (Count)&quot; from 0-100 in increments of 10.\" width=\"300\" height=\"158\" \/>\r\n\r\nIn the upcoming activity, you will need a basic understanding of how contingency tables, stacked bar charts, and side-by-side bar charts are used to describe and analyze data on a single categorical variable for multiple populations or groups. To develop this understanding, let's begin by recalling how we use\u00a0 a more familiar graphical display (a pie chart) to represent a categorical variable for a single population by analyzing percentages of votes cast for presidential candidates.\r\n<h2>Visualizing a Categorical Variable for One Population<\/h2>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nWhich types of displays are appropriate for a categorical variable?\r\n\r\nCore skill:\r\n[reveal-answer q=\"542863\"]Understand what graphs or charts are used to visualize categorical variables[\/reveal-answer]\r\n[hidden-answer a=\"542863\"]\r\n\r\nWe can use pie charts or bar charts to display a categorical variable for a single population.\r\n\r\nWe'll see in this lesson that stacked and side-by-side bar charts are used to display a categorical variable across several groups or populations.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nRecall the techniques you used in <em>What to Know About Displaying Categorical Data: 3A <\/em>to read and interpret the\u00a0following chart, which describes how people in America voted in the 2016 presidential election.[footnote]Bump, P. (2016, November 16). <em>A lot of nonvoters are mad at the election results. If only there were something they could have done<\/em>. The Washington Post. https:\/\/www.washingtonpost.com\/news\/the-fix\/wp\/2016\/11\/16\/a-lot-of-non-voters-are-mad-at-the-election-results-if-only-there-was-something-they-could-have-done\/[\/footnote] Take a moment to familiarize yourself with the chart, then answer Questions 1 - 3 below.\r\n\r\n<img class=\"alignnone wp-image-328 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/27235008\/Temp_Image_PieChart.jpg\" alt=\"A pie chart of How America participated in the election. Data from U.S. Election Project, Dave Wasserman, Census Bureau. The &quot;Ineligible to vote&quot; section is 28.6%, the &quot;Didn't vote&quot; section is 29.9%, the &quot;Voted Trump&quot; section is 19.5%, the &quot;Voted Clinton&quot; section is 19.8%, and the &quot;Voted other&quot; section is 2.2%.\" width=\"413\" height=\"331\" \/>\r\n\r\na)\u00a0 According to the chart above, what percentage of people living in the United States did not participate in the 2016 presidential election?\r\n\r\n[reveal-answer q=\"667191\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"667191\"]The total non-participants include the [latex]29.9[\/latex]% who didn't vote together with the [latex]28.6[\/latex]% who were ineligible to vote, or [latex]58.5[\/latex]% total. [\/hidden-answer]\r\n\r\n<hr \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">b)\u00a0We can see from the chart that more people did not participate than those who did. A large percentage of those were deemed \"ineligible to vote.\"\u00a0<\/span>\r\n\r\nUse the Internet to find out what it means to be \u201cineligible to vote\u201d in a U.S. presidential election. Select all groups from the list below that can be deemed \u201cineligible\u201d within the United States.\r\n<ol>\r\n \t<li><span style=\"color: #000000;\">American adults living in Puerto Rico<\/span><\/li>\r\n \t<li><span style=\"color: #000000;\">American adults living in Guam<\/span><\/li>\r\n \t<li><span style=\"color: #000000;\">American adults who at one time were convicted of felony crimes<\/span><\/li>\r\n \t<li><span style=\"color: #000000;\">Americans under the age of 18<\/span><\/li>\r\n \t<li><span style=\"color: #000000;\">American adults who are deemed mentally incapacitated<\/span><\/li>\r\n \t<li><span style=\"color: #000000;\">Non-citizens and Dreamers (people living in the United States under DACA)<\/span><\/li>\r\n \t<li><span style=\"color: #000000;\"><span style=\"color: #000000;\">All of the above<\/span><\/span><\/li>\r\n<\/ol>\r\n[reveal-answer q=\"686053\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"686053\"]Use a reputable site such as one whose URL ends in .edu or .gov, like <a href=\"https:\/\/www.usa.gov\/who-can-vote\">usa.gov\/who-can-vote<\/a>[\/hidden-answer]\r\n\r\n<hr \/>\r\n\r\n&nbsp;\r\n\r\nc) The\u00a0 variable of interest shown in the chart could be defined as \"Voter Choice,\" with five possible values:\r\n<p style=\"text-align: center;\">Clinton, Trump, Other, Ineligible to vote, and Chose not to vote.<\/p>\r\nWhat is the best description of the population(s) of interest? There is only one correct answer.\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>\r\n \t<li>Three populations of interest: Republicans, Democrats, and Other<\/li>\r\n \t<li>Fifty populations of interest: One for every state that makes up our electoral college<\/li>\r\n \t<li>One population of interest: All people living in the United States<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"969370\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"969370\"]What do <em>you<\/em> think? Does this pie chart illustrate more than one population of interest?[\/hidden-answer]\r\n\r\n<\/div>\r\nWe've seen that a pie chart is a good visual representation of a categorical variable (Voter Choice) from a single population or group (people living in the United States). But what can we do if we want to compare a categorical variable across multiple groups?\r\n\r\nLet's use the variable<em>\u00a0<\/em>from the data above, but instead of grouping all Americans together as a single population of interest, we'll focus on just the voters in a presidential election.\r\n<h2>Displaying a Categorical Variable Across Multiple Populations or Groups<\/h2>\r\nIn this example, we'll explore how to display and interpret changes in a categorical variable of interest (Voter Choice) when comparing multiple populations or groups of interest (Black, White, Latinx, Asian, and Other). We will then convert tables of data called <strong>contingency tables<\/strong> (or two-way tables) into <strong>stacked bar charts<\/strong> and <strong>side-by-side bar charts<\/strong> and make comparisons.\r\n\r\nThe 2016 presidential race was very different from the one in 2020. In 2016, fewer people turned out to vote,[footnote]Schaul, K., Rabinowitz, K., &amp; Mellnik, T. (2020, December 28). <em>2020 turnout is the highest in over a century<\/em>. The Washington Post. <a href=\"https:\/\/www.washingtonpost.com\/graphics\/2020\/elections\/voter-turnout\/\">https:\/\/www.washingtonpost.com\/graphics\/2020\/elections\/voter-turnout\/<\/a>[\/footnote] more people were deemed ineligible ([latex]6[\/latex] million felons in 2016[footnote]Uggen, C., Larson, R., &amp; Shannon, S. (2016, October 16). <em>6 million lost voters: State-level estimates of felony disenfranchisement, 2016<\/em>. The Sentencing Project. <a href=\"https:\/\/www.sentencingproject.org\/publications\/6-million-lost-voters-state-level-estimates-felony-disenfranchisement-2016\/\">https:\/\/www.sentencingproject.org\/publications\/6-million-lost-voters-state-level-estimates-felony-disenfranchisement-2016\/<\/a>[\/footnote] compared to [latex]5.1[\/latex] million felons in 2020),[footnote]Maxouris, C. (2020, October 15). <em>More than 5 million people with felony convictions can\u2019t vote in this year\u2019s election, advocacy group finds<\/em>. CNN. <a href=\"https:\/\/www.cnn.com\/2020\/10\/15\/us\/felony-convictions-voting-sentencing-project-study\/index.html\">https:\/\/www.cnn.com\/2020\/10\/15\/us\/felony-convictions-voting-sentencing-project-study\/index.html<\/a>[\/footnote]\u00a0and the election results were much closer. In 2016, Hillary Clinton won the popular vote, and fewer than [latex]80,000[\/latex] votes out of [latex]137[\/latex] million votes cast determined the outcome of Donald Trump being selected as our president.[footnote]<em>Why voting matters: Supreme Court edition<\/em>. (2018, June 28). Axios. Retrieved from <a href=\"https:\/\/www.axios.com\/hillary-clinton-2016-election-votes-supreme-court-liberal-justice-1b4bc4fc-9fad-44b4-ab54-9ef86aa9c1f1.html\">https:\/\/www.axios.com\/hillary-clinton-2016-election-votes-supreme-court-liberal-justice-1b4bc4fc-9fad-44b4-ab54-9ef86aa9c1f1.html<\/a>[\/footnote]\r\n\r\nLooking to our future, one question might be \u201cIf we increase legitimate voter participation, will one party benefit?\u201d We can better answer this question if we study the voting patterns of different groups within the United States.\r\n<h3 id=\"Contingency Tables\">Contingency Tables (Two-Way Tables)<\/h3>\r\nCNN used an exit poll to estimate the presidential 2020 voting patterns by race.