phd thesis in statistics

Department of Statistics – Academic Commons Link to Recent Ph.D. Dissertations (2011 – present)

2022 Ph.D. Dissertations

Andrew Davison

Statistical Perspectives on Modern Network Embedding Methods

Sponsor: Tian Zheng

Nabarun Deb

Blessing of Dependence and Distribution-Freeness in Statistical Hypothesis Testing

Sponsor: Bodhisattva Sen / Co-Sponsor: Sumit Mukherjee

Elliot Gordon Rodriguez

Advances in Machine Learning for Compositional Data

Sponsor: John Cunningham

Charles Christopher Margossian

Modernizing Markov Chains Monte Carlo for Scientific and Bayesian Modeling

Sponsor: Andrew Gelman

Alejandra Quintos Lima

Dissertation TBA

Sponsor: Philip Protter

Bridgette Lynn Ratcliffe

Statistical approach to tagging stellar birth groups in the Milky Way

Sponsor: Bodhisattva Sen

Chengliang Tang

Latent Variable Models for Events on Social Networks

On Recovering the Best Rank-? Approximation from Few Entries

Sponsor: Ming Yuan

Sponsor: Sumit Mukherjee

2021 Ph.D. Dissertations

On the Construction of Minimax Optimal Nonparametric Tests with Kernel Embedding Methods

Sponsor: Liam Paninski

Advances in Statistical Machine Learning Methods for Neural Data Science

Milad Bakhshizadeh

Phase retrieval in the high-dimensional regime

Chi Wing Chu

Semiparametric Inference of Censored Data with Time-dependent Covariates

Miguel Angel Garrido Garcia

Characterization of the Fluctuations in a Symmetric Ensemble of Rank-Based Interacting Particles

Sponsor: Ioannis Karatzas

Rishabh Dudeja

High-dimensional Asymptotics for Phase Retrieval with Structured Sensing Matrices

Sponsor: Arian Maleki

Statistical Learning for Process Data

Sponsor: Jingchen Liu

Toward a scalable Bayesian workflow

2020 Ph.D. Dissertations

Jonathan Auerbach

Some Statistical Models for Prediction

Sponsor: Shaw-Hwa Lo

Adji Bousso Dieng

Deep Probabilistic Graphical Modeling

Sponsor: David Blei

Guanhua Fang

Latent Variable Models in Measurement: Theory and Application

Sponsor: Zhiliang Ying

Promit Ghosal

Time Evolution of the Kardar-Parisi-Zhang Equation

Sponsor: Ivan Corwin

Partition-based Model Representation Learning

Sihan Huang

Community Detection in Social Networks: Multilayer Networks and Pairwise Covariates

Peter JinHyung Lee

Spike Sorting for Large-scale Multi-electrode Array Recordings in Primate Retina

Statistical Analysis of Complex Data in Survival and Event History Analysis

Multiple Causal Inference with Bayesian Factor Models

New perspectives in cross-validation

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Doctoral Program

Program summary.

Students are required to

• master the material in the prerequisite courses ;
• pass the first-year core program;
• attempt all three parts of the qualifying examinations and show acceptable performance in at least two of them (end of 1st year);
• satisfy the depth and breadth requirements (2nd/3rd/4th year);
• successfully complete the thesis proposal meeting (winter quarter of the 3rd year);
• present a draft of their dissertation and pass the university oral examination (4th/5th year).

The PhD requires a minimum of 135 units. Students are required to take a minimum of nine units of advanced topics courses (for depth) offered by the department (not including literature, research, consulting or Year 1 coursework), and a minimum of nine units outside of the Statistics Department (for breadth). Courses for the depth and breadth requirements must equal a combined minimum of 24 units. In addition, students must enroll in STATS 390 Statistical Consulting, taking it at least twice.

All students who have passed the qualifying exams but have not yet passed the Thesis Proposal Meeting must take STATS 319 at least once each year. For example, a student taking the qualifying exams in the summer after Year 1 and having the dissertation proposal meeting in Year 3, would take 319 in Years 2 and 3. Students in their second year are strongly encouraged to take STATS 399 with at least one faculty member. All details of program requirements can be found in our PhD handbook (available to Stanford affiliates only, using Stanford authentication. Requests for access from non-affiliates will not be approved).

Statistics Department PhD Handbook

All students are expected to abide by the Honor Code and the Fundamental Standard .

Doctoral and Research Advisors

During the first two years of the program, students' academic progress is monitored by the department's Graduate Director. Each student should meet at least once a quarter with the Graduate Director to discuss their academic plans and their progress towards choosing a thesis advisor (before the final study list deadline of spring of the second year). From the third year onward students are advised by their selected advisor.

Qualifying Examinations

Qualifying examinations are part of most PhD programs in the United States. At Stanford these exams are intended to test the student's level of knowledge when the first-year program, common to all students, has been completed. There are separate examinations in the three core subjects of statistical theory and methods, applied statistics, and probability theory, which are typically taken during the summer at the end of the student's first year. Students are expected to attempt all three examinations and show acceptable performance in at least two of them. Letter grades are not given. Qualifying exams may be taken only once. After passing the qualifying exams, students must file for Ph.D. Candidacy, a university milestone, by the end of spring quarter of their second year.

While nearly all students pass the qualifying examinations, those who do not can arrange to have their financial support continued for up to three quarters while alternative plans are made. Usually students are able to complete the requirements for the M.S. degree in Statistics in two years or less, whether or not they have passed the PhD qualifying exams.

Thesis Proposal Meeting and Dissertation Reading Committee 

The thesis proposal meeting is intended to demonstrate a student's depth in some areas of statistics, and to examine the general plan for their research. In the meeting the student gives a 60-minute presentation involving ideas developed to date and plans for completing a PhD dissertation, and for another 60 minutes answers questions posed by the committee. which consists of their advisor and two other members. The meeting must be successfully completed by the end of winter quarter of the third year. If a student does not pass, the exam must be repeated. Repeated failure can lead to a loss of financial support.

The Dissertation Reading Committee consists of the student’s advisor plus two faculty readers, all of whom are responsible for reading the full dissertation. Of these three, at least two must be members of the Statistics Department (faculty with a full or joint appointment in Statistics but excluding for this purpose those with only a courtesy or adjunct appointment). Normally, all committee members are members of the Stanford University Academic Council or are emeritus Academic Council members; the principal dissertation advisor must be an Academic Council member. 

