Editing Statistics and Statistical Programming (Spring 2019)/Problem Set: Week 6

== 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), 197–212. [[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?

== Statistical Questions from OpenIntro §6 ==

: '''SQ0.''' Any questions or clarifications from the OpenIntro text or lecture notes?
: '''SQ1.''' Exercise 6.12 on public opinion about cannabis legalization
: '''SQ2.''' Exercise 6.20 a continuation of 6.12 
: '''SQ3.''' Exercise 6.38 on translating a problem in English into statistical tests
: '''SQ4.''' Exercise 6.50 another voter/public opinion question

== Empirical Paper Questions ==

These questions are for the Buechley and Hill paper on LilyPad Arduino:

: '''EQ0.''' For ''Study 1'', let's focus on the statistical test:
:: (a) What is the unit of analysis? What is the dependent variable? The independent variable? What are groups being compared in the test? Is it a one-way or two-way design?
:: (b) Why not just summarize the results, like we did in week 2? Why bother with the statistical test? How do you decide when to use each statistical procedure?
:: (c) What is the null hypothesis being tested? What is the alternative hypothesis? 
:: (d) Summarize or restate the results in statistical terms. Explain what these results mean in substantive terms? How convincing do you find these results? What should we be taking away?


Now go back to the Shaw and Benkler paper from a few weeks ago:

: '''EQ1.''' Using the data from Table 3 and Figure 2:
:: (a) What statistical procedure produced the p-value in Table 3? What is the null hypothesis being tested?
:: (b) How convincing do you find these results? What are some reasons to be skeptical?
:: (c) Reproduce Figure 2 using the data in Table 3. One thing that's missing from that figure is error bars. Based on the reading from Reinhart §5, what type of error bars do you think you should use? Figure out how to calculate the error bars and figure out if they overlap? What does that tell us? (Bonus: figure out how to add error bars to the bar plot)
:: (d) Should we be concerned about the base rate fallacy described in Reinhart §4? Why or why not?