Editing Statistics and Statistical Programming (Fall 2020)/pset6

<small>[[Statistics_and_Statistical_Programming_(Fall_2020)#Week_9_.2811.2F10.2C_11.2F12.29|← Back to Week 9]]</small>

== Programming challenges (and statistical questions) ==

This week's programming challenges are all about analyzing continuous data. For most of this, I'd like you to replicate some the analysis done in this paper (note: I do not think you need to read it deeply to answer the questions below):

: 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]]

Overall, the goal of this research was to understand whether/how doses of red dye number 40 affect the survival of mice (and, by extension, humans).

=== PC1. Download, import, and reshape the data ===

* 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 particularly "tidy"). 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.
* Import the data into R and 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. Summarize the data === 
Using the two columns you just created, create summary statistics and visualizations for the dataset as a whole and for each of the groups. These descriptive analyses should give you a sense of the shape of the data and relationships across groups.

==== SQ1. Discuss your descriptive analysis ====
Be sure to interpret anything noteworthy.

==== SQ2. State hypotheses ====
The plan here is to use ANOVA to evaluate whether there is a difference in survival time between the groups and then t-tests to compare the average survival times across some specific groups (see PC4 below for more details on which groups). State null and alternative hypotheses that correspond to these tests.

==== SQ3. Address assumptions for the tests ====
Identify any assumptions you may need to make to conduct the ANOVA analysis and t-tests. Do these tests seem appropriate here? Why (not)?

=== PC3. Replicate the ANOVA analysis ===
Estimate an ANOVA analysis using <code>aov()</code> to test the global hypothesis of a difference between the groups.
==== SQ4. Report and interpret your results ====
Make sure to call <code>summary()</code> on the output of your <code>aov()</code> command. 

=== PC4. Estimate differences in means ===
After performing an ANOVA, people sometimes do t-tests between specific groups to test/estimate differences-in-means. In this case, you should do a t-test on the average survival time of 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. 

==== SQ5. Report and interpret your results ==== 

== Empirical paper questions ==

We'll continue our apparent focus on blogs with the following questions about the Sweetser and Metzgar paper.

=== EQ1. Interpret the results re: RQ4 ===
(a) What is the unit of analysis? What is the dependent variable? The independent variable? What are the levels or groups of being compared in the ANOVA?<br>
(b) Clearly State the null hypothesis being tested. What is the alternative hypothesis? <br>
(c) Summarize or restate the results in statistical terms. Explain what these results mean in substantive terms.<br>
(d) How convincing do you find these results? What should we be taking away?

=== EQ2. Interpret the results re: RQ5 ===
Answer the same (a)-(d) questions as you did for RQ4 above, but with RQ5.

=== EQ3. Interpret the results re: RQ6 ===
Answer the same (a)-(d) questions as you did for RQs 4-5 above, but with RQ6.