The Doctoral Dissertation Reading Committee form should be completed and signed at the Dissertation Proposal Meeting. The form must be submitted before approval of TGR status or before scheduling a University Oral Examination.

 For further information on the Dissertation Reading Committee, please see the Graduate Academic Policies and Procedures (GAP) Handbook section 4.8.

University Oral Examinations

The oral examination consists of a public, approximately 60-minute, presentation on the thesis topic, followed by a 60 minute question and answer period attended only by members of the examining committee. The questions relate to the student's presentation and also explore the student's familiarity with broader statistical topics related to the thesis research. The oral examination is normally completed during the last few months of the student's PhD period. The examining committee typically consists of four faculty members from the Statistics Department and a fifth faculty member from outside the department serving as the committee chair. Four out of five passing votes are required and no grades are given. Nearly all students can expect to pass this examination, although it is common for specific recommendations to be made regarding completion of the thesis.

The Dissertation Reading Committee must also read and approve the thesis.

For further information on university oral examinations and committees, please see the Graduate Academic Policies and Procedures (GAP) Handbook section 4.7 .

Dissertation

The dissertation is the capstone of the PhD degree. It is expected to be an original piece of work of publishable quality. The research advisor and two additional faculty members constitute the student's dissertation reading committee.

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Digital Commons @ USF > College of Arts and Sciences > Mathematics and Statistics > Theses and Dissertations

Mathematics and Statistics Theses and Dissertations

Theses/dissertations from 2023 2023.

Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani

Applied Analysis for Learning Architectures , Himanshu Singh

Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze

Theses/Dissertations from 2022 2022

New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana

Advances and Applications of Optimal Polynomial Approximants , Raymond Centner

Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty

On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly

Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He

Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias

Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi

A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman

Theses/Dissertations from 2021 2021

Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri

Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi

Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou

Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando

Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu

Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang

Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang

Theses/Dissertations from 2020 2020

Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi

Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun

Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu

On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman

Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek

Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen

Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan

Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop

On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink

Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang

Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala

Theses/Dissertations from 2019 2019

Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian

Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar

Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil

Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter

Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz

Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi

Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi

Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos

The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva

Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak

Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich

An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado

Power Graphs of Quasigroups , DayVon L. Walker

Theses/Dissertations from 2018 2018

Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed

Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai

A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah

Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa

Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields

Generalizations of Quandles and their cohomologies , Matthew J. Green

Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu

Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou

Human Activity Recognition Based on Transfer Learning , Jinyong Pang

Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham

Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel

Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova

Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang

Theses/Dissertations from 2017 2017

Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack

Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon

On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill

Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill

Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly

Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera

Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao

Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati

Dynamics of Multicultural Social Networks , Kristina B. Hilton

Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi

Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally

Patterns in Words Related to DNA Rearrangements , Lukas Nabergall

Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na

Schreier Graphs of Thompson's Group T , Allen Pennington

Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya

Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo

Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi

Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou

Theses/Dissertations from 2016 2016

A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea

Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery

Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman

On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr

Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim

Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano

Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure

Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru

Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park

Leonard Systems and their Friends , Jonathan Spiewak

Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun

Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu

Global Attractors and Random Attractors of Reaction-Diffusion Systems , Junyi Tu

Time Dependent Kernel Density Estimation: A New Parameter Estimation Algorithm, Applications in Time Series Classification and Clustering , Xing Wang

On Spectral Properties of Single Layer Potentials , Seyed Zoalroshd

Theses/Dissertations from 2015 2015

Analysis of Rheumatoid Arthritis Data using Logistic Regression and Penalized Approach , Wei Chen

Active Tile Self-assembly and Simulations of Computational Systems , Daria Karpenko

Nearest Neighbor Foreign Exchange Rate Forecasting with Mahalanobis Distance , Vindya Kumari Pathirana

Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data , Taysseer Sharaf

Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3 , Richard Alan Warner

Ensemble Learning Method on Machine Maintenance Data , Xiaochuang Zhao

Theses/Dissertations from 2014 2014

Properties of Graphs Used to Model DNA Recombination , Ryan Arredondo

Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability , Jonathan Burns

On the Classification of Groups Generated by Automata with 4 States over a 2-Letter Alphabet , Louis Caponi

Statistical Analysis, Modeling, and Algorithms for Pharmaceutical and Cancer Systems , Bong-Jin Choi

Topological Data Analysis of Properties of Four-Regular Rigid Vertex Graphs , Grant Mcneil Conine

Trend Analysis and Modeling of Health and Environmental Data: Joinpoint and Functional Approach , Ram C. Kafle

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Home > Statistics > Dissertations, Theses, and Student Work

Statistics, Department of

Department of statistics: dissertations, theses, and student work.

Examining the Effect of Word Embeddings and Preprocessing Methods on Fake News Detection , Jessica Hauschild

Exploring Experimental Design and Multivariate Analysis Techniques for Evaluating Community Structure of Bacteria in Microbiome Data , Kelsey Karnik

Human Perception of Exponentially Increasing Data Displayed on a Log Scale Evaluated Through Experimental Graphics Tasks , Emily Robinson

Factors Influencing Student Outcomes in a Large, Online Simulation-Based Introductory Statistics Course , Ella M. Burnham

Comparing Machine Learning Techniques with State-of-the-Art Parametric Prediction Models for Predicting Soybean Traits , Susweta Ray

Using Stability to Select a Shrinkage Method , Dean Dustin

Statistical Methodology to Establish a Benchmark for Evaluating Antimicrobial Resistance Genes through Real Time PCR assay , Enakshy Dutta

Group Testing Identification: Objective Functions, Implementation, and Multiplex Assays , Brianna D. Hitt

Community Impact on the Home Advantage within NCAA Men's Basketball , Erin O'Donnell

Optimal Design for a Causal Structure , Zaher Kmail

Role of Misclassification Estimates in Estimating Disease Prevalence and a Non-Linear Approach to Study Synchrony Using Heart Rate Variability in Chickens , Dola Pathak

A Characterization of a Value Added Model and a New Multi-Stage Model For Estimating Teacher Effects Within Small School Systems , Julie M. Garai

Methods to Account for Breed Composition in a Bayesian GWAS Method which Utilizes Haplotype Clusters , Danielle F. Wilson-Wells

