1. Before computers were widespread, almost all risk analysis was done without simulation. Therefore, only a handful of scenarios could be formulated to understand the risk of a decision. Typically, a best-case and worst-case scenario was determined and decisions were based on these two scenarios. What are some of the drawbacks of this decision-making approach? Specifically, how does the capability to summarize 1,000s of simulated scenarios improve the approach?2. By definition, simulations require a distribution to be specified (e.g., normal, Poisson). Many times, the exact distribution to be used is unknown, so it must be assumed. One argument against using simulations to perform risk analysis is that there is no real benefit because the set of assumptions is simply shifted from assumed parameter values to assumed distributions of parameters. Comment on this argument and justify your opinions with reasons, facts, and examples.

The most common abuse of correlation in studies is to confuse the concepts of correlation with those of causation.Examples:No correlation: Height of a student and good gradesThe height of a student has no relationship to good grades.A correlation but not causation: Good SAT scores and good gradesMany times, you will find students with good SAT scores also making good grades, but good SAT scores do not cause good grades. Many times there are other variables, such as good study habits, that contribute to both.Causation: Study time and good gradesThe amount of time a student studies does CAUSE grades to be GOOD. Note: Causation statements are not the same as a statement in logic. For example: If you jump in a swimming pool, you will get wet. If you don’t jump in the swimming pool, you will not get wet. This will occur all the time if the pool is full of water. Causation is a little different. If you study, you are not guaranteed good grades. If you don’t study, you are not guaranteed bad grades. We still can say that study time is one major cause of good grades. Assignment:Find an example of an article that that relates two variables. Is the article stating that the two variables are correlated or that they have a causal relationship? Does the article confuse correlation and causation? Discuss other variables that could contribute to the relationship between the variables.

Prompt We 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 identified Treat as the explanatory variable and Time 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 with your initial post.  Use StatCrunch to produce the descriptive statistics (a table containing the 5-number summaries for each comparison group). (directions) Copy and paste the StatCrunch output table into your initial post. 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 context 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? This is the side by side that I have made in question Summary statistics for AcuteT: Group by: Treat   Treat n Mean Variance Std. dev. Std. err. Median Range Min Max Q1 Q3     0 37 172.62162 6446.7973 80.29195 13.199915 173 393 48 441 114 211   1 38 183.65789 6782.1771 82.353974 13.359579 166.5 381 47 428 131 212   2 34 202.11765 10590.168 102.90854 17.648669 163.5 442 70 512 140 246