{"id":5462,"date":"2022-08-30T21:15:31","date_gmt":"2022-08-30T21:15:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5462"},"modified":"2022-08-30T21:15:31","modified_gmt":"2022-08-30T21:15:31","slug":"14c-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/14c-coreq\/","title":{"raw":"14C Coreq","rendered":"14C Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to determine\u00a0 whether different groups of data have similar variation. In this corequisite support\u00a0 activity, we\u2019ll explore the use of different tools to explore data before conducting formal\u00a0 analyses.\r\n\r\nWhat Should You Pack?\r\n\r\nSuppose you\u2019re taking a trip across the country to visit several different friends. You\u2019ll\u00a0 be traveling through Miami, Florida, Phoenix, Arizona, and Honolulu, Hawaii, but you\u2019re\u00a0 not sure what kinds of clothes to pack. What\u2019s the weather like in those cities? A quick\u00a0 Internet search tells you that the mean high temperature in each city is as follows:\r\n
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City<\/td>\r\nMean High Temperature[footnote]U.S. climate data. (2021). https:\/\/www.usclimatedata.com\/climate\/united-states\/us[\/footnote]<\/td>\r\n<\/tr>\r\n
Miami<\/td>\r\n84 \u00b0F<\/td>\r\n<\/tr>\r\n
Phoenix<\/td>\r\n87 \u00b0F<\/td>\r\n<\/tr>\r\n
Honolulu<\/td>\r\n84 \u00b0F<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
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Question 1<\/h3>\r\n1) What are your first impressions of the weather in each city? What other information\u00a0 would you like to have before deciding what to pack?<\/div>\r\n
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Question 2<\/h3>\r\n2) Obviously, a single data point is not enough information to help you pack. The\u00a0 following are boxplots representing the daily high temperatures in each city over the\u00a0 course of a year.2\r\n\r\n\"A\r\n\r\nPart A: Which city has the greatest variability in the data? Explain what this means\u00a0 about the weather in this city.\r\n\r\nPart B: Which city has the least variability in the data? Explain what this means\u00a0 about the weather in this city.\r\n\r\n2 U.S. climate data. (2021). https:\/\/www.usclimatedata.com\/climate\/united-states\/us\r\n\r\n<\/div>\r\n
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Question 3<\/h3>\r\n3) For all three cities, the lowest temperatures are seen in December, January, and\u00a0 February. If your trip is in January, how will this affect what clothes you pack?<\/div>\r\n
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Question 4<\/h3>\r\n4) Practice evaluating variability one more time. Which of the following boxplots represents the data with the greatest variability?\r\n\r\n\"A<\/div>\r\nVariance From Summary Statistics\r\n
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Question 5<\/h3>\r\n5) When statistical software provides summary statistics of data, it usually provides\u00a0 standard deviation instead of variance. We can use that to compare the variability\u00a0 between groups.\r\n\r\nLook at the following summary statistics for two groups of data. Which group has\u00a0 more variability? Explain.\r\n\r\n\r\n\r\n\r\n\r\n<\/div>\r\n
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Question 6<\/h3>\r\n6) This example uses four groups instead of two and compares SAT scores in different\u00a0 regions of the United States.\r\n\r\nPart A: Look at the following summary statistics. Which region has the most variability? Explain.\r\n\r\nPart B: Which region has the least variability? Explain.\r\n\r\nPart C: In order for an ANOVA to be appropriate, it is recommended that the largest\u00a0 standard deviation be no more than two times the smallest standard\u00a0 deviation when the sample sizes are equal.\r\n\r\nWould these groups meet that recommendation for using an ANOVA to\u00a0 compare means?\r\n\r\n<\/div>\r\nInterpreting ANOVA Hypotheses\r\n\r\nWhen conducting an ANOVA, the null and alternative hypotheses can be written as:\r\n