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Statistics in Education: Contributions to Teaching and Data Analysis
In this dissertation we present a compilation of the research conducted during the author’s doctoral program. In the first part, we discuss a case study regarding the impact of scholar-ships on student success at Oregon State University (OSU). Specifically, we look at the grad-uation and retention rates and aim to determine how the amount of financial aid provided to the students impacts these metrics, especially those who belong to vulnerable student groups.
In the case study, we analyze data from first-time full-time (FTFT) freshmen that enrolled at OSU between 2011 and 2013. Using statistical models we first quantify and characterize the relationship between the amount of financial aid received by the students and the corre-sponding retention and graduation rates. As expected, the results show that the probabilities of retention and graduation increase as the amount of gift aid increases.
We find that financial aid seems to have a greater impact on first year students. Further-more, we are able to characterize how these probabilities change when comparing students from different demographic groups. We find that these changes are more noticeable when looking at students in groups determined by Pell-eligibility, first-generation student status and financial need, even after accounting for metrics of student performance.
We also discuss the problem of developing accurate models to predict the probability of retention and graduation based on the amount of financial aid offered to students and other relevant information. Such predictive models can be potentially used to guide policies and determine thresholds for scholarship amounts required to achieve the desired levels of grad-uation and retention rates at the university. Moreover, these models can be used to close achievement gaps for students from traditionally under-privileged backgrounds.
We discuss the technical problem of binary classification with an imbalanced response vari-able and overlap in the feature space. These data difficulties present a challenge to the development of good predictive models for classification. The development of solutions to this problem is an area of active research in statistical and machine learning. In order to contribute a solution to this problem we first use simulations to characterize the impacts of imbalance and overlap in a variety of scenarios. The results of the simulation study are used in the creation of our novel algorithm for correcting the technical problem. Upon revisiting the predictive component of our practical problem on student success we found evidence of improved performance in certain cases where our algorithm was applied.
The second part of the dissertation concerns the development and expansion of pedagogical practices for teaching statistical methods in higher education. Specifically, we discuss simple bootstrap methods that are often taught in introductory statistics courses. Bootstrapping and other resampling methods are progressively appearing in the textbooks and curricula of courses that introduce undergraduate students to statistical methods.
Some simple bootstrap-based inferential methods have more relaxed assumptions than their traditional counterparts possibly making it difficult to communicate their importance to students. Students and instructors of introductory statistics courses who are made aware of differences in the performance of these methods will better understand the importance of these assumptions. We detail some of the assumptions that the simple bootstrap relies on when used for uncertainty quantification and hypothesis testing.
We emphasize the importance of these assumptions by using simulations to investigate the performance of these methods when they are or are not met. We also discuss software options for introducing undergraduate students to these bootstrap methods including the newly developed R package bootEd.
The individual parts of this dissertation fall under the unifying theme of statistics in educa-tion. The results of our case study and our novel algorithm contribute to the use of statistics in the education sector. Meanwhile our pedagogical research on the bootstrap contributes to the teaching of statistics in the education sector. The ideas presented in this dissertation can, however, be extended to improve the teaching of subjects other than statistics and the analysis of data generated outside of educational settings. This research could also moti-vate future efforts to increase the functionality of institutions of education, which are quite foundational to a progressive and ethical society