Beta-Binomial Kriging: A New Approach to Modeling Spatially Correlated Proportions , Aimee Schwab

Simulations of a New Response-Adaptive Biased Coin Design , Aleksandra Stein

MODELING THE DYNAMIC PROCESSES OF CHALLENGE AND RECOVERY (STRESS AND STRAIN) OVER TIME , Fan Yang

A New Approach to Modeling Multivariate Time Series on Multiple Temporal Scales , Tucker Zeleny

A Reduced Bias Method of Estimating Variance Components in Generalized Linear Mixed Models , Elizabeth A. Claassen

NEW STATISTICAL METHODS FOR ANALYSIS OF HISTORICAL DATA FROM WILDLIFE POPULATIONS , Trevor Hefley

Informative Retesting for Hierarchical Group Testing , Michael S. Black

A Test for Detecting Changes in Closed Networks Based on the Number of Communications Between Nodes , Christopher S. Wichman

GROUP TESTING REGRESSION MODELS , Boan Zhang

A Comparison of Spatial Prediction Techniques Using Both Hard and Soft Data , Megan L. Liedtke Tesar

STUDYING THE HANDLING OF HEAT STRESSED CATTLE USING THE ADDITIVE BI-LOGISTIC MODEL TO FIT BODY TEMPERATURE , Fan Yang

Estimating Teacher Effects Using Value-Added Models , Jennifer L. Green

SEQUENCE COMPARISON AND STOCHASTIC MODEL BASED ON MULTI-ORDER MARKOV MODELS , Xiang Fang

DETECTING DIFFERENTIALLY EXPRESSED GENES WHILE CONTROLLING THE FALSE DISCOVERY RATE FOR MICROARRAY DATA , SHUO JIAO

Spatial Clustering Using the Likelihood Function , April Kerby

FULLY EXPONENTIAL LAPLACE APPROXIMATION EM ALGORITHM FOR NONLINEAR MIXED EFFECTS MODELS , Meijian Zhou

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PhD Program information

The Statistics PhD program is rigorous, yet welcoming to students with interdisciplinary interests and different levels of preparation. Students in the PhD program take core courses on the theory and application of probability and statistics during their first year. The second year typically includes additional course work and a transition to research leading to a dissertation. PhD thesis topics are diverse and varied, reflecting the scope of faculty research interests. Many students are involved in interdisciplinary research. Students may also have the option to pursue a designated emphasis (DE) which is an interdisciplinary specialization:  Designated Emphasis in Computational and Genomic Biology ,  Designated Emphasis in Computational Precision Health ,  Designated Emphasis in Computational and Data Science and Engineering . The program requires four semesters of residence.

Normal progress entails:

Year 1 . Perform satisfactorily in preliminary coursework. In the summer, students are required to embark on a short-term research project, internship, graduate student instructorship, reading course, or on another research activity. Years 2-3 . Continue coursework. Find a thesis advisor and an area for the oral qualifying exam. Formally choose a chair for qualifying exam committee, who will also serve as faculty mentor separate from the thesis advisor.  Pass the oral qualifying exam and advance to candidacy by the end of Year 3. Present research at BSTARS each year. Years 4-5 . Finish the thesis and give a lecture based on it in a department seminar.

Program Requirements

• Qualifying Exam

Course work and evaluation

Preliminary stage: the first year.

Effective Fall 2019, students are expected to take four semester-long courses for a letter grade during their first year which should be selected from the core first-year PhD courses offered in the department: Probability (204/205A, 205B,), Theoretical Statistics (210A, 210B), and Applied Statistics (215A, 215B). These requirements can be altered by a member of the PhD Program Committee (in consultation with the faculty mentor and by submitting a graduate student petition ) in the following cases:

• Students primarily focused on probability will be allowed to substitute one semester of the four required semester-long courses with an appropriate course from outside the department.
• Students may request to postpone one semester of the core PhD courses and complete it in the second year, in which case they must take a relevant graduate course in their first year in its place. In all cases, students must complete the first year requirements in their second year as well as maintain the overall expectations of second year coursework, described below. Some examples in which such a request might be approved are described in the course guidance below.
• Students arriving with advanced standing, having completed equivalent coursework at another institution prior to joining the program, may be allowed to take other relevant graduate courses at UC Berkeley to satisfy some or all of the first year requirements

Requirements on course work beyond the first year

Students entering the program before 2022 are required to take five additional graduate courses beyond the four required in the first year, resulting in a total of nine graduate courses required for completion of their PhD. In their second year, students are required to take three graduate courses, at least two of them from the department offerings, and in their third year, they are required to take at least two graduate courses. Students are allowed to change the timing of these five courses with approval of their faculty mentor. Of the nine required graduate courses, students are required to take for credit a total of 24 semester hours of courses offered by the Statistics department numbered 204-272 inclusive. The Head Graduate Advisor (in consultation with the faculty mentor and after submission of a graduate student petition) may consent to substitute courses at a comparable level in other disciplines for some of these departmental graduate courses. In addition, the HGA may waive part of this unit requirement.

Starting with the cohort entering in the 2022-23 academic year , students are required to take at least three additional graduate courses beyond the four required in the first year, resulting in a total of seven graduate courses required for completion of their PhD. Of the seven required graduate courses, five of these courses must be from courses offered by the Statistics department and numbered 204-272, inclusive. With these reduced requirements, there is an expectation of very few waivers from the HGA. We emphasize that these are minimum requirements, and we expect that students will take additional classes of interest, for example on a S/U basis, to further their breadth of knowledge. 

For courses to count toward the coursework requirements students must receive at least a B+ in the course (courses taken S/U do not count, except for STAT 272 which is only offered S/U).  Courses that are research credits, directed study, reading groups, or departmental seminars do not satisfy coursework requirements (for courses offered by the Statistics department the course should be numbered 204-272 to satisfy the requirements). Upper-division undergraduate courses in other departments can be counted toward course requirements with the permission of the Head Graduate Advisor. This will normally only be approved if the courses provide necessary breadth in an application area relevant to the student’s thesis research.

First year course work: For the purposes of satisfactory progression in the first year, grades in the core PhD courses are evaluated as: A+: Excellent performance in PhD program A: Good performance in PhD program A-: Satisfactory performance B+: Performance marginal, needs improvement B: Unsatisfactory performance First year and beyond: At the end of each year, students must meet with his or her faculty mentor to review their progress and assess whether the student is meeting expected milestones. The result of this meeting should be the completion of the student’s annual review form, signed by the mentor ( available here ). If the student has a thesis advisor, the thesis advisor must also sign the annual review form.

