MS’25 Research Project

The Research Project

There are two main purposes to this term project. The more-important purpose is to give you the opportunity to add to your portfolio. When finished with this project, you will have something concrete to show your future employers or graduate school departments. Complementing this over-arching purpose, this project helps y’all perform statistical research.

Briefly, you will select one of the Normality test options below and compare that test to the Shapiro-Wilk test in terms of coverage and power. The entire project will produce the following graded components:

Options for the Project

The following are options for the course project. They are all Normality tests. The R package(s) providing that test is given in brackets.

⭐	Anderson-Darling	[`nortest`]
⭐	Anscombe-Glynn test of kurtosis	[`moments`]
⭐	Cramér-von Mises test	[`nortest`]
⭐	D’Agostino’s test of skewness	[`moments`]
⭐	D’Agostino-Pearson omnibus test	[`Rita`]
⭐	Jarque-Bera test	[`tseries`]
⭐	Lilliefors (Kolmogorov-Smirnov) test for normality	[`nortest`]
⭐	Pearson chi-square test for normality	[`nortest`]
⭐	Shapiro-Francia test	[`nortest`]

If you have a different Normality test that is interesting to you, and if you want to test that test, drop by and let me know. I will most likely approve the change.

The Parts of the Course Project

The following explain the parts of the course project in greater detail. It is incumbent upon you to fully understand the expectations… including their due dates (see the calendar).

The Class Presentation

The purpose of the presentation is to convey your research to the audience in a meaningful manner. I thoroughly expect you to have professional-looking slides (PowerPoint or Google Slides or whatever). Part of this grade covers the quality of the slides. A part of this grade covers the logic of the presentation. A part of this grade covers your poise in front of the class.

The presentation should tell a story.

The Research Paper

The research paper needs to be as long as it needs to be. However, I expect it to be somewhere around 10 pages, including graphics and your reference list (use a well-known, standard style). Here is a list of the sections that I expect in the paper (and their particular purposes).

Introduction

The final version of the introduction should be written last… after the conclusion. When I write, I start with a very sketchy introduction that lays out what I want to cover in the paper. Then, when I finish the conclusion, I delete the first introduction and rewrite it correctly.

The final introduction should be two paragraphs long. The first paragraph builds interest in the topic. Its last sentence is the research question. The second paragraph summarizes the rest of the paper. The introduction should be able to stand alone. I should be able to read the introduction and know what you did and what you found out (the answer to your research question).

Literature Review

In general, the purpose of this section is to convey the story of the question. For this research paper, you will show what you know about the Shapiro-Wilk test and what you know about your Normality test. I would expect the first half of this section being about Shapiro-Wilk; the second, your Normality test.

Data and Analysis

What are you trying to accomplish? How will you do this? Give the specifics for both your coverage and your power analysis. Explain how these specifics will test coverage and power.

Results and Discussion

What are the results from your analysis? Which of the two Normality tests is better? Under what circumstances is each better?

Conclusion

This section introduces NOTHING new to the paper. Its sole purpose is to summarize your paper. It should be a couple of paragraphs long. The first for the literature review. The second for the data, analysis, and results.

Finally, the very last paragraph examines the entire research process and evaluates it in terms of weaknesses, strengths, and future endeavors. What would you do differently in the future? What questions remain open?

General Expectations

This is a list of general expectations for this paper. They are a combination of what should always be done when doing research and what is specific to this project paper.

This paper must be typed nicely in LaTeX.
If you have a figure (or table) in your paper (and you definitely need to have several), then you need to ensure it is at the top of the page, with an identifier (e.g., Table 2), with a caption that describes the figure/table, and with a description in the text (with a reference to the figure/table).
You will be doing library research because what you are covering is not “general knowledge.” This means you must cite (in your prose) and reference (at the end on its own page/s) the sources of your information.
Limit yourself to legitimate, academic sources. Encyclopedias, dictionaries, and other tertiary-sources should be ignored by you… as should commercial sources like History, ThoughtCo, and Chegg. Find your information in primary (the original official source) and secondary sources (academic work that summarizes several primary and secondary sources).
BibTeX is helpful in properly formatting your citations and reference list. The best BibTeX style for this course may be either the general alpha or the one used by the Biometrika journal, biometrika (but, if you have a favorite, please use that one). The LaTeX link at the very top of this page provides more information on BibTeX. I encourage you to use it. While it may seem to be more trouble than it is worth, knowing how to use BibTeX will probably save you time in the long-run.
- I suggest you start a bib file early and add sources to it as you go. There is an example one on the LaTeX site.

Mathematical Statistics, II