Are you interested in working with me doing a senior capstone project in probability or statistics? Here are some ideas! (and recommended courses to support them)
*NJ is on sabbatical for the 2024-2025 academic year and will not be the primary adviser for any senior projects during this time
Ask a research question that interests you, and analyze data to answer it! The trickiest part of this idea is often finding/collecting a rich and meaningful enough data set to use. Usually if the data set has multiple variables and is not trivial there are a number of different spins that could make this an interesting capstone project, including questions given below....
How will you treat missing data, and how does that affect the conclusions you make? (treatment of missing data could be an entire project in and of itself). For an introduction, start at p. 189 of Dancey, Reidy, & Rowe (2012) Statistics for the Health Sciences. Recommended prerequisites: Math/Stat 242 and preferrably Math/Stat 442 (487).
How will you handle colinearity (two predictors that are related) and how does that affect the conclusions you make? (Leah Foster-Koth, PLU Math class of 2021 studied this for her capstone with an emphasis on the differences between Type I, II, and III ANOVA analyses.) For an introduction see Chapter 5 of Keith (2006) Multiple Regression and Beyond. Recommended prerequisites: Math/Stat 242. Perhaps also Math/Stat 348 depending on the question. Students who take Math/Stat 442 (487) should not choose this because it will be covered in class.
How will you handle lack of independence (e.g., clustering, etc.) and how does that affect the conclusions you make? (This might be a great entry point for studying hierarchical linear modeling or time series analysis.) Recommended prerequisites: Math/Stat 242 and definitely also Math/Stat 442 (487). This is a challenging problem but accessible for strong students who took Statistical Modeling.
Explore influential points (e.g., outliers) and measures of their influence, and different approaches for dealing with them. See, for example, Section 9.5 of Weisberg (2014) Applied Linear Regression, and Section 6.4.4 of Prium (2011) Foundations and Applications of Statistics: An Introduction using R . Recommended prerequisites: Math/Stat 242 and possibly also Math/Stat 442 (487).
If your dataset has highly correlated predictors, you could use your dataset to illustrate the limitations of some classic stepwise model selection procedures. See, for example, Section 10.2.2 of Weisberg (2014) Applied Linear Regression, Section 3.3 of Kuiper & Sklar (2013) Practicing Statistics: Guided Explorations for the Second Course, p. 92- from Keith (2006) Multiple Regression and Beyond as well as p. 386- of Motulsky (2018) Intuitive Biostatistics. Recommended prerequisites: Math/Stat 242 and Math/Stat 442 (487), and preferrably Math/Stat 342.
2. Stein's Paradox. This is a somewhat more theoretical topic. A great podcast introducing Stein's paradox was given by Linear Digressions on their May 24, 2020 episode. Here is a paper on the topic that is co-authored by Brad Efron, so I expect it to be pretty good. Recommended prerequisite: Math 342.
3. Further exploration of Markov Chains, perhaps exploring two-step dependence or taking Connor Lemma's (PLU Math class of 2022) idea further investigating police stops activity with a more empirical approach. A friendly introduction to Markov chains can be found from Tolver's notes. Recommended prerequisite: Math/Stat 342.
4. Further exploration of the role of sample size in Chi-square tests. This would be an extension of Paige Balut's (PLU Math class of 2021) project analyzing deer in drought and looking at rules of thumb for sample size more deeply. Recommended prerequisites: Math/Stat 242 and Math/Stat 342 and Math/Stat 348 (at least concurrently)
5. Exploration of the phi-coefficient and solutions to the problems related to it. This would be new research into a measure of association for dichotomous variables and NJ would be interested in co-authoring a published paper on this topic. See this paper by Davenport and El-Sanhurry (1991: ask NJ if you need access) for a primer. Recommended prerequisite: Math 342 and perhaps 348 concurrently
6. Explore strategies for correcting for multiple comparisons/ multiple testing. A primer on the topic can be found in this Nature Journal resource. For other introductory resources see, for example, Section 11.2 of Cobb (1997) Introduction to Design and Analysis of Experiments as well as Chapter 22 of Motulsky (2018) Intuitive Biostatistics and Section 7.3.7 of Prium (2011) Foundations and Applications of Statistics: An Introduction Using R. Recommended prerequisites: Math/Stat 242 and perhaps Math/Stat 342.
7. Future Teachers: Oh gosh, there are heaps of open questions in statistics education and many of these could lead to publishable papers. Some of these questions are given below. Recommended prerequisites: Math/Stat 242 and perhaps others depending on the research question
What is a learning trajectory for statistical coding?
What is a learning trajectory for ethics in statistics and data science? What foundational topics must be known in order to discuss various ethical issues?
How can students learn about algorithmic modeling, and how does this interplay with their understanding of probabilistic modeling?
What are students' impressions/conceptions/perceptions of what statistics is, and how does this relate to the way they indentify with and learn in the discipline?
What does good discourse in an online statistics class look like? What types of questions best facilitate healthy discourse?
8. Check out some of the research projects at the Institute for the Quantitative Study of Inclusion, Diversity, and Equity (Qside) and see if anything piques your interest for further exploration: https://qsideinstitute.org/.
9. Check out NJ's Significance magazines on the shelves and tables in ERB. There are lots of articles that may spark your interest!
10. Burnt out? An easy, not very challenging project might be exploring the sign test for medians. I'm not sure this could earn an A grade (we'd need to discuss with capstone teacher).
Got an idea? Pitch it to NJ and ask! She might be able to support it or help you adjust it to a good, manageable project.