Guidance on choosing course work

Choice of courses in the first year: Students enrolling in the fall of 2019 or later are required to take four semesters of the core PhD courses, at least three of which must be taken in their first year. Students have two options for how to schedule their four core courses:

• Option 1 -- Complete Four Core Courses in 1st year: In this option, students would take four core courses in the first year, usually finishing the complete sequence of two of the three sequences.  Students following this option who are primarily interested in statistics would normally take the 210A,B sequence (Theoretical Statistics) and then one of the 205A,B sequence (Probability) or the 215A,B sequence (Applied Statistics), based on their interests, though students are allowed to mix and match, where feasible. Students who opt for taking the full 210AB sequence in the first year should be aware that 210B requires some graduate-level probability concepts that are normally introduced in 205A (or 204).
• Option 2 -- Postponement of one semester of a core course to the second year: In this option, students would take three of the core courses in the first year plus another graduate course, and take the remaining core course in their second year. An example would be a student who wanted to take courses in each of the three sequences. Such a student could take the full year of one sequence and the first semester of another sequence in the first year, and the first semester of the last sequence in the second year (e.g. 210A, 215AB in the first year, and then 204 or 205A in the second year). This would also be a good option for students who would prefer to take 210A and 215A in their first semester but are concerned about their preparation for 210B in the spring semester.  Similarly, a student with strong interests in another discipline, might postpone one of the spring core PhD courses to the second year in order to take a course in that discipline in the first year.  Students who are less mathematically prepared might also be allowed to take the upper division (under-graduate) courses Math 104 and/or 105 in their first year in preparation for 205A and/or 210B in their second year. Students who wish to take this option should consult with their faculty mentor, and then must submit a graduate student petition to the PhD Committee to request permission for  postponement. Such postponement requests will be generally approved for only one course. At all times, students must take four approved graduate courses for a letter grade in their first year.

After the first year: Students with interests primarily in statistics are expected to take at least one semester of each of the core PhD sequences during their studies. Therefore at least one semester (if not both semesters) of the remaining core sequence would normally be completed during the second year. The remaining curriculum for the second and third years would be filled out with further graduate courses in Statistics and with courses from other departments. Students are expected to acquire some experience and proficiency in computing. Students are also expected to attend at least one departmental seminar per week. The precise program of study will be decided in consultation with the student’s faculty mentor.

Remark. Stat 204 is a graduate level probability course that is an alternative to 205AB series that covers probability concepts most commonly found in the applications of probability. It is not taught all years, but does fulfill the requirements of the first year core PhD courses. Students taking Stat 204, who wish to continue in Stat 205B, can do so (after obtaining the approval of the 205B instructor), by taking an intensive one month reading course over winter break.

Designated Emphasis: Students with a Designated Emphasis in Computational and Genomic Biology or Designated Emphasis in Computational and Data Science and Engineering should, like other statistics students, acquire a firm foundation in statistics and probability, with a program of study similar to those above. These programs have additional requirements as well. Interested students should consult with the graduate advisor of these programs. 

Starting in the Fall of 2019, PhD students are required in their first year to take four semesters of the core PhD courses. Students intending to specialize in Probability, however, have the option to substitute an advanced mathematics class for one of these four courses. Such students will thus be required to take Stat 205A/B in the first year,  at least one of Stat 210A/B or Stat 215A/B in the first year, in addition to an advanced mathematics course. This substitute course will be selected in consultation with their faculty mentor, with some possible courses suggested below. Students arriving with advanced coursework equivalent to that of 205AB can obtain permission to substitute in other advanced probability and mathematics coursework during their first year, and should consult with the PhD committee for such a waiver.

During their second and third years, students with a probability focus are expected to take advanced probability courses (e.g., Stat 206 and Stat 260) to fulfill the coursework requirements that follow the first year. Students are also expected to attend at least one departmental seminar per week, usually the probability seminar. If they are not sufficiently familiar with measure theory and functional analysis, then they should take one or both of Math 202A and Math 202B. Other recommended courses from the department of Mathematics or EECS include:

Math 204, 222 (ODE, PDE) Math 205 (Complex Analysis) Math 258 (Classical harmonic analysis) EE 229 (Information Theory and Coding) CS 271 (Randomness and computation)

The Qualifying Examination 

The oral qualifying examination is meant to determine whether the student is ready to enter the research phase of graduate studies. It consists of a 50-minute lecture by the student on a topic selected jointly by the student and the thesis advisor. The examination committee consists of at least four faculty members to be approved by the department.  At least two members of the committee must consist of faculty from the Statistics and must be members of the Academic Senate. The chair must be a member of the student’s degree-granting program.

Qualifying Exam Chair. For qualifying exam committees formed in the Fall of 2019 or later, the qualifying exam chair will also serve as the student’s departmental mentor, unless a student already has two thesis advisors. The student must select a qualifying exam chair and obtain their agreement to serve as their qualifying exam chair and faculty mentor. The student's prospective thesis advisor cannot chair the examination committee. Selection of the chair can be done well in advance of the qualifying exam and the rest of the qualifying committee, and because the qualifying exam chair also serves as the student’s departmental mentor (unless the student has co-advisors), the chair is expected to be selected by the beginning of the third year or at the beginning of the semester of the qualifying exam, whichever comes earlier. For more details regarding the selection of the Qualifying Exam Chair, see the "Mentoring" tab.  

Paperwork and Application. Students at the point of taking a qualifying exam are assumed to have already found a thesis advisor and to should have already submitted the internal departmental form to the Graduate Student Services Advisor ( found here ).  Selection of a qualifying exam chair requires that the faculty member formally agree by signing the internal department form ( found here ) and the student must submit this form to the Graduate Student Services Advisor.  In order to apply to take the exam, the student must submit the Application for the Qualifying Exam via CalCentral at least three weeks prior to the exam. If the student passes the exam, they can then officially advance to candidacy for the Ph.D. If the student fails the exam, the committee may vote to allow a second attempt. Regulations of the Graduate Division permit at most two attempts to pass the oral qualifying exam. After passing the exam, the student must submit the Application for Candidacy via CalCentral .

