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Statistics and Statistical Programming (Spring 2019)/Problem Set: Week 6
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== Programming Challenges == We're going to evaluate and replicate the analysis done in this paper: : Lagakos, S., & Mosteller, F. (1981). A case study of statistics in the regulatory process: the FD&C Red No. 40 experiments. ''Journal of the National Cancer Institute'', 66(1), 197β212. [[https://www.gwern.net/docs/statistics/1981-lagakos.pdf PDF]] : '''PC0.''' Download the dataset by clicking through on the "Red Dye Number 40" link on [http://college.cengage.com/mathematics/brase/understandable_statistics/7e/students/datasets/owan/frames/frame.html this webpage]. You'll find that the it's not in an ideal setup. It's an Excel file (XLS) with a series of columns labeled X1.. X4. The format is not exactly tabular. If you look at the website with the data and/or Table 1 in the paper you should be able to figure out what each column stands for. : '''PC1.''' Load the data into R. Now get to work on reshaping the dataset. I think a good format would be a data frame with two columns: <code>group</code> and <code>weeks_alive</code>. : '''PC2.''' Create summary statistics and visualizations for each group. These visualizations should both (a) give you a visual sense of the shape of the data and relationships between groups and (b) the degree to which the assumptions for t-tests and ANOVA hold. What is the global mean of your dependent variable? : '''PC3.''' Estimate an ANOVA analysis using <code>aov()</code> to see if there is a difference between the groups. Be ready to report, interpret, and discuss the results in substantive terms. : '''PC4.''' After performing an ANOVA analysis, people sometimes do t-tests between the groups. Do a t-test between mice with ''none'' RD40 and mice with ''any'' (i.e., at least a small amount). Next, run a t-test between the group with a high dosage and control group. How would you go about doing it using formula notation? Be ready to report, interpret, and discuss the results in substantive terms. How should you interpret p-values if you do these tests after an ANOVA analysis?
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