[footnote]<em>Exit polls<\/em>. (2020). CNN Politics. Retrieved from <a href=\"https:\/\/www.cnn.com\/election\/2020\/exit-polls\/president\/national-results\">https:\/\/www.cnn.com\/election\/2020\/exit-polls\/president\/national-results<\/a>[\/footnote] The following is a table of the results, where the rows describe the different groups of people of interest (White, Black, Latinx, Asian, and Other) and the columns represent the vote choices (Biden, Trump, or Other).\r\n<div class=\"textbox tryit\">\r\n<h3>reading a contingency table<\/h3>\r\n<span style=\"background-color: #99cc00;\"><strong>[Worked Example Video \u2014 a 3-instructors video illustrating the how to read a contingency table (how to see a single categorical variable measured on different sub-groups of a larger population -- and how the data in the table is distributed into stacked and side-by-side bar charts]<\/strong><\/span>\r\n\r\n<\/div>\r\n<table style=\"border-collapse: collapse; width: 100%; height: 84px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 927.396px; text-align: center;\" colspan=\"4\"><strong>Presidential 2020 Voting Patterns by Race<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Biden<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Trump<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>White<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]58[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Black<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]87[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Latinx<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]65[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]32[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Asian<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]61[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]34[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]55[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAmong Asians, for example, [latex]61[\/latex]% voted for Biden, [latex]34[\/latex]% voted for Trump, and the remaining [latex]5[\/latex]% voted for someone else.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]240985[\/ohm_question]\r\n\r\n[reveal-answer q=\"330970\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"330970\"]What category is represented in the first column? What category is represented in the first row?[\/hidden-answer]\r\n\r\n<\/div>\r\nBecause this table displays the results of two categorical variables simultaneously, it is called a two-way table. It is also called a <strong>contingency table<\/strong>. The advantage of a contingency table is you can see each precise percentage of responses (or count of responses). A disadvantage is that the table does not present a strong visual comparison between the groups. Distributing the data from a contingency table into a stacked bar chart or side-by-side bar chart can help\u00a0 us visually compare the groups.\r\n<h3 id=\"Side by Side Bar Graphs\">Side-by-side Bar Graphs<\/h3>\r\nSide-by-side bar graphs present data for two categorical variables from more than one group by creating two bars on the chart for each group -- one bar for each variable. See the interactive example below for a demonstration.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSay a sample of the members of four student organizations at your college were asked whether they preferred chocolate ice cream or vanilla. Here is a contingency table containing a summary of their responses.\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Student Organization<\/td>\r\n<td style=\"width: 33.3333%;\">Chocolate<\/td>\r\n<td style=\"width: 33.3333%;\">Vanilla<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">A<\/td>\r\n<td style=\"width: 33.3333%;\">23<\/td>\r\n<td style=\"width: 33.3333%;\">12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">B<\/td>\r\n<td style=\"width: 33.3333%;\">13<\/td>\r\n<td style=\"width: 33.3333%;\">15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">C<\/td>\r\n<td style=\"width: 33.3333%;\">9<\/td>\r\n<td style=\"width: 33.3333%;\">21<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">D<\/td>\r\n<td style=\"width: 33.3333%;\">17<\/td>\r\n<td style=\"width: 33.3333%;\">14<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\nThe side-by-side bar chart below contains the same data as the two-way table above. Each of the four groups are represented along the horizontal axis with two vertical bars indicating the frequency of their responses, one for chocolate preference and one for vanilla. The key to the right of the chart identifies which bar is which by color.\r\n\r\n<img class=\"aligncenter size-full wp-image-978\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10152250\/OrgIceCreamPref_Sidebyside.png\" alt=\"A graph displays two vertical bars labeled chocolate and vanilla over the horizontal axis labeled with the groups A, B, C, D. The chocolate bar for A rises above 20 and vanilla bar raises above 10. The chocolate bar for B raises above 10 and the vanilla bar raises to 15. The chocolate bar for group C raises just below 10 and the vanilla bar raises above 20. The chocolate bar for group D raises above 15 and the vanilla bar raises just below 15. \" width=\"735\" height=\"360\" \/>\r\n<ol>\r\n \t<li>Which organization shows a clear preference for chocolate?<\/li>\r\n \t<li>Which organization shows a clear preference for vanilla?<\/li>\r\n \t<li>Which display, the table or the chart, is easier for understanding precise counts for each variable? Which gives a strong visual comparison between the groups?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"960984\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"960984\"]\r\n<ol>\r\n \t<li>Organization A<\/li>\r\n \t<li>Organization C<\/li>\r\n \t<li>The two-way table provides exact counts while the side-by-side barchart gives a strong visual comparison.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nSee the video below for a perspective on reading a side-by-side bar graph.\r\n<div class=\"textbox tryit\">\r\n<h3>Reading a side-by-side Bar Graph<\/h3>\r\n<span style=\"background-color: #ffff00;\">[We can insert another short video demonstration of how to read this graph.]--&gt; this video would be great from 1:38-2:10<\/span>\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=5Sbov4QY26c[\/embed]\r\n\r\n<\/div>\r\nNow let's turn back to the table of voting patterns we looked at above and compare it to a side-by-side graph containing the same information.\u00a0 [reveal-answer q=\"848144\"]Presidential 2020 Voting Patterns by Race[\/reveal-answer]\r\n[hidden-answer a=\"848144\"]\r\n<table style=\"border-collapse: collapse; width: 100%; height: 84px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 927.396px; text-align: center;\" colspan=\"4\"><strong>Presidential 2020 Voting Patterns by Race<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Biden<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Trump<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>White<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]58[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Black<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]87[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Latinx<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]65[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]32[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Asian<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]61[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]34[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]55[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\r\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\nFor Questions 2\u20135, refer to the standard<strong> side-by-side bar chart<\/strong>\u00a0below, which contains the exact same information about 2020 voting patterns as the two-way table above.\r\n\r\n<img class=\"alignnone wp-image-1442 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17214333\/3B-3.png\" alt=\"A side-by-side bar chart of How America Voted in 2020 estimated using a CNN exit poll. On the right is a legend titled &quot;Vote&quot; that shows Blue indicates Biden, red indicates Trump, and yellow indicates other. The vertical axis of the graph is labeled &quot;Percent (%)&quot; and the horizontal axis is labeled &quot;Race.