{"id":2001,"date":"2022-01-26T20:43:10","date_gmt":"2022-01-26T20:43:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=2001"},"modified":"2022-02-09T19:02:23","modified_gmt":"2022-02-09T19:02:23","slug":"14b","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/14b\/","title":{"raw":"14B","rendered":"14B"},"content":{"raw":"
\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
Arts and Humanities<\/strong><\/td>\r\nSTEM<\/strong><\/td>\r\nEducation<\/strong><\/td>\r\nBusiness<\/strong><\/td>\r\n<\/tr>\r\n
16<\/td>\r\n18<\/td>\r\n14<\/td>\r\n16<\/td>\r\n<\/tr>\r\n
18<\/td>\r\n20<\/td>\r\n18<\/td>\r\n20<\/td>\r\n<\/tr>\r\n
17.5<\/td>\r\n18.5<\/td>\r\n16<\/td>\r\n15.5<\/td>\r\n<\/tr>\r\n
19<\/td>\r\n22<\/td>\r\n15.5<\/td>\r\n14<\/td>\r\n<\/tr>\r\n
15<\/td>\r\n18<\/td>\r\n16.5<\/td>\r\n12<\/td>\r\n<\/tr>\r\n
17.5<\/td>\r\n20.5<\/td>\r\n17<\/td>\r\n12<\/td>\r\n<\/tr>\r\n
15.5<\/td>\r\n16.5<\/td>\r\n13<\/td>\r\n15<\/td>\r\n<\/tr>\r\n
19.5<\/td>\r\n14<\/td>\r\n19<\/td>\r\n16.5<\/td>\r\n<\/tr>\r\n
21<\/td>\r\n17<\/td>\r\n15<\/td>\r\n17.5<\/td>\r\n<\/tr>\r\n
14<\/td>\r\n19<\/td>\r\n16<\/td>\r\n17<\/td>\r\n<\/tr>\r\n
18<\/td>\r\n23<\/td>\r\n20<\/td>\r\n15<\/td>\r\n<\/tr>\r\n
16.5<\/td>\r\n16<\/td>\r\n12<\/td>\r\n18<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/strong><\/td>\r\ndf<\/strong><\/td>\r\nSum of Squares<\/strong><\/td>\r\nMean Square<\/strong><\/td>\r\nF-Statistic<\/strong><\/td>\r\nP-value<\/strong><\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n2<\/td>\r\n73.04<\/td>\r\n36.52<\/td>\r\n2.198<\/td>\r\n0.11<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n250<\/td>\r\n4154.00<\/td>\r\n16.62<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n252<\/td>\r\n4227.00<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Fertilizer Level<\/strong><\/td>\r\nHeight of Plant (inches)<\/strong><\/td>\r\n<\/tr>\r\n
Low<\/td>\r\n23.2, 20.9, 21.5, 25.3<\/td>\r\n<\/tr>\r\n
Medium<\/td>\r\n24.6, 27.7, 22.5, 30.1<\/td>\r\n<\/tr>\r\n
High<\/td>\r\n29.2, 30.2, 31.1, 33.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/strong><\/td>\r\nDegrees of Freedom (df)<\/strong><\/td>\r\nSum of Squares<\/strong><\/td>\r\nMean Square<\/strong><\/td>\r\nF-Statistic<\/strong><\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n1\r\n\r\n(The number of groups minus 1)<\/td>\r\nSSGroup<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n(The total number of data points minus the number of groups)<\/td>\r\nSSError<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n\u00a01\r\n\r\n(The total number of data points minus 1)<\/td>\r\nSSGroup + SSError<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/strong><\/td>\r\nDegrees of Freedom (df)<\/strong><\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/strong><\/td>\r\nDegrees of Freedom (df)<\/strong><\/td>\r\nSum of Squares<\/strong><\/td>\r\nMean Square<\/strong><\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n2<\/td>\r\n55.9134<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n9<\/td>\r\n140.0108<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n11<\/td>\r\n195.9242<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Skill or Concept: I can . . .<\/strong><\/td>\r\nQuestions to check your understanding<\/strong><\/td>\r\nRating\r\nfrom 1 to 5<\/strong><\/td>\r\n<\/tr>\r\n
