{"id":5452,"date":"2022-08-30T02:47:00","date_gmt":"2022-08-30T02:47:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5452"},"modified":"2022-08-30T02:47:00","modified_gmt":"2022-08-30T02:47:00","slug":"14a-inclass","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/14a-inclass\/","title":{"raw":"14A InClass","rendered":"14A InClass"},"content":{"raw":"<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\n1) A researcher is interested in comparing the average weight loss over a 12-week\u00a0 period between individuals randomly assigned to one of four groups:\r\n<ul>\r\n \t<li>Diet only<\/li>\r\n \t<li>Diet and assorted cardio routines four days a week<\/li>\r\n \t<li>Diet and cycling activities four days a week<\/li>\r\n \t<li>Diet and combination of strength training and cardio activities four days a week Explain why a one-way ANOVA should be considered for this situation.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\n2) Write the null hypothesis for the weight loss situation. Be sure to define each\u00a0 parameter.<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\n3) Write the alternative hypothesis for this situation.<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\n4) Before conducting a formal hypothesis test, the researcher would like to visually\u00a0 assess the data. The following boxplots and dotplots compare the distributions of\u00a0 each group. The sample means for each group, as well as the grand mean (e.g.,\u00a0 17.1 pounds (lb) is the mean of all the data values), are provided.\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202708\/Picture461-300x137.png\" alt=\"Side-by-side box plots with \u201cWeight Loss (lb)\u201d on the horizontal axis and \u201cDiet,\u201d \u201cDiet + Cardio,\u201d \u201cDiet + Cycling,\u201d and \u201cDiet + Strength Training + Cardio\u201d on the vertical axis. There is a dash on the horizontal axis labeled \u201cX bar = 17.1 lb.\u201d For Diet, the low point is at approximately 11.5 and the high point is at approximately 14. The low end of the box is at approximately 12.25, the high end of the box is at approximately 13.75, and the middle line is at approximately 12.5. There is a label reading \u201cX bar sub 1 = 12.8 lb.\u201d For Diet + Cardio, the low point is at approximately 15 and the high point is at approximately 17.5. The low end of the box is at approximately 15.25, the high end of the box is at approximately 17, and the middle line is at approximately 16.25. There is a label reading \u201cX bar sub 2 = 16.2 lb.\u201d For Diet + Cycling, the low point is at approximately 17.25 and the high point is at approximately 19.5. The low end of the box is at approximately 17.5, the high end is at approximately 19.25, and the middle line is at approximately 18. There is a label reading \u201cX bar sub 3 = 18.3 lb.\u201d For Diet + Strength Training + Cardio, the low point is at approximately 19.75 and the high point is at approximately 22. The low end of the box is at approximately 20, the high end is at approximately 21.75, and the middle line is at approximately 21.7. There is also a label reading \u201cx bar sub 4 equals 21.1 lb.\u201d\" width=\"569\" height=\"260\" \/>\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202713\/Picture471-300x156.png\" alt=\"Side-by-side dot plots with \u201cWeight Loss (lb)\u201d on the horizontal axis. The first plot is labeled \u201cDiet\u201d and has dots at approximately 11.5, 12.4, 12.6, 13.8, and 14.2. The second plot is labeled \u201cDiet + Cardio\u201d and shows dots at approximately 14.9, 15.3, 16.3, 17, and 17.5. The third plot is labeled \u201cDiet + Cycling\u201d and shows dots at approximately 17.3, 17.4, 17.9, 19.3, and 19.5. The last plot is labeled \u201cDiet + Strength Training + Cardio\u201d and has dots at approximately 19.8, 19.9, 21.6, 21.6, and 21.8.\" width=\"537\" height=\"279\" \/>\r\n\r\nBased on these graphs alone, does it appear there is visual evidence that the diets differ in average weight loss? That is, is there visual evidence to reject the null\u00a0 hypothesis in favor of the alternative hypothesis? Explain.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 5<\/h3>\r\n5) Suppose the results are different than those presented in Question 4. An alternative\u00a0 result is reflected in the following boxplot and dotplot.\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202718\/Picture481-300x137.png\" alt=\"Side-by-side box plots with \u201cWeight Loss (lb)\u201d on the horizontal axis and \u201cDiet,\u201d \u201cDiet + Cardio,\u201d \u201cDiet + Cycling,\u201d and \u201cDiet + Strength Training + Cardio\u201d on the vertical axis. There is a dash on the horizontal axis labeled \u201cX bar = 17.1 lb.