&quot; For the white group, the blue bar reaches to approximately 40%, the red bar reaches almost to 60%, and the yellow bar is slightly above zero. For the black group, the blue bar reaches above 80, the red bar reached about two thirds of the way to 20%, and the yellow bar is slightly above zero. For the Latinx group, the blue bar reaches slightly above 60%, the red bar reaches to approximately halfway between 20% and 40%, and the yellow line reaches about one fifth of the way to 20%. For the Asian group, the blue bar reaches to approximately 60%, the red line reaches to approximately two thirds of the way between 20% and 40%, and the yellow line reaches about one third of the way to 20%. For the Other group, the blue bar reaches almost to 60%, the red bar reaches approximately to 40%, and the yellow bar reaches approximately one fourth of the way to 20%.e bar chart is titled &quot;How America Voted in 2020 (Estimated using a CNN exit poll)&quot;. The x-axis is labeled &quot;Race&quot; and includes White, Black, Latinx, Asian, and Other. The y-axis is labeled &quot;Percent&quot; and includes 0-80 in increments of 20. The bars display as follows: White (40% Biden, 59% Trump, 1% Other), Black (83% Biden, 16% Trump, 1% Other), Latinx (63% Biden, 33% Trump, 4% Other), Asian (60% Biden, 33% Trump, 7% Other), and Other (56% Biden, 40% Trump, 4% Other).\" width=\"1024\" height=\"388\" \/>The groups of interest are listed on the horizontal axis (Whites, Blacks, Latinx, Asian, and Other) and the percentages associated with each voter choice are on the vertical axis. <strong>Note<\/strong>: within each group, the heights of the three bars sum to total [latex]100[\/latex], representing [latex]100[\/latex]% of all responses within that group. Also, since this side-by-side bar chart chose to represent percentages within groups (as opposed to the numbers of actual ballots cast within groups), you cannot make conclusions about counts of votes; rather, you can make conclusions about relative proportions or percentages within each group.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]240636[\/ohm_question]\r\n\r\n[reveal-answer q=\"336616\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"336616\"]The percentage of Biden voters is represented by the blue bars. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]240638[\/ohm_question]\r\n\r\n[reveal-answer q=\"805085\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"805085\"]The percentage of Trump voters is represented by the red bars.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240639[\/ohm_question]\r\n\r\n[reveal-answer q=\"338413\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"338413\"]Compare the heights of all [latex]3[\/latex] bars for each group.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240802[\/ohm_question]\r\n\r\n[reveal-answer q=\"746419\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"746419\"]Compare the heights of the red bars.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"Stacked Bar Graphs\">Stacked Bar Graphs<\/h3>\r\n<span style=\"background-color: #ffff00;\">At this point, students will be presented with two datasets. They will be able to choose which one they would like to use to answer example questions.<\/span>\r\n\r\nStacked bar graphs display the same type of data as a contingency table (two-way table) and a side-by-side bar graph. This type of chart offers a different perspective of a visual comparison between the groups. See the interactive example below for a demonstration.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nRecall the\u00a0contingency table containing a summary of responses collected from members of four student organizations\r\n\r\nSay a sample of the members of four student organizations at your college were asked whether they preferred chocolate ice cream or vanilla. Here is a contingency table containing a summary of their responses.\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Student Organization<\/td>\r\n<td style=\"width: 33.3333%;\">Chocolate<\/td>\r\n<td style=\"width: 33.3333%;\">Vanilla<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">A<\/td>\r\n<td style=\"width: 33.3333%;\">23<\/td>\r\n<td style=\"width: 33.3333%;\">12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">B<\/td>\r\n<td style=\"width: 33.3333%;\">13<\/td>\r\n<td style=\"width: 33.3333%;\">15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">C<\/td>\r\n<td style=\"width: 33.3333%;\">9<\/td>\r\n<td style=\"width: 33.3333%;\">21<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">D<\/td>\r\n<td style=\"width: 33.3333%;\">17<\/td>\r\n<td style=\"width: 33.3333%;\">14<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"aligncenter size-full wp-image-982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10154708\/OrgIceCreamPref_Stacked.png\" alt=\"Four bars, each labeled A, B, C, or D are arranged along a horizontal axis. Each bar contains two shades, one for chocolate and one for vanilla. The vertical axis is labeled &quot;Count.&quot; The bar above A contains the chocolate shading from the bottom to a point above 20, then the vanilla shading to a point above 30. The bar labeled B contains chocolate shading to a point above 10 and vanilla shading from that point to just beneath 30. The bar labeled C contains chocolate shading to a point just below 10 and vanilla shading form that point to just above 30. The bar labeled D contains chocolate shading to a point at approximately 15 and vanilla shading from that point to just above 30.\" width=\"735\" height=\"360\" \/>\r\n<ol>\r\n \t<li>True or false: the stacked bar chart shows that more students in organization C preferred chocolate than students in organization A.<\/li>\r\n \t<li>Which organization does the graph indicate has the greatest preference for chocolate ice cream?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"134160\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"134160\"]\r\n<ol>\r\n \t<li>False<\/li>\r\n \t<li>Organization A<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox tryit\">\r\n<h3>Reading a stacked Bar Graph<\/h3>\r\n<span style=\"background-color: #ffff00;\">[We can insert another short video demonstration of how to read this chart.]--&gt; this video is pretty cool from 0:18-2:14<\/span>\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=21-cIdGhbn0[\/embed]\r\n\r\n<\/div>\r\nFor Questions 6 and 7, consider the following standard <strong>stacked bar chart<\/strong> showing the exact same information as the previous table and <strong>side-by-side bar chart<\/strong>.\r\n\r\n<img class=\"alignnone wp-image-1443 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17214523\/3B-4.png\" alt=\"A stacked bar chart of How America Voted in 2020 estimated using a CNN exit poll. The vertical axis is labeled &quot;Percent (%)&quot; and the horizontal axis is labeled &quot;Race.&quot; There is a legend on the right side labeled &quot;Vote&quot; showing that yellow indicates &quot;Other,&quot; red indicates &quot;Trump,&quot; and blue indicates &quot;Biden.&quot; For the White group, the blue section of the bar extends approximately to 40%, the red section extends from there nearly to 100%, and the yellow section extends the rest of the way to 100%. For the Black group, the blur bar extends to approximately two thirds of the way between 80% and 100%, the red section extends nearly to 100%, and the yellow section extends the rest of the way to 100%. For the Latinx group, the blue section extends to approximately one quarter of the way between 60% and 80%, the red section extends from there to approximately four fifths of the way between 80% and 100%, and the yellow section extends the rest of the way to 100%. For the Asian group, the blue bar extends to approximately 60%, the red section extends from there to about two thirds of the way between 80% and 100%, and the yellow section extends the rest of the way to 100%. For the Other group, the blue section extends to approximately two thirds of the way between 40% and 60%, the red section extends from there to approximately three quarters of the way between 80% and 100%, and they yellow section extends the rest of the way to 100%.\" width=\"1024\" height=\"376\" \/>\r\n\r\nIn this stacked bar chart, each bar represents the responses of one group. The height of each color within that bar represents a percentage of a particular response, and the combination of all colors represents the total ([latex]100[\/latex]%) of all responses within that group.\u00a0 Like the side-by-side bar chart where percentage is plotted along the vertical axis, you cannot make conclusions or comparisons regarding the absolute counts of responses within or between groups.\r\n\r\nNote: A single stacked bar chart is very similar to a pie chart, but it uses rectangular regions rather than pie slices to represent each category.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240641[\/ohm_question]\r\n\r\n[reveal-answer q=\"984566\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"984566\"]The green regions represent votes cast for a candidate other than Trump or Biden.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240642[\/ohm_question]\r\n\r\n[reveal-answer q=\"446266\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"446266\"]First locate the bars associated with these groups, then compare the blue regions.