Make connections between the values presented in an ANOVA table.<\/td>\r\n1\u20133<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Describe the shape of the F Distribution.<\/td>\r\n4<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Describe how the P-value is represented on the F Distribution.<\/td>\r\n5<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Describe how the F-statistic is used in hypothesis testing for a one-way ANOVA.<\/td>\r\n6<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Use the P-value to make a conclusion about an ANOVA.<\/td>\r\n7, 8<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Several \"A\r\n\r\nANOVA Table:<\/span>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/strong><\/td>\r\ndf<\/strong><\/td>\r\nSum of Squares<\/strong><\/td>\r\nMean Square<\/strong><\/td>\r\nF Statistic<\/strong><\/td>\r\nP-value<\/strong><\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n3<\/td>\r\n0.7708<\/td>\r\n0.2569<\/td>\r\n0.2736<\/td>\r\n0.8444<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n249<\/td>\r\n233.8<\/td>\r\n0.939<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n252<\/td>\r\n234.5708<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"A\r\n\r\nANOVA Table:<\/span>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/strong><\/td>\r\ndf<\/strong><\/td>\r\nSum of Squares<\/strong><\/td>\r\nMean Square<\/strong><\/td>\r\nF Statistic<\/strong><\/td>\r\nP-value<\/strong><\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n2<\/td>\r\n5.466<\/td>\r\n2.734<\/td>\r\n3.2<\/td>\r\n0.0456<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n87<\/td>\r\n74.34<\/td>\r\n0.8545<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n89<\/td>\r\n79.808<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"A \"A\r\n
\r\n \t
error sum of squares (SSError)<\/dt>\r\n \t
the total variation within the groups of interest.<\/dd>\r\n<\/dl>\r\n
\r\n \t
group sum of squares (SSGroup)<\/dt>\r\n \t
the total variation between the groups of interest.<\/dd>\r\n<\/dl>\r\n
\r\n \t
mean square<\/dt>\r\n \t
the sum of square values divided by the degrees of freedom associated with the respective source (i.e., Group or Error).<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Arts and Humanities<\/strong><\/td>\nSTEM<\/strong><\/td>\nEducation<\/strong><\/td>\nBusiness<\/strong><\/td>\n<\/tr>\n
16<\/td>\n18<\/td>\n14<\/td>\n16<\/td>\n<\/tr>\n
18<\/td>\n20<\/td>\n18<\/td>\n20<\/td>\n<\/tr>\n
17.5<\/td>\n18.5<\/td>\n16<\/td>\n15.5<\/td>\n<\/tr>\n
19<\/td>\n22<\/td>\n15.5<\/td>\n14<\/td>\n<\/tr>\n
15<\/td>\n18<\/td>\n16.5<\/td>\n12<\/td>\n<\/tr>\n
17.5<\/td>\n20.5<\/td>\n17<\/td>\n12<\/td>\n<\/tr>\n
15.5<\/td>\n16.5<\/td>\n13<\/td>\n15<\/td>\n<\/tr>\n
19.5<\/td>\n14<\/td>\n19<\/td>\n16.5<\/td>\n<\/tr>\n
21<\/td>\n17<\/td>\n15<\/td>\n17.5<\/td>\n<\/tr>\n
14<\/td>\n19<\/td>\n16<\/td>\n17<\/td>\n<\/tr>\n
18<\/td>\n23<\/td>\n20<\/td>\n15<\/td>\n<\/tr>\n
16.5<\/td>\n16<\/td>\n12<\/td>\n18<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
Source<\/strong><\/td>\ndf<\/strong><\/td>\nSum of Squares<\/strong><\/td>\nMean Square<\/strong><\/td>\nF-Statistic<\/strong><\/td>\nP-value<\/strong><\/td>\n<\/tr>\n
Group<\/td>\n2<\/td>\n73.04<\/td>\n36.52<\/td>\n2.198<\/td>\n0.11<\/td>\n<\/tr>\n
Error<\/td>\n250<\/td>\n4154.00<\/td>\n16.62<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Total<\/td>\n252<\/td>\n4227.00<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n\n\n\n\n\n\n
Fertilizer Level<\/strong><\/td>\nHeight of Plant (inches)<\/strong><\/td>\n<\/tr>\n
Low<\/td>\n23.2, 20.9, 21.5, 25.3<\/td>\n<\/tr>\n
Medium<\/td>\n24.6, 27.7, 22.5, 30.1<\/td>\n<\/tr>\n
High<\/td>\n29.2, 30.2, 31.1, 33.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n\n\n\n\n\n\n
Source<\/strong><\/td>\nDegrees of Freedom (df)<\/strong><\/td>\nSum of Squares<\/strong><\/td>\nMean Square<\/strong><\/td>\nF-Statistic<\/strong><\/td>\n<\/tr>\n
Group<\/td>\n1<\/p>\n

