CT 3 stat 156

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Colorado State University, Global Campus *

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Statistics

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Feb 20, 2024

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1 Probabilities of Graduation and Publication Gage Korell Colorado State University-Global Stat-156 Mary Dereshiwsky 1/11/2024

2 Probabilities of Graduation and Publication In this study, three universities are keeping a close eye on a group of professors to see how many students attend their classes, how many of these students graduate, and if any publish their work. The goal is to understand the impact these professors have on their students' academic journeys, exploring aspects like enrollment, graduation rates, and the publication of students' work. This research aims to uncover the diverse ways these professors contribute to their student's academic success and shed light on the broader effects of effective teaching in higher education. This study is designed with the overarching goal of uncovering the probabilities associated with student graduation and publication across various professors' courses. Although establishing a direct causal relationship between a professor and student outcomes may prove challenging, our approach involves a comprehensive ranking of professors. This ranking is derived from the diverse probabilities identified within the datasets, as elaborated upon in the subsequent sections. By meticulously analyzing these probabilities, we aim to shed light on the subtle dynamics between professors and student achievements, exploring potential patterns and trends that contribute to our understanding of the educational landscape. Through this research, we seek to provide valuable insights into the multifaceted aspects of student success and scholarly contributions within the academic realm. The Overall Probability of Students Graduating at Each University The study examines the graduation probabilities of students across three distinct universities: WWCC, EWCC, and NWCC. The calculated probabilities for student graduation are as follows: WWCC: 0.86452

3 EWCC: 0.85264 NWCC: 0.88102 Through this it becomes evident that NWCC boasts the highest likelihood of student graduation, standing at 0.88102. In contrast, EWCC exhibits the lowest probability among the three universities in terms of student graduation, with a probability of 0.85264. This disparity in graduation probabilities provides valuable insights into the academic dynamics at each university, suggesting variations in the factors influencing student success and completion. The subsequent sections of this study delve into a detailed analysis of these probabilities, aiming to unravel the underlying factors contributing to the observed trends in graduation outcomes across WWCC, EWCC, and NWCC. The Overall Probability of Students Having a Publication at Each University This segment of the study investigates the probabilities of students achieving publications across three distinct universities: WWCC, EWCC, and NWCC. The calculated probabilities for students having publications are outlined as follows: WWCC: 0.32193 EWCC: 0.31640 NWCC: 0.31090 A closer look of these probabilities reveals that WWCC exhibits the highest likelihood of students achieving publications, with a probability of 0.32193. Following closely is EWCC, with a substantial probability of 0.31640. In contrast, NWCC presents the lowest probability among the three universities in terms of students having publications, standing at 0.31090. This variation in publication probabilities prompts further exploration into the academic and research environments at each university, aiming to unveil the distinctive factors influencing students' scholarly contributions. Subsequent sections of this study will show an in-depth analysis of these probabilities, shedding light on the underlying dynamics contributing to the observed trends in student publications across WWCC, EWCC, and NWCC.

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4 The Overall Probability of Students that will have a Publication and Graduate This section of the study delves into the nuanced relationship between students' graduation and the subsequent probability of them having a publication at three distinct universities: WWCC, EWCC, and NWCC. The calculated probabilities for students having publications given that they graduated are as follows: WWCC: 0.32193 EWCC: 0.31640 NWCC: 0.31090 A detailed examination of these probabilities unveils intriguing patterns. WWCC stands out with the highest probability of students having a publication after graduation, registering at 0.32193. Following closely is EWCC, where the probability of students having a publication post-graduation is notably high at 0.31640. In contrast, NWCC presents the lowest probability among the three universities concerning students having publications given that they graduated, with a probability of 0.31090. This intricate interplay between graduation and subsequent scholarly contributions prompts a deeper exploration into the academic landscapes of WWCC, EWCC, and NWCC. Subsequent sections of this study will dissect these probabilities, shedding light on the underlying dynamics influencing students' scholarly achievements post-graduation at each university. Probability of a Student Graduating from Each Professor This segment of the study undertakes a detailed examination of the probability of students graduating under the guidance of various professors across three distinct universities: WWCC, EWCC, and NWCC. The probabilities for student graduation associated with specific professors are outlined in the table below:

5 These figures illuminate the diverse landscape of graduation probabilities associated with different professors. Notably, C.F. Viney, D.S. Smith, and D.R. Jones emerge as the top- performing professors from WWCC, EWCC, and NWCC, respectively, boasting the highest probabilities of student graduation. Specifically, C.F. Viney leads with an impressive probability of 0.99038, followed closely by D.S. Smith at 0.98913, and D.R. Jones with a commendable probability of 0.96986. Conversely, a contrasting analysis reveals professors with the lowest probabilities of guiding students to graduation at each university: WWCC: Professor W.H. Greiner with a probability of 0.75015 EWCC: Professor I.A. Frank with a probability of 0.78000 NWCC: Professor P.R. Neighbors with a probability of 0.75012 These findings not only provide insights into the differential impacts of professors on student graduation rates but also pave the way for further exploration into the factors influencing these probabilities. Subsequent sections will delve into the implications of professor-student