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"DiffInGraphs\">When to use Side-by-Side vs. Stacked Bar Graphs<\/h3>\r\nNote the difference between a side-by-side bar graph and a stacked bar graph displaying the same information. Each is useful to display a categorical variable across multiple groups. They only differ depending upon the perspective of the information you wish to present.\u00a0 A side-by-side bar graph is similar to a bar graph. If you felt a bar graph would best display your data, but you don't want to use separate bar graphs (one for each group), then use a side-by-side bar graph to combine the two-way data into a single graph. If you felt a pie chart would best display your data, but didn't want to use separate pie charts for each group, you could use a stacked bar graph to combine all three groups into one graph.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA sample of members from four student organizations where asked whether they prefer chocolate or vanilla ice cream.\r\n\r\nTheir responses are shown below in both a side-by-side barchart and a stacked barchart.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-978\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10152250\/OrgIceCreamPref_Sidebyside.png\" alt=\"A graph displays two vertical bars labeled chocolate and vanilla over the horizontal axis labeled with the groups A, B, C, D. The chocolate bar for A rises above 20 and vanilla bar raises above 10. The chocolate bar for B raises above 10 and the vanilla bar raises to 15. The chocolate bar for group C raises just below 10 and the vanilla bar raises above 20. The chocolate bar for group D raises above 15 and the vanilla bar raises just below 15.\" width=\"735\" height=\"360\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10154708\/OrgIceCreamPref_Stacked.png\" alt=\"Four bars, each labeled A, B, C, or D are arranged along a horizontal axis. Each bar contains two shades, one for chocolate and one for vanilla. The vertical axis is labeled &quot;Count.&quot; The bar above A contains the chocolate shading from the bottom to a point above 20, then the vanilla shading to a point above 30. The bar labeled B contains chocolate shading to a point above 10 and vanilla shading from that point to just beneath 30. The bar labeled C contains chocolate shading to a point just below 10 and vanilla shading form that point to just above 30. The bar labeled D contains chocolate shading to a point at approximately 15 and vanilla shading from that point to just above 30.\" width=\"735\" height=\"360\" \/>\r\n<ol>\r\n \t<li>Which type of graph is more like a set of pie charts?<\/li>\r\n \t<li>Which type of graph allows you to represent a collection of bar graphs all in the same display?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"25896\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"25896\"]\r\n<ol>\r\n \t<li>Stacked barchart<\/li>\r\n \t<li>Side-by-side barchart<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>stacked versus side-by-side bar chart<\/h3>\r\n<span style=\"background-color: #99cc00;\">[Perspective video -- a 3-instructor video showing how to think which kind of display to use for which situation (advantages and disadvantages): stacked vs side-by-side bar chart.]<\/span>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\n[ohm_question hide_question_numbers=1]240804[\/ohm_question]\r\n\r\n[reveal-answer q=\"852443\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"852443\"]Which is more similar to a bar graph: a side-by-side graph or a stacked bar graph?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]240806[\/ohm_question]\r\n\r\n[reveal-answer q=\"943155\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"943155\"]Which is more similar to a pie chart: a side-by-side graph or a stacked bar graph?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Summary<\/h2>\r\nIn this section, you've seen representations of voter patterns by race in the 2020 presidential election. In the following Forming Connections activity, we'll explore the possibility of making predictions about how future election outcomes by asking a research question about racial composition in the United States. Let's summarize all the skills and tasks you've applied so far before you dive into the next activity.\r\n<ul>\r\n \t<li>In Questions 1 - 3, you read and interpreted information from a pie chart.<\/li>\r\n \t<li>in Question 4, you read and interpreted information from a two-way (contingency) table.<\/li>\r\n \t<li>In Questions 5 - 8, you read and interpreted a side-by-side bar chart.<\/li>\r\n \t<li>In Questions 9 - 10, you read and interpreted a stacked bar chart.<\/li>\r\n \t<li>In Questions 11 - 12, you explained the differences between side-by-side charts and stacked bar charts.<\/li>\r\n<\/ul>\r\nPie charts are good tools for visualizing a single categorical variable for multiple populations or groups. When we want to display and interpret changes in a categorical variable of interest while comparing multiple populations or groups, we can organize the data into a contingency table (two-way table), which we can then convert into\u00a0side-by-side bar charts or stacked bar charts. These kinds of charts provide a stronger visual comparison between the groups than the two-way table does.\r\n\r\nIf you feel comfortable with these ideas, it's time to move on to Forming Connections in the next activity!","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<p>After completing this section, you should feel comfortable performing these skills.<\/p>\n<ul>\n<li><a href=\"#Contingency Tables\">Read and interpret a two-way table.<\/a><\/li>\n<li><a href=\"#Side by Side Bar Graphs\">Make comparisons of different groups using side-by-side bar graphs.<\/a><\/li>\n<li><a href=\"#Stacked Bar Graphs\">Make comparisons of different groups using stacked bar graphs.<\/a><\/li>\n<li><a href=\"#DiffInGraphs\">Identify the differences between side-by-side and stacked bar graphs.<\/a><\/li>\n<li style=\"list-style-type: none;\"><\/li>\n<\/ul>\n<p>Click on a skill above to jump to its location in this section.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1720 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/20223832\/Screen-Shot-2022-01-20-at-5.37.07-PM-300x123.png\" alt=\"A generic contingency (or two-way) table between &quot;Snack of Choice&quot; (Pretzels, Skittles, Cookies, M&amp;Ms, Twizzlers) and &quot;Board Game of Choice&quot; (Monopoly, Clue, Life, Scrabble).\" width=\"300\" height=\"123\" \/>\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1743 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/21203826\/Screen-Shot-2022-01-21-at-3.37.51-PM-300x156.png\" alt=\"A generic stacked bar graph between &quot;Hours Studied&quot; (0-7 in increments of 1) and &quot;Course&quot; (Math, Science, History, English).\" width=\"300\" height=\"156\" \/>\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1745 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/21205442\/Screen-Shot-2022-01-21-at-3.54.28-PM-300x158.png\" alt=\"A generic side-by-side bar graph of &quot;Handedness&quot; (Left or right) amongst Faculty and students, and &quot;Frequency (Count)&quot; from 0-100 in increments of 10.\" width=\"300\" height=\"158\" \/><\/p>\n<p>In the upcoming activity, you will need a basic understanding of how contingency tables, stacked bar charts, and side-by-side bar charts are used to describe and analyze data on a single categorical variable for multiple populations or groups. To develop this understanding, let&#8217;s begin by recalling how we use\u00a0 a more familiar graphical display (a pie chart) to represent a categorical variable for a single population by analyzing percentages of votes cast for presidential candidates.<\/p>\n<h2>Visualizing a Categorical Variable for One Population<\/h2>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>Which types of displays are appropriate for a categorical variable?<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q542863\">Understand what graphs or charts are used to visualize categorical variables<\/span><\/p>\n<div id=\"q542863\" class=\"hidden-answer\" style=\"display: none\">\n<p>We can use pie charts or bar charts to display a categorical variable for a single population.<\/p>\n<p>We&#8217;ll see in this lesson that stacked and side-by-side bar charts are used to display a categorical variable across several groups or populations.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Recall the techniques you used in <em>What to Know About Displaying Categorical Data: 3A <\/em>to read and interpret the\u00a0following chart, which describes how people in America voted in the 2016 presidential election.