The Doctoral Thesis

The Ph.D. degree is granted upon completion of an original thesis acceptable to a committee of at least three faculty members. The majority or at least half of the committee must consist of faculty from Statistics and must be members of the Academic Senate. The thesis should be presented at an appropriate seminar in the department prior to filing with the Dean of the Graduate Division. See Alumni if you would like to view thesis titles of former PhD Students.

Graduate Division offers various resources, including a workshop, on how to write a thesis, from beginning to end. Requirements for the format of the thesis are rather strict. For workshop dates and guidelines for submitting a dissertation, visit the Graduate Division website.

Students who have advanced from candidacy (i.e. have taken their qualifying exam and submitted the advancement to candidacy application) must have a joint meeting with their QE chair and their PhD advisor to discuss their thesis progression; if students are co-advised, this should be a joint meeting with their co-advisors. This annual review is required by Graduate Division.  For more information regarding this requirement, please see  https://grad.berkeley.edu/ policy/degrees-policy/#f35- annual-review-of-doctoral- candidates .

Teaching Requirement

For students enrolled in the graduate program before Fall 2016, students are required to serve as a Graduate Student Instructor (GSI) for a minimum of 20 hours (equivalent to a 50% GSI appointment) during a regular academic semester by the end of their third year in the program.

Effective with the Fall 2016 entering class, students are required to serve as a GSI for a minimum of two 50% GSI appointment during the regular academic semesters prior to graduation (20 hours a week is equivalent to a 50% GSI appointment for a semester) for Statistics courses numbered 150 and above. Exceptions to this policy are routinely made by the department.

Each spring, the department hosts an annual conference called BSTARS . Both students and industry alliance partners present research in the form of posters and lightning talks. All students in their second year and beyond are required to present a poster at BSTARS each year. This requirement is intended to acclimate students to presenting their research and allow the department generally to see the fruits of their research. It is also an opportunity for less advanced students to see examples of research of more senior students. However, any students who do not yet have research to present can be exempted at the request of their thesis advisor (or their faculty mentors if an advisor has not yet been determined).

Mentoring for PhD Students

Initial Mentoring: PhD students will be assigned a faculty mentor in the summer before their first year. This faculty mentor at this stage is not expected to be the student’s PhD advisor nor even have research interests that closely align with the student. The job of this faculty mentor is primarily to advise the student on how to find a thesis advisor and in selecting appropriate courses, as well as other degree-related topics such as applying for fellowships.  Students should meet with their faculty mentors twice a semester. This faculty member will be the designated faculty mentor for the student during roughly their first two years, at which point students will find a qualifying exam chair who will take over the role of mentoring the student.

Research-focused mentoring : Once students have found a thesis advisor, that person will naturally be the faculty member most directly overseeing the student’s progression. However, students will also choose an additional faculty member to serve as a the chair of their qualifying exam and who will also serve as a faculty mentor for the student and as a member of his/her thesis committee. (For students who have two thesis advisors, however, there is not an additional faculty mentor, and the quals chair does NOT serve as the faculty mentor).

The student will be responsible for identifying and asking a faculty member to be the chair of his/her quals committee. Students should determine their qualifying exam chair either at the beginning of the semester of the qualifying exam or in the fall semester of the third year, whichever is earlier. Students are expected to have narrowed in on a thesis advisor and research topic by the fall semester of their third year (and may have already taken qualifying exams), but in the case where this has not happened, such students should find a quals chair as soon as feasible afterward to serve as faculty mentor.

Students are required to meet with their QE chair once a semester during the academic year. In the fall, this meeting will generally be just a meeting with the student and the QE chair, but in the spring it must be a joint meeting with the student, the QE chair, and the PhD advisor. If students are co-advised, this should be a joint meeting with their co-advisors.

If there is a need for a substitute faculty mentor (e.g. existing faculty mentor is on sabbatical or there has been a significant shift in research direction), the student should bring this to the attention of the PhD Committee for assistance.

PhD Student Forms:

Important milestones: .

Each of these milestones is not complete until you have filled out the requisite form and submitted it to the GSAO. If you are not meeting these milestones by the below deadline, you need to meet with the Head Graduate Advisor to ask for an extension. Otherwise, you will be in danger of not being in good academic standing and being ineligible for continued funding (including GSI or GSR appointments, and many fellowships). 

†Students who are considering a co-advisor, should have at least one advisor formally identified by the end of the second year; the co-advisor should be identified by the end of the fall semester of the 3rd year in lieu of finding a Research Mentor/QE Chair.

Expected Progress Reviews: 

* These meetings do not need to be held in the semester that you take your Qualifying Exam, since the relevant people should be members of your exam committee and will discuss your research progress during your qualifying exam

** If you are being co-advised by someone who is not your primary advisor because your primary advisor cannot be your sole advisor, you should be meeting with that person like a research mentor, if not more frequently, to keep them apprised of your progress. However, if both of your co-advisors are leading your research (perhaps independently) and meeting with you frequently throughout the semester, you do not need to give a fall research progress report.

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Department of Statistics

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The department encourages research in both theoretical and applied statistics. Faculty members of the department have been leaders in research on a multitude of topics that include statistical inference, statistical computing and Monte-Carlo methods, analysis of missing data, causal inference, stochastic processes, multilevel models, experimental design, network models and the interface of statistics and the social, physical, and biological sciences. A unique feature of the department lies in the fact that apart from methodological research, all the faculty members are also heavily involved in applied research, developing novel methodology that can be applied to a wide array of fields like astrophysics, biology, chemistry, economics, engineering, public policy, sociology, education and many others.

Two carefully designed special courses offered to Ph.D. students form a unique feature of our program. Among these, Stat 303 equips students with the  basic skills necessary to teach statistics , as well as to be better overall statistics communicators. Stat 399 equips them with generic skills necessary for problem solving abilities.

Our Ph.D. students often receive substantial guidance from several faculty members, not just from their primary advisors, and in several settings. For example, every Ph.D. candidate who passes the qualifying exam gives a 30 minute presentation each semester (in Stat 300 ), in which the faculty ask questions and make comments. The Department recently introduced an award for Best Post-Qualifying Talk (up to two per semester), to further encourage and reward inspired research and presentations.