6 dynamics, shedding light on the intricacies of student success across various academic mentors at WWCC, EWCC, and NWCC. Probability of a Student Having a Publication for Each Professor The study further explores the realm of student publications by scrutinizing the probabilities associated with different professors across three distinguished universities: WWCC, EWCC, and NWCC. The probabilities for students having publications under the mentorship of specific professors are meticulously detailed in the table below: This breakdown highlights the variances in publication probabilities tied to distinct professors. Notably, L.M. Edwards, Professor D.S. Smith, and Professor T.J. Black emerge as the top-performing professors from WWCC, EWCC, and NWCC, respectively, boasting the highest probabilities of students having publications. Specifically, L.M. Edwards leads with a substantial probability of 0.49002, followed closely by Professor D.S. Smith at 0.42609, and Professor T.J. Black with a commendable probability of 0.46494.

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7 Furthermore, a cross-examination reveals the professors with the lowest probabilities of guiding students towards publications at each university: WWCC: Professor E.A. Thomas with a probability of 0.21522 EWCC: Professor S.D. Gundel with a probability of 0.21588 NWCC: Professor C.R. Heines with a probability of 0.22124. These findings offer nuanced insights into the distinctive impacts of professors on student publication rates and pave the way for further exploration into the factors influencing these probabilities. Subsequent sections will delve into the implications of professor-student dynamics, unraveling the intricacies of student achievements in publications across diverse academic mentors at WWCC, EWCC, and NWCC. The Probability of a Student Having a Publication Given that they Graduated The study further scrutinizes the intersection of student graduation and subsequent publications by evaluating the probabilities linked to different professors across three distinguished universities: WWCC, EWCC, and NWCC. The nuanced relationship between student graduation and the likelihood of subsequent publications is meticulously detailed in the table below:

8 This breakdown unveils the varying probabilities associated with student publications given their graduation under the guidance of specific professors. L.M. Edwards, Professor D.S. Smith, and Professor T.J. Black stand out as the top-performing professors from WWCC, EWCC, and NWCC, respectively, demonstrating the highest probabilities of students having publications after graduating. Notably, L.M. Edwards leads with a substantial probability of 0.49002, followed closely by Professor D.S. Smith at 0.42609, and Professor T.J. Black with a commendable probability of 0.46494. Lastly, comparing analysis reveals the professors with the lowest probabilities of guiding students towards publications given their graduation at each university: WWCC: Professor E.A. Thomas with a probability of 0.21522 EWCC: Professor S.D. Gundel with a probability of 0.21588 NWCC: Professor C.R. Heines with a probability of 0.22124 It is important to note that the probability of a student having a publication, given that they graduated, is not mutually exclusive and is inherently conditional on the student having successfully graduated. This nuanced exploration delves into the interconnected dynamics of student achievement, shedding light on the conditional probabilities associated with graduation and subsequent scholarly publications under the mentorship of distinct professors at WWCC, EWCC, and NWCC. Professor Ranking at Each University The examination of professor rankings across three universities provides a nuanced understanding of their performance based on critical parameters such as the probability of graduated students (P(G)), publications (P(P)), publications given that the student graduated (P(P|G)), and the overall ranking(See Tables Below).

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10 Each university's professorial lineup exhibits unique strengths and areas of expertise. Noteworthy individuals emerge as leaders in specific categories, elucidating their distinct contributions to student success and scholarly achievements. For instance, at WWCC, professors E.A. Thomas, R.H. Doughty, and I.D. Jackson secured the top overall rankings, showcasing their comprehensive impact. Similarly, S.D. Gundel, J.A. O’Dell, and J.P. Trost lead the way at EWCC, while C.R. Heines, P.R. Neighbors, and P.T. Grey demonstrate excellence at NWCC. This thorough analysis unveils the multifaceted strengths of professors at each institution, fostering a deeper understanding of their role in shaping academic outcomes. Conclusion The data analysis we conducted offers valuable insights into the professors and universities with the highest chances of students graduating, publishing, and achieving publications post-graduation. Additionally, it highlights those with the lowest probabilities for graduation and publication after graduating. What's intriguing is the similarity between the probabilities of publication and publication after graduation. The numbers show a consistent pattern, suggesting a uniform likelihood of publication regardless of graduation status. This

11 finding adds an interesting dimension to our understanding of academia, indicating a potential balance in the factors influencing student publications across different universities and professors.

12 Resources OpenStax. (2019). Introductory statistics . OpenStax College. https://cnx.org/contents/MBiUQmmY@23.21:kcV4GRqc@17/Preface

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