<a class=\"footnote\" title=\"Bump, P. (2016, November 16). A lot of nonvoters are mad at the election results. If only there were something they could have done. The Washington Post. https:\/\/www.washingtonpost.com\/news\/the-fix\/wp\/2016\/11\/16\/a-lot-of-non-voters-are-mad-at-the-election-results-if-only-there-was-something-they-could-have-done\/\" id=\"return-footnote-233-1\" href=\"#footnote-233-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Take a moment to familiarize yourself with the chart, then answer Questions 1 &#8211; 3 below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-328 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/27235008\/Temp_Image_PieChart.jpg\" alt=\"A pie chart of How America participated in the election. Data from U.S. Election Project, Dave Wasserman, Census Bureau. The &quot;Ineligible to vote&quot; section is 28.6%, the &quot;Didn't vote&quot; section is 29.9%, the &quot;Voted Trump&quot; section is 19.5%, the &quot;Voted Clinton&quot; section is 19.8%, and the &quot;Voted other&quot; section is 2.2%.\" width=\"413\" height=\"331\" \/><\/p>\n<p>a)\u00a0 According to the chart above, what percentage of people living in the United States did not participate in the 2016 presidential election?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q667191\">Show Solution<\/span><\/p>\n<div id=\"q667191\" class=\"hidden-answer\" style=\"display: none\">The total non-participants include the [latex]29.9[\/latex]% who didn&#8217;t vote together with the [latex]28.6[\/latex]% who were ineligible to vote, or [latex]58.5[\/latex]% total. <\/div>\n<\/div>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">b)\u00a0We can see from the chart that more people did not participate than those who did. A large percentage of those were deemed &#8220;ineligible to vote.&#8221;\u00a0<\/span><\/p>\n<p>Use the Internet to find out what it means to be \u201cineligible to vote\u201d in a U.S. presidential election. Select all groups from the list below that can be deemed \u201cineligible\u201d within the United States.<\/p>\n<ol>\n<li><span style=\"color: #000000;\">American adults living in Puerto Rico<\/span><\/li>\n<li><span style=\"color: #000000;\">American adults living in Guam<\/span><\/li>\n<li><span style=\"color: #000000;\">American adults who at one time were convicted of felony crimes<\/span><\/li>\n<li><span style=\"color: #000000;\">Americans under the age of 18<\/span><\/li>\n<li><span style=\"color: #000000;\">American adults who are deemed mentally incapacitated<\/span><\/li>\n<li><span style=\"color: #000000;\">Non-citizens and Dreamers (people living in the United States under DACA)<\/span><\/li>\n<li><span style=\"color: #000000;\"><span style=\"color: #000000;\">All of the above<\/span><\/span><\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q686053\">Hint<\/span><\/p>\n<div id=\"q686053\" class=\"hidden-answer\" style=\"display: none\">Use a reputable site such as one whose URL ends in .edu or .gov, like <a href=\"https:\/\/www.usa.gov\/who-can-vote\">usa.gov\/who-can-vote<\/a><\/div>\n<\/div>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>c) The\u00a0 variable of interest shown in the chart could be defined as &#8220;Voter Choice,&#8221; with five possible values:<\/p>\n<p style=\"text-align: center;\">Clinton, Trump, Other, Ineligible to vote, and Chose not to vote.<\/p>\n<p>What is the best description of the population(s) of interest? There is only one correct answer.<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li>Three populations of interest: Republicans, Democrats, and Other<\/li>\n<li>Fifty populations of interest: One for every state that makes up our electoral college<\/li>\n<li>One population of interest: All people living in the United States<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q969370\">Hint<\/span><\/p>\n<div id=\"q969370\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think? Does this pie chart illustrate more than one population of interest?<\/div>\n<\/div>\n<\/div>\n<p>We&#8217;ve seen that a pie chart is a good visual representation of a categorical variable (Voter Choice) from a single population or group (people living in the United States). But what can we do if we want to compare a categorical variable across multiple groups?<\/p>\n<p>Let&#8217;s use the variable<em>\u00a0<\/em>from the data above, but instead of grouping all Americans together as a single population of interest, we&#8217;ll focus on just the voters in a presidential election.<\/p>\n<h2>Displaying a Categorical Variable Across Multiple Populations or Groups<\/h2>\n<p>In this example, we&#8217;ll explore how to display and interpret changes in a categorical variable of interest (Voter Choice) when comparing multiple populations or groups of interest (Black, White, Latinx, Asian, and Other). We will then convert tables of data called <strong>contingency tables<\/strong> (or two-way tables) into <strong>stacked bar charts<\/strong> and <strong>side-by-side bar charts<\/strong> and make comparisons.<\/p>\n<p>The 2016 presidential race was very different from the one in 2020. In 2016, fewer people turned out to vote,<a class=\"footnote\" title=\"Schaul, K., Rabinowitz, K., &amp; Mellnik, T. (2020, December 28). 2020 turnout is the highest in over a century. The Washington Post. https:\/\/www.washingtonpost.com\/graphics\/2020\/elections\/voter-turnout\/\" id=\"return-footnote-233-2\" href=\"#footnote-233-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> more people were deemed ineligible ([latex]6[\/latex] million felons in 2016<a class=\"footnote\" title=\"Uggen, C., Larson, R., &amp; Shannon, S. (2016, October 16). 6 million lost voters: State-level estimates of felony disenfranchisement, 2016. The Sentencing Project. https:\/\/www.sentencingproject.org\/publications\/6-million-lost-voters-state-level-estimates-felony-disenfranchisement-2016\/\" id=\"return-footnote-233-3\" href=\"#footnote-233-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a> compared to [latex]5.1[\/latex] million felons in 2020),<a class=\"footnote\" title=\"Maxouris, C. (2020, October 15). More than 5 million people with felony convictions can\u2019t vote in this year\u2019s election, advocacy group finds. CNN. https:\/\/www.cnn.com\/2020\/10\/15\/us\/felony-convictions-voting-sentencing-project-study\/index.html\" id=\"return-footnote-233-4\" href=\"#footnote-233-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a>\u00a0and the election results were much closer. In 2016, Hillary Clinton won the popular vote, and fewer than [latex]80,000[\/latex] votes out of [latex]137[\/latex] million votes cast determined the outcome of Donald Trump being selected as our president.<a class=\"footnote\" title=\"Why voting matters: Supreme Court edition. (2018, June 28). Axios. Retrieved from https:\/\/www.axios.com\/hillary-clinton-2016-election-votes-supreme-court-liberal-justice-1b4bc4fc-9fad-44b4-ab54-9ef86aa9c1f1.html\" id=\"return-footnote-233-5\" href=\"#footnote-233-5\" aria-label=\"Footnote 5\"><sup class=\"footnote\">[5]<\/sup><\/a><\/p>\n<p>Looking to our future, one question might be \u201cIf we increase legitimate voter participation, will one party benefit?\u201d We can better answer this question if we study the voting patterns of different groups within the United States.<\/p>\n<h3 id=\"Contingency Tables\">Contingency Tables (Two-Way Tables)<\/h3>\n<p>CNN used an exit poll to estimate the presidential 2020 voting patterns by race.<a class=\"footnote\" title=\"Exit polls. (2020). CNN Politics. Retrieved from https:\/\/www.cnn.com\/election\/2020\/exit-polls\/president\/national-results\" id=\"return-footnote-233-6\" href=\"#footnote-233-6\" aria-label=\"Footnote 6\"><sup class=\"footnote\">[6]<\/sup><\/a> The following is a table of the results, where the rows describe the different groups of people of interest (White, Black, Latinx, Asian, and Other) and the columns represent the vote choices (Biden, Trump, or Other).<\/p>\n<div class=\"textbox tryit\">\n<h3>reading a contingency table<\/h3>\n<p><span style=\"background-color: #99cc00;\"><strong>[Worked Example Video \u2014 a 3-instructors video illustrating the how to read a contingency table (how to see a single categorical variable measured on different sub-groups of a larger population &#8212; and how the data in the table is distributed into stacked and side-by-side bar charts]<\/strong><\/span><\/p>\n<\/div>\n<table style=\"border-collapse: collapse; width: 100%; height: 84px;\">\n<tbody>\n<tr>\n<td style=\"width: 927.396px; text-align: center;\" colspan=\"4\"><strong>Presidential 2020 Voting Patterns by Race<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Biden<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Trump<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>White<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]58[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Black<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]87[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Latinx<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]65[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]32[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]3[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Asian<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]61[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]34[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]55[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Among Asians, for example, [latex]61[\/latex]% voted for Biden, [latex]34[\/latex]% voted for Trump, and the remaining [latex]5[\/latex]% voted for someone else.