PhD Program Requirements

PhD Program Admissions Process

• PhD Admissions FAQ
• AM in Statistics
• Stat 300: Research in Statistics
• Stat 303: The Art and Practice of Teaching Statistics

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Cornell University does not offer a separate Masters of Science (MS) degree program in the field of Statistics. Applicants interested in obtaining a masters-level degree in statistics should consider applying to Cornell's MPS Program in Applied Statistics.

Choosing a Field of Study

There are many graduate fields of study at Cornell University. The best choice of graduate field in which to pursue a degree depends on your major interests. Statistics is a subject that lies at the interface of theory, applications, and computing. Statisticians must therefore possess a broad spectrum of skills, including expertise in statistical theory, study design, data analysis, probability, computing, and mathematics. Statisticians must also be expert communicators, with the ability to formulate complex research questions in appropriate statistical terms, explain statistical concepts and methods to their collaborators, and assist them in properly communicating their results. If the study of statistics is your major interest then you should seriously consider applying to the Field of Statistics.

There are also several related fields that may fit even better with your interests and career goals. For example, if you are mainly interested in mathematics and computation as they relate to modeling genetics and other biological processes (e.g, protein structure and function, computational neuroscience, biomechanics, population genetics, high throughput genetic scanning), you might consider the Field of Computational Biology . You may wish to consider applying to the Field of Electrical and Computer Engineering if you are interested in the applications of probability and statistics to signal processing, data compression, information theory, and image processing. Those with a background in the social sciences might wish to consider the Field of Industrial and Labor Relations with a major or minor in the subject of Economic and Social Statistics. Strong interest and training in mathematics or probability might lead you to choose the Field of Mathematics . Lastly, if you have a strong mathematics background and an interest in general problem-solving techniques (e.g., optimization and simulation) or applied stochastic processes (e.g., mathematical finance, queuing theory, traffic theory, and inventory theory) you should consider the Field of Operations Research .

Residency Requirements

Students admitted to PhD program must be "in residence" for at least four semesters, although it is generally expected that a PhD will require between 8 and 10 semesters to complete. The chair of your Special Committee awards one residence unit after the satisfactory completion of each semester of full-time study. Fractional units may be awarded for unsatisfactory progress.

Your Advisor and Special Committee

The Director of Graduate Studies is in charge of general issues pertaining to graduate students in the field of Statistics. Upon arrival, a temporary Special Committee is also declared for you, consisting of the Director of Graduate Studies (chair) and two other faculty members in the field of Statistics. This temporary committee shall remain in place until you form your own Special Committee for the purposes of writing your doctoral dissertation. The chair of your Special Committee serves as your primary academic advisor; however, you should always feel free to contact and/or chat with any of the graduate faculty in the field of Statistics.

The formation of a Special Committee for your dissertation research should serve your objective of writing the best possible dissertation. The Graduate School requires that this committee contain at least three members that simultaneously represent a certain combination of subjects and concentrations. The chair of the committee is your principal dissertation advisor and always represents a specified concentration within the subject & field of Statistics. The Graduate School additionally requires PhD students to have at least two minor subjects represented on your special committee. For students in the field of Statistics, these remaining two members must either represent (i) a second concentration within the subject of Statistics, and one external minor subject; or, (ii) two external minor subjects. Each minor advisor must agree to serve on your special committee; as a result, the identification of these minor members should occur at least 6 months prior to your A examination.

Some examples of external minors include Computational Biology, Demography, Computer Science, Economics, Epidemiology, Mathematics, Applied Mathematics and Operations Research. The declaration of an external minor entails selecting (i) a field other than Statistics in which to minor; (ii) a subject & concentration within the specified field; and, (iii) a minor advisor representing this field/subject/concentration that will work with you in setting the minor requirements. Typically, external minors involve gaining knowledge in 3-5 graduate courses in the specified field/subject, though expectations can vary by field and even by the choice of advisor. While any choice of external minor subject is technically acceptable, the requirement that the minor representative serve on your Special Committee strongly suggests that the ideal choice(s) should share some natural connection with your choice of dissertation topic.

The fields, subjects and concentrations represented on your committee must be officially recognized by the Graduate School ; the Degrees, Subjects & Concentrations tab listed under each field of study provides this information. Information on the concentrations available for committee members chosen to represent the subject of Statistics can be found on the Graduate School webpage . 

Statistics PhD Travel Support

The Department of Statistics and Data Science has established a fund for professional travel for graduate students. The intent of the Department is to encourage travel that enhances the Statistics community at Cornell by providing funding for graduate students in statistics that will be presenting at conferences. Please review the Graduate Student Travel Award Policy website for more information. 

Completion of the PhD Degree

In addition to the specified residency requirements, students must meet all program requirements as outlined in Program Course Requirements and Timetables and Evaluations and Examinations, as well as complete a doctoral dissertation approved by your Special Committee. The target time to PhD completion is between 4 and 5 years; the actual time to completion varies by student.

Students should consult both the Guide to Graduate Study and Code of Legislation of the Graduate Faculty (available at www.gradschool.cornell.edu ) for further information on all academic and procedural matters pertinent to pursuing a graduate degree at Cornell University.

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Dissertations & Theses

The following is a list of recent statistics and biostatistics PhD Dissertations and Masters Theses.

Jeffrey Gory (2017) PhD Dissertation (Statistics): Marginally Interpretable Generalized Linear Mixed Models Advisors: Peter Craigmile & Steven MacEachern

Yi Lu (2017) PhD Dissertation (Statistics): Function Registration from a Bayesian Perspective Advisors: Radu Herbei & Sebastian Kurtek

Michael Matthews (2017) PhD Dissertation (Statistics):  Extending Ranked Sampling in Inferential Procedures Advisor: Douglas Wolfe

Anna Smith (2017) PhD Dissertation (Statistics):  Statistical Methodology for Multiple Networks Advisor: Catherine Calder

Weiyi Xie (2017) PhD Dissertation (Statistics): A Geometric Approach to Visualization of Variability in Univariate and Multivariate Functional Data Advisor: Sebastian Kurtek

Jingying Zeng (2017) Masters Thesis (Statistics): Latent Factor Models for Recommender Systems and Market Segmentation Through Clustering Advisors: Matthew Pratola & Laura Kubatko

Han Zhang (2017) PhD Dissertation (Statistics): Detecting Rare Haplotype-Environmental Interaction and Nonlinear Effects of Rare Haplotypes using Bayesian LASSO on Quantitative Traits Advisor: Shili Lin

