QuestionProgress CheckUse this activity to assess whether you and your peers can:Use StatCrunch to create the appropriate visual display.Use StatCrunch to create the appropriate numerical summaries.Use the appropriate variables to analyze the data and answer the questions we are investigating.Use the appropriate visual display to summarize the data.Use the appropriate numerical summaries to analyze the data.Use appropriate statistical vocabulary to analyze the data and answer the questions we are investigating.ConClinical depression is a recurrent illness requiring treatment and often hospitalization. Nearly 50% of people who have an episode of major depression will have a recurrence within 2-3 years. Being able to prevent the recurrence of depression in people who are at risk for the disease would go a long way to alleviate the pain and suffering of patients.During the 1980’s the federal government, through the National Institutes of Health (NIH), sponsored a large clinical trial to evaluate two drugs for depression. There were 3 treatment groups. Patients received either Imipramine (Imip), Lithium (Li), or a Placebo (Pl). Researchers randomly assigned patients to one of the 3 treatment groups and followed them for 2-4 years to track any recurrences of depression.(Prien et al.,Archives of General Psychiatry, 1984).VariablesHospt: Which hospital the patient was from: Labeled 1, 2, 3, 5 or 6Treat: 0=Lithium; 1=Imipramine; 2=PlaceboOutcome: 0=Success 1=Failure (recurrence of depression)Time: Number of weeks until a recurrence (if outcome=1) or until study ended (if outcome=0)AcuteT: How long the patient was depressed before the start of the current study, measured in daysAge: Age in yearsGender: 1=Female 2=MaleDataIf you have not already done so, open the depression data set in the Stats at Cuyamaca College group on StatCrunch (directions – opens in a new tab).PromptWe will analyze the data to answer the second research question: Which of the drugs (if either)delayed the recurrence of depression longer relative to the placebo?In the previous lab-preparation activity, we identifiedTreat as the explanatory variable andTime as the response variable. We also determined that we will analyze the data using side-by-side boxplots and descriptive statistics (i.e. 5-number summaries since the graphs are boxplots).Make graphs and tables.Use StatCrunch to produce side-by-side boxplots. (directions)Embed your graphs into the box, and be sure to include the Alt . To recall how to embed a picture into a box, see the StatCrunch directions below.Use StatCrunch to produce the descriptive statistics (a single table containing the 5-number summaries for each comparison group). (directions)Copy and paste the StatCrunch output table into the box.Analyze the data: Compare the distributions for the treatment groups as demonstrated in Unit 2. For example, compare medians and intervals of typical values. Describe the shape and any outliers. Be sure to write your comparisons so the reader can understand the con of the numbers. For example, don’t just say the median is 30; instead, say something like this: on average patients taking the placebo relapsed in 30 days (Q2=30 days).Draw a conclusion : What can we conclude from your analysis? Did one drug successfully delay a relapse of depression better than the others? What evidence supports your conclusion?Summarize your conclusions in response to both research questions: In this lab you compared three treatments (two drugs and the placebo) using two different variables. In Part 1 you compared whether or not a relapse into depression occurred for each of the two drugs and the placebo. In Part 2 you compared the length of time until the next relapse for the two drugs and the placebo. What can you conclude in light of both analyses? Is one treatment better than the other? How does the data support your conclusion?MathStatistics and Probability MATH 160

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