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240985\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240985&theme=oea&iframe_resize_id=ohm240985\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q330970\">Hint<\/span><\/p>\n<div id=\"q330970\" class=\"hidden-answer\" style=\"display: none\">What category is represented in the first column? What category is represented in the first row?<\/div>\n<\/div>\n<\/div>\n<p>Because this table displays the results of two categorical variables simultaneously, it is called a two-way table. It is also called a <strong>contingency table<\/strong>. The advantage of a contingency table is you can see each precise percentage of responses (or count of responses). A disadvantage is that the table does not present a strong visual comparison between the groups. Distributing the data from a contingency table into a stacked bar chart or side-by-side bar chart can help\u00a0 us visually compare the groups.<\/p>\n<h3 id=\"Side by Side Bar Graphs\">Side-by-side Bar Graphs<\/h3>\n<p>Side-by-side bar graphs present data for two categorical variables from more than one group by creating two bars on the chart for each group &#8212; one bar for each variable. See the interactive example below for a demonstration.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Say a sample of the members of four student organizations at your college were asked whether they preferred chocolate ice cream or vanilla. Here is a contingency table containing a summary of their responses.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">Student Organization<\/td>\n<td style=\"width: 33.3333%;\">Chocolate<\/td>\n<td style=\"width: 33.3333%;\">Vanilla<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">A<\/td>\n<td style=\"width: 33.3333%;\">23<\/td>\n<td style=\"width: 33.3333%;\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">B<\/td>\n<td style=\"width: 33.3333%;\">13<\/td>\n<td style=\"width: 33.3333%;\">15<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">C<\/td>\n<td style=\"width: 33.3333%;\">9<\/td>\n<td style=\"width: 33.3333%;\">21<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">D<\/td>\n<td style=\"width: 33.3333%;\">17<\/td>\n<td style=\"width: 33.3333%;\">14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>The side-by-side bar chart below contains the same data as the two-way table above. Each of the four groups are represented along the horizontal axis with two vertical bars indicating the frequency of their responses, one for chocolate preference and one for vanilla. The key to the right of the chart identifies which bar is which by color.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-978\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10152250\/OrgIceCreamPref_Sidebyside.png\" alt=\"A graph displays two vertical bars labeled chocolate and vanilla over the horizontal axis labeled with the groups A, B, C, D. The chocolate bar for A rises above 20 and vanilla bar raises above 10. The chocolate bar for B raises above 10 and the vanilla bar raises to 15. The chocolate bar for group C raises just below 10 and the vanilla bar raises above 20. The chocolate bar for group D raises above 15 and the vanilla bar raises just below 15.\" width=\"735\" height=\"360\" \/><\/p>\n<ol>\n<li>Which organization shows a clear preference for chocolate?<\/li>\n<li>Which organization shows a clear preference for vanilla?<\/li>\n<li>Which display, the table or the chart, is easier for understanding precise counts for each variable? Which gives a strong visual comparison between the groups?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q960984\">Show Solution<\/span><\/p>\n<div id=\"q960984\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Organization A<\/li>\n<li>Organization C<\/li>\n<li>The two-way table provides exact counts while the side-by-side barchart gives a strong visual comparison.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>See the video below for a perspective on reading a side-by-side bar graph.<\/p>\n<div class=\"textbox tryit\">\n<h3>Reading a side-by-side Bar Graph<\/h3>\n<p><span style=\"background-color: #ffff00;\">[We can insert another short video demonstration of how to read this graph.]&#8211;&gt; this video would be great from 1:38-2:10<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Side by Side Column Graph\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/5Sbov4QY26c?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>Now let&#8217;s turn back to the table of voting patterns we looked at above and compare it to a side-by-side graph containing the same information.\u00a0 <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q848144\">Presidential 2020 Voting Patterns by Race<\/span><\/p>\n<div id=\"q848144\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"border-collapse: collapse; width: 100%; height: 84px;\">\n<tbody>\n<tr>\n<td style=\"width: 927.396px; text-align: center;\" colspan=\"4\"><strong>Presidential 2020 Voting Patterns by Race<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Biden<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Trump<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>White<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]58[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Black<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]87[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]1[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Latinx<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]65[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]32[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]3[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Asian<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]61[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]34[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 222.396px; height: 14px; text-align: center;\"><strong>Other<\/strong><\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]55[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]41[\/latex]<\/td>\n<td style=\"width: 222.396px; height: 14px; text-align: center;\">[latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>For Questions 2\u20135, refer to the standard<strong> side-by-side bar chart<\/strong>\u00a0below, which contains the exact same information about 2020 voting patterns as the two-way table above.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1442 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17214333\/3B-3.png\" alt=\"A side-by-side bar chart of How America Voted in 2020 estimated using a CNN exit poll. On the right is a legend titled &quot;Vote&quot; that shows Blue indicates Biden, red indicates Trump, and yellow indicates other. The vertical axis of the graph is labeled &quot;Percent (%)&quot; and the horizontal axis is labeled &quot;Race.&quot; For the white group, the blue bar reaches to approximately 40%, the red bar reaches almost to 60%, and the yellow bar is slightly above zero. For the black group, the blue bar reaches above 80, the red bar reached about two thirds of the way to 20%, and the yellow bar is slightly above zero. For the Latinx group, the blue bar reaches slightly above 60%, the red bar reaches to approximately halfway between 20% and 40%, and the yellow line reaches about one fifth of the way to 20%. For the Asian group, the blue bar reaches to approximately 60%, the red line reaches to approximately two thirds of the way between 20% and 40%, and the yellow line reaches about one third of the way to 20%. For the Other group, the blue bar reaches almost to 60%, the red bar reaches approximately to 40%, and the yellow bar reaches approximately one fourth of the way to 20%.e bar chart is titled &quot;How America Voted in 2020 (Estimated using a CNN exit poll)&quot;. The x-axis is labeled &quot;Race&quot; and includes White, Black, Latinx, Asian, and Other. The y-axis is labeled &quot;Percent&quot; and includes 0-80 in increments of 20. The bars display as follows: White (40% Biden, 59% Trump, 1% Other), Black (83% Biden, 16% Trump, 1% Other), Latinx (63% Biden, 33% Trump, 4% Other), Asian (60% Biden, 33% Trump, 7% Other), and Other (56% Biden, 40% Trump, 4% Other).