{"id":5505,"date":"2022-09-19T16:20:06","date_gmt":"2022-09-19T16:20:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5505"},"modified":"2022-10-04T18:46:55","modified_gmt":"2022-10-04T18:46:55","slug":"15e-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/15e-coreq\/","title":{"raw":"15E Coreq","rendered":"15E Coreq"},"content":{"raw":"
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In the next preview assignment and in the next class, you will need to read contingency tables and be able to logically combine cells of contingency tables. Organizing Categorical Bivariate Data A teacher asks a group of 11 students the following questions:<\/div>\r\n
\u2022Do you have a driver\u2019s license? \u2022Do you own a bicycle? The answers are recorded asfollows:<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nDriver\u2019s License?<\/strong><\/td>\r\nBicycle?<\/strong><\/td>\r\n<\/tr>\r\n
Student 1<\/strong><\/td>\r\nYes<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n
Student 2<\/strong><\/td>\r\nYes<\/td>\r\nNo<\/td>\r\n<\/tr>\r\n
Student 3<\/strong><\/td>\r\nNo<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n
Student 4<\/strong><\/td>\r\nNo<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n
Student 5<\/strong><\/td>\r\nYes<\/td>\r\nNo<\/td>\r\n<\/tr>\r\n
Student 6<\/strong><\/td>\r\nNo<\/td>\r\nNo<\/td>\r\n<\/tr>\r\n
Student 7<\/strong><\/td>\r\nNo<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n
Student 8<\/strong><\/td>\r\nYes<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n
Student 9<\/strong><\/td>\r\nYes<\/td>\r\nNo<\/td>\r\n<\/tr>\r\n
Student 10<\/strong><\/td>\r\nYes<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n
Student 11<\/strong><\/td>\r\nNo<\/td>\r\nYes<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n
\r\n

Question 1<\/h3>\r\n1) Is the variable Do you have a driver\u2019s license categorical or quantitative?\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 2<\/h3>\r\n2) Is the variable Do you own a bicycle categorical or quantitative? From looking at this table, it might be difficult to get a good sense of any patterns in the dataset. The teacher decides to organize the information into a contingency table. Previously, you have used this tool to organize bivariate, categorical data. In each cell, there is an integer, representing a frequency or count.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

Question 3<\/h3>\r\n3) Fill in the cells in the following table, using the labels as a guide.\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nYes, has a driver\u2019s license<\/strong><\/td>\r\nNo, does not have a driver\u2019s license<\/strong><\/td>\r\n<\/tr>\r\n
Yes, owns a bicycle<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
No, does not own a bicycle<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 4<\/h3>\r\n4) How many students have driver\u2019s licenses but do not own bicycles?\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 5<\/h3>\r\n5) In a sentence, explain what the number four represents in the previous table. Contingency tables are particularly useful when datasets are large. Consider the following example.\r\n\r\n<\/div>\r\n<\/div>\r\n
Questions 6\u201310: On March 23, 2021, S.937: COVID-19 Hate Crimes Act was presented to the United States Senate, the purpose of which is to \u201cfacilitate the expedited review of COVID-19 hate crimes, and for other purposes.\u201d[footnote]GovTrack. (2021, May 19). S.937: COVID-19 Hate Crimes Act.https:\/\/www.govtrack.us\/congress\/bills\/117\/s937\/text[\/footnote] On April 22, 2021, it passed in the Senate. The votes on the bill are in the following table.<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nRepublicans<\/strong><\/td>\r\nDemocrats<\/strong><\/td>\r\nIndependents<\/strong><\/td>\r\n<\/tr>\r\n
Yes<\/strong><\/td>\r\n46<\/td>\r\n46<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
No<\/strong><\/td>\r\n1<\/td>\r\n0<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
Not Voting<\/strong><\/td>\r\n3<\/td>\r\n2<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n
\r\n

Question 6<\/h3>\r\n6) How many people did not vote on the bill?\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 7<\/h3>\r\n7) How many senators are not Republicans?\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 8<\/h3>\r\n8) How many senators are Democrats or Independents?\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
Note that the answers to Questions 7 and 8 are the same! Asking about a person not being a Republican is the same as asking if they fit into the Democrat or Independent category!<\/div>\r\n
\r\n
\r\n

Question 9<\/h3>\r\n9) In a sentence, explain what the number three in the previous table represents.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 10<\/h3>\r\n
10) Suppose that a researcher wanted to reorganize the data with different labels. Fill in the following table, using the labels as a guide.<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nRepublicans<\/strong><\/td>\r\nOther<\/strong><\/td>\r\n<\/tr>\r\n
Yes<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Other<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 11<\/h3>\r\n
11) Using the answer to Question 10, how many senators are not Republicans? Note that Questions 7 and 11 are the same, as are the answers. Reorganizing the data will not change the answer to a question\u2014but it does change what questions we can answer!<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