Mark Burch (2016) PhD Dissertation (Biostatistics): Statistical Methods for Network Epidemic Models Advisor: Grzegorz Rempala

Po-hsu Chen (2016) PhD Dissertation (Statistics):  Modeling Multivariate Simulator Outputs with Applications to Prediction and Sequential Pareto Minimization Advisors: Thomas Santner & Angela Dean

Yanan Jia (2016) PhD Dissertation (Statistics): Generalized Bilinear Mixed-Effects Models for Multi-Indexed Multivariate Data Advisor: Catherine Calder

Rong Lu (2016) PhD Dissertation (Biostatistics): Statistical Methods for Functional Genomics Studies Using Observational Data Advisor: Grzegorz Rempala (Public Health)

Junyan Wang (2016) PhD Dissertation (Statistics): Empirical Bayes Model Averaging in the Presence of Model Misfit Advisors: Mario Peruggia & Christopher Hans

Ran Wei (2016) PhD Dissertation (Statistics):  On Estimation Problems in Network Sampling Advisors: David Sivakoff & Elizabeth Stasny

Hui Yang (2016) PhD Dissertation (Statistics):  Adjusting for Bounding and Time-in-Sample Eects in the National Crime Victimization Survey (NCVS) Property Crime Rate Estimation Advisors: Elizabeth Stasny & Asuman Turkmen

Matthew Brems (2015) Masters Thesis (Statistis): The Rare Disease Assumption: The Good, The Bad, and The Ugly Advisor: Shili Lin

Linchao Chen (2015) PhD Dissertation (Statistics):  Predictive Modeling of Spatio-Temporal Datasets in High Dimensions Advisors: Mark Berliner & Christopher Hans

Casey Davis (2015) PhD Dissertation (Statistics):  A Bayesian Approach to Prediction and Variable Selection Using Nonstationary Gaussian Processes Advisors: Christopher Hans & Thomas Santner

Victor Gendre (2015) Masters Thesis (Statistics): Predicting short term exchange rates with Bayesian autoregressive state space models: an investigation of the Metropolis Hastings algorithm forecasting efficiency Advisor: Radu Herbei

Zhengyu Hu (2015) PhD Dissertation (Statistics):  Initializing the EM Algorithm for Data Clustering and Sub-population Detection Advisors: Steven MacEachern & Joseph Verducci

David Kline (2015) PhD Dissertation (Biostatistics): Systematically Missing Subject-Level Data in Longitudinal Research Synthesis Advisors: Eloise Kaizar, Rebecca Andridge (Public Health)

Andrew Landgraf (2015) PhD Dissertation (Statistics): Generalized Principal Component Analysis: Dimensionality Reduction through the Projection of Natural Parameters Advisor: Yoonkyung Lee

Andrew Olsen (2015) PhD Dissertation (Statistics):  When Infinity is Too Long to Wait: On the Convergence of Markov Chain Monte Carlo Methods Advisor: Radu Herbei

Elizabeth   Petraglia (2015) PhD Dissertation (Statistics):  Estimating County-Level Aggravated Assault Rates by Combining Data from the National Crime Victimization Survey (NCVS) and the National Incident-Based Reporting System (NIBRS) Advisor: Elizabeth Stasny

Mark   Risser (2015) PhD Dissertation (Statistics):  Spatially-Varying Covariance Functions for Nonstationary Spatial Process Modeling Advisor: Catherine Calder

John Stettler (2015) PhD Dissertation (Statistics):  The Discrete Threshold Regression Model Advisor: Mario Peruggia

Zachary   Thomas (2015) PhD Dissertation (Statistics):  Bayesian Hierarchical Space-Time Clustering Methods Advisor: Mark Berliner

Sivaranjani   Vaidyanathan (2015) PhD Dissertation (Statistics):  Bayesian Models for Computer Model Calibration and Prediction Advisor: Mark Berliner

Xiaomu Wang (2015) PhD Dissertation (Statistics): Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation Advisor: Mark Berliner

Staci White (2015) PhD Dissertation (Statistics):  Quantifying Model Error in Bayesian Parameter Estimation Advisor: Radu Herbei

Jiaqi Zaetz (2015) PhD Dissertation (Statistics): A Riemannian Framework for Shape Analysis of Annotated 3D Objects Advisor: Sebastian Kurtek

Fangyuan Zhang (2015) PhD Dissertation (Biostatistics): Detecting genomic imprinting and maternal effects in family-based association studies Advisor: Shili Lin

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Thesis Defense

Smd statistics thesis guide supplement, purpose of this document.

This document provides a guide for the structure and content of a Statistics PhD thesis document. Because thesis topics and methods vary greatly, the requirements for any given thesis may vary from the guidelines presented here as is required to facilitate coherent presentation. However, notwithstanding such exceptions, the structure and content provided below is the standard for a Statistics PhD thesis at the University of Rochester.

This document is meant to be a supplement to the general guidelines of the University of Rochester for preparation of a thesis (“Preparing Your Thesis: a Manual for Graduate Students”), which can be found at the website http://www.rochester.edu/Theses/ThesesManual.pdf , and which governs all theses at this university. This document does not supersede the general guidelines.

Overview of thesis contents

A thesis is a description and interpretation of the research conducted by the candidate that qualifies him/her for the degree of PhD.

Wherever possible (particularly the introductory and final chapters), the thesis should be written so that the material is accessible to those not working in the specialized area of research. Every member of the thesis examination committee should be able to understand the main ideas in the document as a whole, and the details of each section must be understandable to at least one committee member with the expertise to verify that its content is sound.

The document should be written in English with correct spelling and grammar. It is not the job of the committee to proof-read the text. Having the text of the thesis corrected and edited for clarity by a second person is acceptable and highly recommended. A committee member can refuse to accept a thesis with excessive grammatical or typographical errors.

There is no formal minimum or maximum length. The thesis must give an in-depth account of the background and the research question addressed, as well as a detailed description of the methods and results that is typically more specific than that found in the published literature.

Organization of the thesis

The manual titled “Preparing Your Thesis: a Manual for Graduate Students” outlines the overall structure of the thesis in terms of general formatting and required parts such as the Title Page, Abstract, etc. This manual should be consulted for specifications regarding these components. This manual, however, does not address the substantive chapters of the thesis. That guidance is provided herein.

