statistics project ideas for college students

statistics project ideas for college students

Innovative Statistics Project Ideas for College Students

1. Introduction to Statistics Projects

The ideas assembled here have been developed to start conversations not only with students and instructors but also with those individuals, not on the math track, who would generally benefit from developing an understanding of these concepts through experiential learning opportunities. Not all questions are perfect for such activities, but we (the community of statistics educators and practitioners) should not limit our students through our own predetermination of what is or is not a question. We can do so by encouraging students, and others, to express their own questions and then really address those from their creativity. I hope that this resource will provide the conversation starter and enable others to develop similar (read, better) resources. I’ll be sincerely grateful for any feedback and ideas for further expansions.

It is common for students in college and high school to think of data as a fixed entity where the goal with research is to “go and get data” from some external “document” to bring back for analysis. In this fixed data understanding, students fail to appreciate the data generation process and how data can be manipulated through random sampling. From this, students fail to grasp the difference between the process, descriptive statistics, and inferential statistics methods. To help students understand this foundational issue, I’ve created a set of ideas for creative statistics projects which are available on the blog. Below is taken directly from the post and includes both pre/post notes and content from the activity.

2. Exploratory Data Analysis and Visualization

Possible research projects: 1. Use color and shape to create multidimensional data visualizations that will represent the most interesting or salient features of student responses to a series of concept-construction tasks. 2. Compare graphical representations of correct vs. incorrect responses to data visualizations. 3. Use multidimensional data visualizations to explore patterns of item difficulty and item discrimination between correct and incorrect item responses. 4. Examine in greater detail how the mathematical structure of concept-construction tasks, in which students are asked to construct a particular numerical value or concept by selecting a numerical response, can be used to gain insight into patterns of student mathematical reasoning. 5. Build out a pedagogical tool designed to provide teachers real-time information on students’ level of learning during virtual play sessions. Teachers can use the information to inform their instructional practice, providing more targeted feedback.

In the context of educational data mining, exploratory data analysis is the process of uncovering underlying relationships within data collected by a pedagogical tool, which yields insights into the specific learning processes that unfold within the data. This understanding can be especially useful when compared to other subject domains because the nature and scale of the observed conceptual development has the potential to illuminate well-understood theories about the nature of mathematics learning. Data visualizations play a crucial role in managing and making sense of the massive amounts of information produced by educational video games.

3. Hypothesis Testing and Statistical Inference

1. Collect existing data and write survey questions to investigate a particular topic. 2. Design your own study with respect to any topic of interest (and collect data). 3. Adjust and analyze data from an existing study, or analyze raw data from a newly designed study.

Students often learn the concept behind hypothesis testing and statistical inference in introductory statistics courses, but they may not appreciate the critical thinking behind selecting an appropriate test, analyzing whether the data meet the conditions to use the test, carrying out the test, and interpreting the results. Moreover, in many basic statistics courses, students learn only the most common test statistics for means (t and z), counts (Chi-Square), and proportions. In fact, there are many different test statistics available for different hypothesis tests depending on the nature of your data and question, such as the Wilcoxon Rank Sum, Mann Whitney U, and Shapiro-Wilk tests for two independent, non-normally distributed data, the sign test, Wilcoxon signed rank, and regression test for two dependent, non-normally distributed data, and the Fisher Exact test for two dependent binary or categorical data.

4. Advanced Statistical Modeling Techniques

4.2. Mixture Models A natural target of students with a background in statistical computations should involve statistical models that go beyond the standard methods one learns early in a data analysis course or even in an elementary statistical modeling course. Mixture models are a natural candidate for this type of project; in particular, they can be used to make modest improvements to ordinary general linear models by incorporating a non-zero probability of having a zero response which the generalized linear model would conceptually struggle to articulate. Mixture models are generally models in which the sample is composed of two or more sub-samples each would ideally be fit with its own statistical model; the mixing of the base models is achieved by weighting their likelihoods.

4.1. Bayesian Analysis Also a frequent project suggestion at this level, students could explore Bayesian statistical methodology and apply models in a data analysis. Tools such as JAGS and Stan can make fitting Bayesian models an easier task, especially for routine models, and offer free projects flexibility in terms of computational requirements. In particular, your students might be encouraged to leverage existing software to construct custom prior distributions or other more flexible elements of Bayesian inference.

5. Conclusion and Future Directions

Plus, researchers may consider making clear the connection between the activity and the learning goals and corresponding theorems and concepts, so that teaching and learning both statistical themes can occur in courses beyond mathematical ones and be assessed. In particular, we will explore how to grade data analysis and statistics projects fairly and encourage active learning on concepts such as average, probability choices, permutation, conditional probability, random variables, binomial, and approximately normal distributions. Although project-based learning has pointed instruction for students previously in college mathematics, when teaching and learning innovations can be used for first college courses in data analysis and statistics. Our materials aim to make the concepts meaningful and help students enjoy their experience in the process.

Clearly, data analysis and statistics topics engage college students as well as adult learners in a wide variety of different mathematical and non-mathematical programs and courses. Beyond introductory college statistics, these twelve projects may be useful recruitment tools to attract and retain a strong, diverse student population in such settings that are not solely mathematics and administration-driven. Future directions in working with the innovative statistics as data analysis projects include incorporating these materials into pre-collegiate classrooms as well as other undergraduate and graduate courses.