Question 12<\/h3>\r\n
12) A physician organizes her practice\u2019s patient database based on their ages and the frequency of weekly exercise that they report to do. The following table describes the data.<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n20\u201329 years<\/strong><\/td>\r\n30\u201339 years<\/strong><\/td>\r\n40\u201349 years<\/strong><\/td>\r\n50\u201359 years<\/strong><\/td>\r\n60\u201369 years<\/strong><\/td>\r\n70\u201379 years<\/strong><\/td>\r\n80\u201389 years<\/strong><\/td>\r\n<\/tr>\r\n
0\u20131 days per week<\/strong><\/td>\r\n7<\/td>\r\n12<\/td>\r\n55<\/td>\r\n40<\/td>\r\n30<\/td>\r\n4<\/td>\r\n9<\/td>\r\n<\/tr>\r\n
2\u20134 days per week<\/strong><\/td>\r\n35<\/td>\r\n41<\/td>\r\n45<\/td>\r\n50<\/td>\r\n55<\/td>\r\n30<\/td>\r\n12<\/td>\r\n<\/tr>\r\n
5\u20137 days per week<\/strong><\/td>\r\n31<\/td>\r\n44<\/td>\r\n49<\/td>\r\n40<\/td>\r\n24<\/td>\r\n12<\/td>\r\n1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
Part A: Collapse the frequency counts in this dataset as indicated by the labels in the following table.<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n20\u201349 years<\/strong><\/td>\r\n50\u201389 years<\/strong><\/td>\r\n<\/tr>\r\n
0\u20131 days per week <\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
2+ days per week<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
Part B: Would it make sense to collapse the cells as indicated in the following table? Explain.(Note: Do not fill in the table, just consider the labels to answer the question).<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n20\u201329 and 70\u201389 years<\/strong><\/td>\r\n30\u201369 years<\/strong><\/td>\r\n<\/tr>\r\n
0\u20131 days per week<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
2+ days per week<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
Part C: Determine whether this statement is true or false:The total sum of frequencies changes when cells are collapsed.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
In the next preview assignment and in the next class, you will need to read contingency tables and be able to logically combine cells of contingency tables. Organizing Categorical Bivariate Data A teacher asks a group of 11 students the following questions:<\/div>\n
\u2022Do you have a driver\u2019s license? \u2022Do you own a bicycle? The answers are recorded asfollows:<\/div>\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
<\/td>\nDriver\u2019s License?<\/strong><\/td>\nBicycle?<\/strong><\/td>\n<\/tr>\n
Student 1<\/strong><\/td>\nYes<\/td>\nYes<\/td>\n<\/tr>\n
Student 2<\/strong><\/td>\nYes<\/td>\nNo<\/td>\n<\/tr>\n
Student 3<\/strong><\/td>\nNo<\/td>\nYes<\/td>\n<\/tr>\n
Student 4<\/strong><\/td>\nNo<\/td>\nYes<\/td>\n<\/tr>\n
Student 5<\/strong><\/td>\nYes<\/td>\nNo<\/td>\n<\/tr>\n
Student 6<\/strong><\/td>\nNo<\/td>\nNo<\/td>\n<\/tr>\n
Student 7<\/strong><\/td>\nNo<\/td>\nYes<\/td>\n<\/tr>\n
Student 8<\/strong><\/td>\nYes<\/td>\nYes<\/td>\n<\/tr>\n
Student 9<\/strong><\/td>\nYes<\/td>\nNo<\/td>\n<\/tr>\n
Student 10<\/strong><\/td>\nYes<\/td>\nYes<\/td>\n<\/tr>\n
Student 11<\/strong><\/td>\nNo<\/td>\nYes<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n
\n

Question 1<\/h3>\n

1) Is the variable Do you have a driver\u2019s license categorical or quantitative?<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 2<\/h3>\n

2) Is the variable Do you own a bicycle categorical or quantitative? From looking at this table, it might be difficult to get a good sense of any patterns in the dataset. The teacher decides to organize the information into a contingency table. Previously, you have used this tool to organize bivariate, categorical data. In each cell, there is an integer, representing a frequency or count.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
\n

Question 3<\/h3>\n

3) Fill in the cells in the following table, using the labels as a guide.<\/p>\n\n\n\n\n\n
<\/td>\nYes, has a driver\u2019s license<\/strong><\/td>\nNo, does not have a driver\u2019s license<\/strong><\/td>\n<\/tr>\n
Yes, owns a bicycle<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
No, does not own a bicycle<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Question 4<\/h3>\n