\" width=\"1024\" height=\"388\" \/>The groups of interest are listed on the horizontal axis (Whites, Blacks, Latinx, Asian, and Other) and the percentages associated with each voter choice are on the vertical axis. <strong>Note<\/strong>: within each group, the heights of the three bars sum to total [latex]100[\/latex], representing [latex]100[\/latex]% of all responses within that group. Also, since this side-by-side bar chart chose to represent percentages within groups (as opposed to the numbers of actual ballots cast within groups), you cannot make conclusions about counts of votes; rather, you can make conclusions about relative proportions or percentages within each group.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240636\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240636&theme=oea&iframe_resize_id=ohm240636\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q336616\">Hint<\/span><\/p>\n<div id=\"q336616\" class=\"hidden-answer\" style=\"display: none\">The percentage of Biden voters is represented by the blue bars. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240638\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240638&theme=oea&iframe_resize_id=ohm240638\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q805085\">Hint<\/span><\/p>\n<div id=\"q805085\" class=\"hidden-answer\" style=\"display: none\">The percentage of Trump voters is represented by the red bars.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240639\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240639&theme=oea&iframe_resize_id=ohm240639\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q338413\">Hint<\/span><\/p>\n<div id=\"q338413\" class=\"hidden-answer\" style=\"display: none\">Compare the heights of all [latex]3[\/latex] bars for each group.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240802\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240802&theme=oea&iframe_resize_id=ohm240802\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q746419\">Hint<\/span><\/p>\n<div id=\"q746419\" class=\"hidden-answer\" style=\"display: none\">Compare the heights of the red bars.<\/div>\n<\/div>\n<\/div>\n<h3 id=\"Stacked Bar Graphs\">Stacked Bar Graphs<\/h3>\n<p><span style=\"background-color: #ffff00;\">At this point, students will be presented with two datasets. They will be able to choose which one they would like to use to answer example questions.<\/span><\/p>\n<p>Stacked bar graphs display the same type of data as a contingency table (two-way table) and a side-by-side bar graph. This type of chart offers a different perspective of a visual comparison between the groups. See the interactive example below for a demonstration.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Recall the\u00a0contingency table containing a summary of responses collected from members of four student organizations<\/p>\n<p>Say a sample of the members of four student organizations at your college were asked whether they preferred chocolate ice cream or vanilla. Here is a contingency table containing a summary of their responses.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">Student Organization<\/td>\n<td style=\"width: 33.3333%;\">Chocolate<\/td>\n<td style=\"width: 33.3333%;\">Vanilla<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">A<\/td>\n<td style=\"width: 33.3333%;\">23<\/td>\n<td style=\"width: 33.3333%;\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">B<\/td>\n<td style=\"width: 33.3333%;\">13<\/td>\n<td style=\"width: 33.3333%;\">15<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">C<\/td>\n<td style=\"width: 33.3333%;\">9<\/td>\n<td style=\"width: 33.3333%;\">21<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">D<\/td>\n<td style=\"width: 33.3333%;\">17<\/td>\n<td style=\"width: 33.3333%;\">14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10154708\/OrgIceCreamPref_Stacked.png\" alt=\"Four bars, each labeled A, B, C, or D are arranged along a horizontal axis. Each bar contains two shades, one for chocolate and one for vanilla. The vertical axis is labeled &quot;Count.&quot; The bar above A contains the chocolate shading from the bottom to a point above 20, then the vanilla shading to a point above 30. The bar labeled B contains chocolate shading to a point above 10 and vanilla shading from that point to just beneath 30. The bar labeled C contains chocolate shading to a point just below 10 and vanilla shading form that point to just above 30. The bar labeled D contains chocolate shading to a point at approximately 15 and vanilla shading from that point to just above 30.\" width=\"735\" height=\"360\" \/><\/p>\n<ol>\n<li>True or false: the stacked bar chart shows that more students in organization C preferred chocolate than students in organization A.<\/li>\n<li>Which organization does the graph indicate has the greatest preference for chocolate ice cream?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q134160\">Show Solution<\/span><\/p>\n<div id=\"q134160\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>False<\/li>\n<li>Organization A<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox tryit\">\n<h3>Reading a stacked Bar Graph<\/h3>\n<p><span style=\"background-color: #ffff00;\">[We can insert another short video demonstration of how to read this chart.]&#8211;&gt; this video is pretty cool from 0:18-2:14<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Reading Stacked Bar Graphs\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/21-cIdGhbn0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>For Questions 6 and 7, consider the following standard <strong>stacked bar chart<\/strong> showing the exact same information as the previous table and <strong>side-by-side bar chart<\/strong>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1443 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17214523\/3B-4.png\" alt=\"A stacked bar chart of How America Voted in 2020 estimated using a CNN exit poll. The vertical axis is labeled &quot;Percent (%)&quot; and the horizontal axis is labeled &quot;Race.&quot; There is a legend on the right side labeled &quot;Vote&quot; showing that yellow indicates &quot;Other,&quot; red indicates &quot;Trump,&quot; and blue indicates &quot;Biden.&quot; For the White group, the blue section of the bar extends approximately to 40%, the red section extends from there nearly to 100%, and the yellow section extends the rest of the way to 100%. For the Black group, the blur bar extends to approximately two thirds of the way between 80% and 100%, the red section extends nearly to 100%, and the yellow section extends the rest of the way to 100%. For the Latinx group, the blue section extends to approximately one quarter of the way between 60% and 80%, the red section extends from there to approximately four fifths of the way between 80% and 100%, and the yellow section extends the rest of the way to 100%. For the Asian group, the blue bar extends to approximately 60%, the red section extends from there to about two thirds of the way between 80% and 100%, and the yellow section extends the rest of the way to 100%. For the Other group, the blue section extends to approximately two thirds of the way between 40% and 60%, the red section extends from there to approximately three quarters of the way between 80% and 100%, and they yellow section extends the rest of the way to 100%.\" width=\"1024\" height=\"376\" \/><\/p>\n<p>In this stacked bar chart, each bar represents the responses of one group. The height of each color within that bar represents a percentage of a particular response, and the combination of all colors represents the total ([latex]100[\/latex]%) of all responses within that group.\u00a0 Like the side-by-side bar chart where percentage is plotted along the vertical axis, you cannot make conclusions or comparisons regarding the absolute counts of responses within or between groups.<\/p>\n<p>Note: A single stacked bar chart is very similar to a pie chart, but it uses rectangular regions rather than pie slices to represent each category.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240641\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240641&theme=oea&iframe_resize_id=ohm240641\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q984566\">Hint<\/span><\/p>\n<div id=\"q984566\" class=\"hidden-answer\" style=\"display: none\">The green regions represent votes cast for a candidate other than Trump or Biden.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240642\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240642&theme=oea&iframe_resize_id=ohm240642\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q446266\">Hint<\/span><\/p>\n<div id=\"q446266\" class=\"hidden-answer\" style=\"display: none\">First locate the bars associated with these groups, then compare the blue regions.<\/div>\n<\/div>\n<\/div>\n<h3 id=\"DiffInGraphs\">When to use Side-by-Side vs. Stacked Bar Graphs<\/h3>\n<p>Note the difference between a side-by-side bar graph and a stacked bar graph displaying the same information. Each is useful to display a categorical variable across multiple groups. They only differ depending upon the perspective of the information you wish to present.