\u201d For Diet, the low point is at approximately 7.5 and the high point is at approximately 19.5. The low end of the box is at approximately 10, the high end of the box is at approximately 15, and the middle line is at approximately 12.5. There is a label reading \u201cX bar sub 1 = 12.8 lb.\u201d For Diet + Cardio, the low point is at approximately 9.5 and the high point is at approximately 22. The low end of the box is at approximately 12, the high end of the box is at approximately 20, and the middle line is at approximately 18. There is a label reading \u201cX bar sub 2 = 16.2 lb.\u201d For Diet + Cycling, the low point is at approximately 10.5 and the high point is at approximately 24. The low end of the box is at approximately 14, the high end is at approximately 23.5, and the middle line is at approximately 19.5. There is a label reading \u201cX bar sub 3 = 18.3 lb.\u201d For Diet + Strength Training + Cardio, the low point is at approximately 13 and the high point is at approximately 26.5. The low end of the box is at approximately 18, the high end is at approximately 25, and the middle line is at approximately 22.5. There is also a label reading \u201cx bar sub 4 equals 21.1 lb.\u201d\" width=\"488\" height=\"223\" \/>\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202723\/Picture491-300x156.png\" alt=\"Side-by-side dot plots labeled \u201cWeight Loss (lb)\u201d on the horizontal axis. The first plot is labeled \u201cDiet\u201d and shows dots at approximately 6, 12, 13, 15, and 20. The second plot is labeled \u201cDiet + Cardio\u201d and has dots at approximately 9, 12, 17, 19, and 22. The third plot is labeled \u201cDiet + Cycling\u201d and has dots at approximately 10.5, 14.5, 19.5, 23.5, and 24. The last plot is labeled \u201cDiet + Strength Training + Cardio\u201d and has points at approximately 13, 20, 22, 25, and 26.5.\" width=\"504\" height=\"262\" \/>\r\n\r\nBased on these graphs alone, does it appear there is visual evidence that the diets\u00a0 differ in average weight loss? That is, is there visual evidence to reject the null\u00a0 hypothesis in favor of the alternative hypothesis? Explain.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 6<\/h3>\r\n6) Compare and contrast the graphical displays in Questions 4 and 5.\r\n\r\nPart A: How are they similar and how are they different?\r\n\r\nPart B: Which one appeared to provide more convincing evidence? What might the differences suggest about making a conclusion about the null hypothesis in a\u00a0 one-way ANOVA?\r\n\r\n<\/div>\r\nThe test statistic and P-value are calculated by considering the ratio of variation within\u00a0 each of the groups to the variation between each of the groups. That is, when the\u00a0 variation between each of the groups is significantly greater than the variation within each of the groups, we will reject the null hypothesis and conclude that at least two of\u00a0 the means are different (similar to what we saw in Question 4).\r\n\r\nHowever, when there is a significant amount of variation within groups, relative to the\u00a0 variation between groups (like in Question 5), we will have less evidence of a difference\u00a0 and may fail to reject the null hypothesis.\r\n\r\nThe statistic measuring the variation within the groups is the error sum of squares.\u00a0 This is calculated by summing the variation within each of the groups. The variation\u00a0 within each of the groups is visualized in the boxplot by the size of the box and in the\u00a0 dotplot as the spread of the dots within each group.\r\n\r\nA statistic measuring the variation between the groups is the group sum of squares. This is calculated by summing the variation between each of the group means and the\u00a0 grand mean (i.e., the mean of all the data values).\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 7<\/h3>\r\n7) Given the information about the error sum of squares, which data (Question 4 or 5)\u00a0 do you think would have the greater error sum of squares value? Explain.<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 8<\/h3>\r\n8) Given the information about the group sum of squares, which data (Question 4 or 5)\u00a0 do you think would have the greater group sum of squares value? Explain.