4) How many students have driver\u2019s licenses but do not own bicycles?<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 5<\/h3>\n

5) In a sentence, explain what the number four represents in the previous table. Contingency tables are particularly useful when datasets are large. Consider the following example.<\/p>\n<\/div>\n<\/div>\n

Questions 6\u201310: On March 23, 2021, S.937: COVID-19 Hate Crimes Act was presented to the United States Senate, the purpose of which is to \u201cfacilitate the expedited review of COVID-19 hate crimes, and for other purposes.\u201d[1]<\/sup><\/a> On April 22, 2021, it passed in the Senate. The votes on the bill are in the following table.<\/div>\n
\n\n\n\n\n\n\n
<\/td>\nRepublicans<\/strong><\/td>\nDemocrats<\/strong><\/td>\nIndependents<\/strong><\/td>\n<\/tr>\n
Yes<\/strong><\/td>\n46<\/td>\n46<\/td>\n2<\/td>\n<\/tr>\n
No<\/strong><\/td>\n1<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
Not Voting<\/strong><\/td>\n3<\/td>\n2<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n
\n

Question 6<\/h3>\n

6) How many people did not vote on the bill?<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 7<\/h3>\n

7) How many senators are not Republicans?<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 8<\/h3>\n

8) How many senators are Democrats or Independents?<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
Note that the answers to Questions 7 and 8 are the same! Asking about a person not being a Republican is the same as asking if they fit into the Democrat or Independent category!<\/div>\n
\n
\n

Question 9<\/h3>\n

9) In a sentence, explain what the number three in the previous table represents.<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 10<\/h3>\n
10) Suppose that a researcher wanted to reorganize the data with different labels. Fill in the following table, using the labels as a guide.<\/div>\n
\n\n\n\n\n\n
<\/td>\nRepublicans<\/strong><\/td>\nOther<\/strong><\/td>\n<\/tr>\n
Yes<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Other<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 11<\/h3>\n
11) Using the answer to Question 10, how many senators are not Republicans? Note that Questions 7 and 11 are the same, as are the answers. Reorganizing the data will not change the answer to a question\u2014but it does change what questions we can answer!<\/div>\n<\/div>\n
\n
\n
\n

Question 12<\/h3>\n
12) A physician organizes her practice\u2019s patient database based on their ages and the frequency of weekly exercise that they report to do. The following table describes the data.<\/div>\n
\n\n\n\n\n\n\n
<\/td>\n20\u201329 years<\/strong><\/td>\n30\u201339 years<\/strong><\/td>\n40\u201349 years<\/strong><\/td>\n50\u201359 years<\/strong><\/td>\n60\u201369 years<\/strong><\/td>\n70\u201379 years<\/strong><\/td>\n80\u201389 years<\/strong><\/td>\n<\/tr>\n
0\u20131 days per week<\/strong><\/td>\n7<\/td>\n12<\/td>\n55<\/td>\n40<\/td>\n30<\/td>\n4<\/td>\n9<\/td>\n<\/tr>\n
2\u20134 days per week<\/strong><\/td>\n35<\/td>\n41<\/td>\n45<\/td>\n50<\/td>\n55<\/td>\n30<\/td>\n12<\/td>\n<\/tr>\n
5\u20137 days per week<\/strong><\/td>\n31<\/td>\n44<\/td>\n49<\/td>\n40<\/td>\n24<\/td>\n12<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
Part A: Collapse the frequency counts in this dataset as indicated by the labels in the following table.<\/div>\n
\n\n\n\n\n\n
<\/td>\n20\u201349 years<\/strong><\/td>\n50\u201389 years<\/strong><\/td>\n<\/tr>\n
0\u20131 days per week <\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
2+ days per week<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
Part B: Would it make sense to collapse the cells as indicated in the following table? Explain.(Note: Do not fill in the table, just consider the labels to answer the question).<\/div>\n
\n\n\n\n\n\n
<\/td>\n20\u201329 and 70\u201389 years<\/strong><\/td>\n30\u201369 years<\/strong><\/td>\n<\/tr>\n
0\u20131 days per week<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
2+ days per week<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
Part C: Determine whether this statement is true or false:The total sum of frequencies changes when cells are collapsed.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
  1. GovTrack. (2021, May 19). S.937: COVID-19 Hate Crimes Act.https:\/\/www.govtrack.us\/congress\/bills\/117\/s937\/text ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"menu_order":13,"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-5505","chapter","type-chapter","status-publish","hentry"],"part":5479,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5505","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5505\/revisions"}],"predecessor-version":[{"id":5614,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5505\/revisions\/5614"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5479"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5505\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5505"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5505"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5505"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}