\u00a0 A side-by-side bar graph is similar to a bar graph. If you felt a bar graph would best display your data, but you don&#8217;t want to use separate bar graphs (one for each group), then use a side-by-side bar graph to combine the two-way data into a single graph. If you felt a pie chart would best display your data, but didn&#8217;t want to use separate pie charts for each group, you could use a stacked bar graph to combine all three groups into one graph.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A sample of members from four student organizations where asked whether they prefer chocolate or vanilla ice cream.<\/p>\n<p>Their responses are shown below in both a side-by-side barchart and a stacked barchart.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-978\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10152250\/OrgIceCreamPref_Sidebyside.png\" alt=\"A graph displays two vertical bars labeled chocolate and vanilla over the horizontal axis labeled with the groups A, B, C, D. The chocolate bar for A rises above 20 and vanilla bar raises above 10. The chocolate bar for B raises above 10 and the vanilla bar raises to 15. The chocolate bar for group C raises just below 10 and the vanilla bar raises above 20. The chocolate bar for group D raises above 15 and the vanilla bar raises just below 15.\" width=\"735\" height=\"360\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/10154708\/OrgIceCreamPref_Stacked.png\" alt=\"Four bars, each labeled A, B, C, or D are arranged along a horizontal axis. Each bar contains two shades, one for chocolate and one for vanilla. The vertical axis is labeled &quot;Count.&quot; The bar above A contains the chocolate shading from the bottom to a point above 20, then the vanilla shading to a point above 30. The bar labeled B contains chocolate shading to a point above 10 and vanilla shading from that point to just beneath 30. The bar labeled C contains chocolate shading to a point just below 10 and vanilla shading form that point to just above 30. The bar labeled D contains chocolate shading to a point at approximately 15 and vanilla shading from that point to just above 30.\" width=\"735\" height=\"360\" \/><\/p>\n<ol>\n<li>Which type of graph is more like a set of pie charts?<\/li>\n<li>Which type of graph allows you to represent a collection of bar graphs all in the same display?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q25896\">Show Solution<\/span><\/p>\n<div id=\"q25896\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Stacked barchart<\/li>\n<li>Side-by-side barchart<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>stacked versus side-by-side bar chart<\/h3>\n<p><span style=\"background-color: #99cc00;\">[Perspective video &#8212; a 3-instructor video showing how to think which kind of display to use for which situation (advantages and disadvantages): stacked vs side-by-side bar chart.]<\/span><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240804\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240804&theme=oea&iframe_resize_id=ohm240804\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q852443\">Hint<\/span><\/p>\n<div id=\"q852443\" class=\"hidden-answer\" style=\"display: none\">Which is more similar to a bar graph: a side-by-side graph or a stacked bar graph?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240806\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240806&theme=oea&iframe_resize_id=ohm240806\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q943155\">Hint<\/span><\/p>\n<div id=\"q943155\" class=\"hidden-answer\" style=\"display: none\">Which is more similar to a pie chart: a side-by-side graph or a stacked bar graph?<\/div>\n<\/div>\n<\/div>\n<h2>Summary<\/h2>\n<p>In this section, you&#8217;ve seen representations of voter patterns by race in the 2020 presidential election. In the following Forming Connections activity, we&#8217;ll explore the possibility of making predictions about how future election outcomes by asking a research question about racial composition in the United States. Let&#8217;s summarize all the skills and tasks you&#8217;ve applied so far before you dive into the next activity.<\/p>\n<ul>\n<li>In Questions 1 &#8211; 3, you read and interpreted information from a pie chart.<\/li>\n<li>in Question 4, you read and interpreted information from a two-way (contingency) table.<\/li>\n<li>In Questions 5 &#8211; 8, you read and interpreted a side-by-side bar chart.<\/li>\n<li>In Questions 9 &#8211; 10, you read and interpreted a stacked bar chart.<\/li>\n<li>In Questions 11 &#8211; 12, you explained the differences between side-by-side charts and stacked bar charts.<\/li>\n<\/ul>\n<p>Pie charts are good tools for visualizing a single categorical variable for multiple populations or groups. When we want to display and interpret changes in a categorical variable of interest while comparing multiple populations or groups, we can organize the data into a contingency table (two-way table), which we can then convert into\u00a0side-by-side bar charts or stacked bar charts. These kinds of charts provide a stronger visual comparison between the groups than the two-way table does.<\/p>\n<p>If you feel comfortable with these ideas, it&#8217;s time to move on to Forming Connections in the next activity!<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-233-1\">Bump, P. (2016, November 16). <em>A lot of nonvoters are mad at the election results. If only there were something they could have done<\/em>. The Washington Post. https:\/\/www.washingtonpost.com\/news\/the-fix\/wp\/2016\/11\/16\/a-lot-of-non-voters-are-mad-at-the-election-results-if-only-there-was-something-they-could-have-done\/ <a href=\"#return-footnote-233-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-233-2\">Schaul, K., Rabinowitz, K., &amp; Mellnik, T. (2020, December 28). <em>2020 turnout is the highest in over a century<\/em>. The Washington Post. <a href=\"https:\/\/www.washingtonpost.com\/graphics\/2020\/elections\/voter-turnout\/\">https:\/\/www.washingtonpost.com\/graphics\/2020\/elections\/voter-turnout\/<\/a> <a href=\"#return-footnote-233-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-233-3\">Uggen, C., Larson, R., &amp; Shannon, S. (2016, October 16). <em>6 million lost voters: State-level estimates of felony disenfranchisement, 2016<\/em>. The Sentencing Project. <a href=\"https:\/\/www.sentencingproject.org\/publications\/6-million-lost-voters-state-level-estimates-felony-disenfranchisement-2016\/\">https:\/\/www.sentencingproject.org\/publications\/6-million-lost-voters-state-level-estimates-felony-disenfranchisement-2016\/<\/a> <a href=\"#return-footnote-233-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><li id=\"footnote-233-4\">Maxouris, C. (2020, October 15). <em>More than 5 million people with felony convictions can\u2019t vote in this year\u2019s election, advocacy group finds<\/em>. CNN. <a href=\"https:\/\/www.cnn.com\/2020\/10\/15\/us\/felony-convictions-voting-sentencing-project-study\/index.html\">https:\/\/www.cnn.com\/2020\/10\/15\/us\/felony-convictions-voting-sentencing-project-study\/index.html<\/a> <a href=\"#return-footnote-233-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">&crarr;<\/a><\/li><li id=\"footnote-233-5\"><em>Why voting matters: Supreme Court edition<\/em>. (2018, June 28). Axios. Retrieved from <a href=\"https:\/\/www.axios.com\/hillary-clinton-2016-election-votes-supreme-court-liberal-justice-1b4bc4fc-9fad-44b4-ab54-9ef86aa9c1f1.html\">https:\/\/www.axios.com\/hillary-clinton-2016-election-votes-supreme-court-liberal-justice-1b4bc4fc-9fad-44b4-ab54-9ef86aa9c1f1.html<\/a> <a href=\"#return-footnote-233-5\" class=\"return-footnote\" aria-label=\"Return to footnote 5\">&crarr;<\/a><\/li><li id=\"footnote-233-6\"><em>Exit polls<\/em>. (2020). CNN Politics. Retrieved from <a href=\"https:\/\/www.cnn.com\/election\/2020\/exit-polls\/president\/national-results\">https:\/\/www.cnn.com\/election\/2020\/exit-polls\/president\/national-results<\/a> <a href=\"#return-footnote-233-6\" class=\"return-footnote\" aria-label=\"Return to footnote 6\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":175116,"menu_order":9,"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-233","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/users\/175116"}],"version-history":[{"count":19,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/233\/revisions"}],"predecessor-version":[{"id":1251,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/233\/revisions\/1251"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/233\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=233"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=233"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=233"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}