(The number of groups minus 1)<\/td>\n

SSGroup<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Error<\/td>\n(The total number of data points minus the number of groups)<\/td>\nSSError<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Total<\/td>\n\u00a01<\/p>\n

(The total number of data points minus 1)<\/td>\n

SSGroup + SSError<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n\n\n\n\n\n\n
Source<\/strong><\/td>\nDegrees of Freedom (df)<\/strong><\/td>\n<\/tr>\n
Group<\/td>\n<\/td>\n<\/tr>\n
Error<\/td>\n<\/td>\n<\/tr>\n
Total<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n\n\n\n\n\n\n
Source<\/strong><\/td>\nDegrees of Freedom (df)<\/strong><\/td>\nSum of Squares<\/strong><\/td>\nMean Square<\/strong><\/td>\n<\/tr>\n
Group<\/td>\n2<\/td>\n55.9134<\/td>\n<\/td>\n<\/tr>\n
Error<\/td>\n9<\/td>\n140.0108<\/td>\n<\/td>\n<\/tr>\n
Total<\/td>\n11<\/td>\n195.9242<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n\n\n\n\n\n\n\n\n
Skill or Concept: I can . . .<\/strong><\/td>\nQuestions to check your understanding<\/strong><\/td>\nRating
\nfrom 1 to 5<\/strong><\/td>\n<\/tr>\n
Make connections between the values presented in an ANOVA table.<\/td>\n1\u20133<\/td>\n<\/td>\n<\/tr>\n
Describe the shape of the F Distribution.<\/td>\n4<\/td>\n<\/td>\n<\/tr>\n
Describe how the P-value is represented on the F Distribution.<\/td>\n5<\/td>\n<\/td>\n<\/tr>\n
Describe how the F-statistic is used in hypothesis testing for a one-way ANOVA.<\/td>\n6<\/td>\n<\/td>\n<\/tr>\n
Use the P-value to make a conclusion about an ANOVA.<\/td>\n7, 8<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Several \"A<\/p>\n

ANOVA Table:<\/span><\/p>\n\n\n\n\n\n\n
Source<\/strong><\/td>\ndf<\/strong><\/td>\nSum of Squares<\/strong><\/td>\nMean Square<\/strong><\/td>\nF Statistic<\/strong><\/td>\nP-value<\/strong><\/td>\n<\/tr>\n
Group<\/td>\n3<\/td>\n0.7708<\/td>\n0.2569<\/td>\n0.2736<\/td>\n0.8444<\/td>\n<\/tr>\n
Error<\/td>\n249<\/td>\n233.8<\/td>\n0.939<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Total<\/td>\n252<\/td>\n234.5708<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"A<\/p>\n

ANOVA Table:<\/span><\/p>\n\n\n\n\n\n\n
Source<\/strong><\/td>\ndf<\/strong><\/td>\nSum of Squares<\/strong><\/td>\nMean Square<\/strong><\/td>\nF Statistic<\/strong><\/td>\nP-value<\/strong><\/td>\n<\/tr>\n
Group<\/td>\n2<\/td>\n5.466<\/td>\n2.734<\/td>\n3.2<\/td>\n0.0456<\/td>\n<\/tr>\n
Error<\/td>\n87<\/td>\n74.34<\/td>\n0.8545<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Total<\/td>\n89<\/td>\n79.808<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"A \"A<\/p>\n

\n
error sum of squares (SSError)<\/dt>\n
the total variation within the groups of interest.<\/dd>\n<\/dl>\n
\n
group sum of squares (SSGroup)<\/dt>\n
the total variation between the groups of interest.<\/dd>\n<\/dl>\n
\n
mean square<\/dt>\n
the sum of square values divided by the degrees of freedom associated with the respective source (i.e., Group or Error).<\/dd>\n<\/dl>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":47,"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-2001","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2001","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":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2001\/revisions"}],"predecessor-version":[{"id":2987,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2001\/revisions\/2987"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2001\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=2001"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=2001"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=2001"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=2001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}