<\/div>","rendered":"<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>1) A researcher is interested in comparing the average weight loss over a 12-week\u00a0 period between individuals randomly assigned to one of four groups:<\/p>\n<ul>\n<li>Diet only<\/li>\n<li>Diet and assorted cardio routines four days a week<\/li>\n<li>Diet and cycling activities four days a week<\/li>\n<li>Diet and combination of strength training and cardio activities four days a week Explain why a one-way ANOVA should be considered for this situation.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>2) Write the null hypothesis for the weight loss situation. Be sure to define each\u00a0 parameter.<\/p><\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>3) Write the alternative hypothesis for this situation.<\/p><\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>4) Before conducting a formal hypothesis test, the researcher would like to visually\u00a0 assess the data. The following boxplots and dotplots compare the distributions of\u00a0 each group. The sample means for each group, as well as the grand mean (e.g.,\u00a0 17.1 pounds (lb) is the mean of all the data values), are provided.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202708\/Picture461-300x137.png\" alt=\"Side-by-side box plots with \u201cWeight Loss (lb)\u201d on the horizontal axis and \u201cDiet,\u201d \u201cDiet + Cardio,\u201d \u201cDiet + Cycling,\u201d and \u201cDiet + Strength Training + Cardio\u201d on the vertical axis. There is a dash on the horizontal axis labeled \u201cX bar = 17.1 lb.\u201d For Diet, the low point is at approximately 11.5 and the high point is at approximately 14. The low end of the box is at approximately 12.25, the high end of the box is at approximately 13.75, and the middle line is at approximately 12.5. There is a label reading \u201cX bar sub 1 = 12.8 lb.\u201d For Diet + Cardio, the low point is at approximately 15 and the high point is at approximately 17.5. The low end of the box is at approximately 15.25, the high end of the box is at approximately 17, and the middle line is at approximately 16.25. There is a label reading \u201cX bar sub 2 = 16.2 lb.\u201d For Diet + Cycling, the low point is at approximately 17.25 and the high point is at approximately 19.5. The low end of the box is at approximately 17.5, the high end is at approximately 19.25, and the middle line is at approximately 18. There is a label reading \u201cX bar sub 3 = 18.3 lb.\u201d For Diet + Strength Training + Cardio, the low point is at approximately 19.75 and the high point is at approximately 22. The low end of the box is at approximately 20, the high end is at approximately 21.75, and the middle line is at approximately 21.7. There is also a label reading \u201cx bar sub 4 equals 21.1 lb.\u201d\" width=\"569\" height=\"260\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202713\/Picture471-300x156.png\" alt=\"Side-by-side dot plots with \u201cWeight Loss (lb)\u201d on the horizontal axis. The first plot is labeled \u201cDiet\u201d and has dots at approximately 11.5, 12.4, 12.6, 13.8, and 14.2. The second plot is labeled \u201cDiet + Cardio\u201d and shows dots at approximately 14.9, 15.3, 16.3, 17, and 17.5. The third plot is labeled \u201cDiet + Cycling\u201d and shows dots at approximately 17.3, 17.4, 17.9, 19.3, and 19.5. The last plot is labeled \u201cDiet + Strength Training + Cardio\u201d and has dots at approximately 19.8, 19.9, 21.6, 21.6, and 21.8.\" width=\"537\" height=\"279\" \/><\/p>\n<p>Based on these graphs alone, does it appear there is visual evidence that the diets differ in average weight loss? That is, is there visual evidence to reject the null\u00a0 hypothesis in favor of the alternative hypothesis? Explain.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 5<\/h3>\n<p>5) Suppose the results are different than those presented in Question 4. An alternative\u00a0 result is reflected in the following boxplot and dotplot.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202718\/Picture481-300x137.png\" alt=\"Side-by-side box plots with \u201cWeight Loss (lb)\u201d on the horizontal axis and \u201cDiet,\u201d \u201cDiet + Cardio,\u201d \u201cDiet + Cycling,\u201d and \u201cDiet + Strength Training + Cardio\u201d on the vertical axis. There is a dash on the horizontal axis labeled \u201cX bar = 17.1 lb.\u201d For Diet, the low point is at approximately 7.5 and the high point is at approximately 19.5. The low end of the box is at approximately 10, the high end of the box is at approximately 15, and the middle line is at approximately 12.5. There is a label reading \u201cX bar sub 1 = 12.8 lb.\u201d For Diet + Cardio, the low point is at approximately 9.5 and the high point is at approximately 22. The low end of the box is at approximately 12, the high end of the box is at approximately 20, and the middle line is at approximately 18. There is a label reading \u201cX bar sub 2 = 16.2 lb.\u201d For Diet + Cycling, the low point is at approximately 10.5 and the high point is at approximately 24. The low end of the box is at approximately 14, the high end is at approximately 23.5, and the middle line is at approximately 19.5. There is a label reading \u201cX bar sub 3 = 18.3 lb.\u201d For Diet + Strength Training + Cardio, the low point is at approximately 13 and the high point is at approximately 26.5. The low end of the box is at approximately 18, the high end is at approximately 25, and the middle line is at approximately 22.5. There is also a label reading \u201cx bar sub 4 equals 21.1 lb.\u201d\" width=\"488\" height=\"223\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26202723\/Picture491-300x156.png\" alt=\"Side-by-side dot plots labeled \u201cWeight Loss (lb)\u201d on the horizontal axis. The first plot is labeled \u201cDiet\u201d and shows dots at approximately 6, 12, 13, 15, and 20. The second plot is labeled \u201cDiet + Cardio\u201d and has dots at approximately 9, 12, 17, 19, and 22. The third plot is labeled \u201cDiet + Cycling\u201d and has dots at approximately 10.5, 14.5, 19.5, 23.5, and 24. The last plot is labeled \u201cDiet + Strength Training + Cardio\u201d and has points at approximately 13, 20, 22, 25, and 26.5.\" width=\"504\" height=\"262\" \/><\/p>\n<p>Based on these graphs alone, does it appear there is visual evidence that the diets\u00a0 differ in average weight loss? That is, is there visual evidence to reject the null\u00a0 hypothesis in favor of the alternative hypothesis? Explain.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 6<\/h3>\n<p>6) Compare and contrast the graphical displays in Questions 4 and 5.<\/p>\n<p>Part A: How are they similar and how are they different?<\/p>\n<p>Part B: Which one appeared to provide more convincing evidence? What might the differences suggest about making a conclusion about the null hypothesis in a\u00a0 one-way ANOVA?<\/p>\n<\/div>\n<p>The test statistic and P-value are calculated by considering the ratio of variation within\u00a0 each of the groups to the variation between each of the groups. That is, when the\u00a0 variation between each of the groups is significantly greater than the variation within each of the groups, we will reject the null hypothesis and conclude that at least two of\u00a0 the means are different (similar to what we saw in Question 4).<\/p>\n<p>However, when there is a significant amount of variation within groups, relative to the\u00a0 variation between groups (like in Question 5), we will have less evidence of a difference\u00a0 and may fail to reject the null hypothesis.<\/p>\n<p>The statistic measuring the variation within the groups is the error sum of squares.\u00a0 This is calculated by summing the variation within each of the groups. The variation\u00a0 within each of the groups is visualized in the boxplot by the size of the box and in the\u00a0 dotplot as the spread of the dots within each group.<\/p>\n<p>A statistic measuring the variation between the groups is the group sum of squares. This is calculated by summing the variation between each of the group means and the\u00a0 grand mean (i.e., the mean of all the data values).<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 7<\/h3>\n<p>7) Given the information about the error sum of squares, which data (Question 4 or 5)\u00a0 do you think would have the greater error sum of squares value? Explain.<\/p><\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 8<\/h3>\n<p>8) Given the information about the group sum of squares, which data (Question 4 or 5)\u00a0 do you think would have the greater group sum of squares value? Explain.<\/p><\/div>\n","protected":false},"author":23592,"menu_order":2,"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-5452","chapter","type-chapter","status-publish","hentry"],"part":5448,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5452","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":1,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5452\/revisions"}],"predecessor-version":[{"id":5453,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5452\/revisions\/5453"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5448"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5452\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5452"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5452"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5452"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}