A PhD thesis in Statistics is expected to involve the development of novel statistical methodology and/or provide important contributions to the theory of statistics. It should consist of original work of publishable quality that addresses a unified theme, as opposed to a collection of unrelated methodological developments. A Statistics PhD thesis will typically contain five chapters (although this may vary):

Chapter 1. Introduction

This chapter introduces the research problem and outlines the relevant background. While expansive details of all relevant published works should be avoided, this chapter should summarize all pertinent scientific literature to provide the information necessary for understanding what is currently known and how the thesis will contribute in an important way to expanding this knowledge. This chapter provides the requisite arguments to establish the importance of the problem as a statistical research topic. Often, example data from actual scientific studies are highly useful for motivating the research problem. The chapter should conclude by briefly summarizing the research approach to the thesis and the organization of the remaining chapters.

Chapters 2-4. Distinct Aspects of the Research

Each of these chapters typically addresses a distinct sub-problem related to the general theme of the dissertation. The mathematical development of the novel methodology should be presented in detail. New theorems and proofs (as well as relevant existing theorems) should be provided as necessary for analytical evaluation of the properties of the new methods. Simulation studies may be necessary to empirically evaluate the properties of these methods; the simulation designs should be described in sufficient detail to allow replication of the results by others. Comparisons should be made to existing methods, if any, for addressing the same research problem. Results of the evaluations should be clearly and thoroughly presented in figures and tables that are self-contained.

Example data from actual scientific studies should be used whenever possible (and applicable) to illustrate the utility of the new methodology.

Chapter 5. Conclusions and Future Work

The final chapter should discuss the research findings in a unified framework and provide an overall perspective for the reader, including limitations of the research and future work to be performed. It may be helpful to briefly recapitulate the state of the field at the outset of the research, summarize the main results of the thesis, explain how the current work provides an important contribution to existing knowledge, point out any limitations of the newly-developed methods, raise new questions that may have arisen out of the research, and propose future work to address existing gaps in knowledge.

PhD Dissertations

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College of Liberal Arts and Sciences

Department of Statistics

Ph.d. in statistics.

The Doctor of Philosophy (Ph.D.) in Statistics provides students with rigorous training in the theory, methodology, computation, and application of statistics.

View Admissions Requirements

Program Details

UConn statistics Ph.D. students work closely with faculty on advanced research topics over a wide range of theory and application areas. They also engage with an active community of scholars and students who engage with peers on campus and with professional networks beyond UConn.

Through their coursework, mentorship, and community engagement experiences, our students develop diverse skills that allow them to collaborate and innovate with researchers in applied fields. Graduates of our program go on to high profile positions in academia, industry, and government as both statisticians and data scientists.

Academic Requirements

UConn’s Ph.D. in Statistics offers students rigorous training in statistical theories and methodologies, which they can apply to a wide range of academic and professional fields. Starting in their second year, Ph.D. students establish an advisory committee, consisting of a major advisor and two associate advisors. Together they develop an individualized plan of study based on the students career goals and interests.

All Ph.D. students are required to complete:

• A sequence of required core courses and elective courses from another field of study.
• A qualifying examination and general examination.
• A dissertation.

View full degree requirements

Students entering the program with a bachelor’s degree are typically required to take 16 to 18 courses to earn a Ph.D. in Statistics.

Core Courses

The following core courses are required for all Ph.D. students:

• STAT 5545 and 5555. Mathematical Statistics.
• STAT 5505 and 5605. Applied Statistics.
• STAT 5725 and 5735. Linear Models.
• STAT 6315 and 6515. Theory of Statistics.
• STAT 6325 and 6894. Measure Theory and Probability Theory.
• STAT 5515. Design of Experiments.
• STAT 5091. Statistics Internship or
• STAT 5094. Seminars in Statistics.

Each core course carries three credits, except for the one-credit STAT 5091 or 5094, for a total of 34 credits. Additional credits can be earned from the list of elective courses.

Elective Courses

In general, Ph.D. students are required to elect one or two courses from other departments. However, it is sufficient to take one graduate-level course from the Department of Mathematics. Ph.D. students are also encouraged to take courses in computer science and in application areas such as biology or economics. The elective course(s) must be approved by the student’s major advisor.

Under certain circumstances, a major advisor can exempt their student from the above requirement, if the student has had internships or a research assistantship in interdisciplinary areas.

Browse the UConn graduate course catalog.

Financial Aid

The Department expects Ph.D. students to finish their studies within four years. For students arriving without an MS degree in mathematics or statistics, the Department may provide up to five years of financial support. For those arriving with such a degree, the Department may provide up to four years of financial support.

In order to receive continuous support, Ph.D. students should take at at least nine credits per semester until taking the Ph.D. qualifying exam.

Learn more about financial aid

February 1 (early deadline) April 1 (final deadline)

Please apply by February 1 if you wish to be considered for financial aid.

Individuals with a bachelor’s degree in any major, with a background in mathematics and statistics, are encouraged to apply.

International students must consult with UConn International Student and Scholar Services for visa rules and University requirements.

Full Admissions Requirements

  Please note: The Department does not offer a joint MS/Ph.D. program. Current UConn students enrolled in a statistics master’s program who wish to pursue the Ph.D. in Statistics must reapply to the Graduate School.

For questions about the Ph.D. in Statistics, please contact:

Vladimir Pozdnyakov

Professor and Director of Graduate Admission [email protected]

PhD in Statistics

The PhD degree in statistics is designed for students who wish to pursue a career in statistics research in academia, government, or industry. The curriculum is designed to provide a strong in-depth and broad training in statistical theory, methodology, computation, and applications. Students begin their research experience in the first year and participate in on- or off-campus internships in the second year. These provide a well-rounded, solid education for graduates to assume and advance their roles as university professors, senior statisticians, or data scientists.

Dissertations

While PhD students are engaged in research from the first year, they formally begin their dissertation work after completing their doctoral preliminary exams. Dissertations may be oriented toward applied statistics, computational methods, theoretical statistics, or probability. It typically takes one to two years to complete and defend the dissertation work. The dissertation is expected to be of publishable quality in reputable academic journals. Almost all PhD students complete the degree in five years.

College Resources for Graduate Students

Visit CLA’s website for graduate students to learn about collegiate funding opportunities, student support, career services, and more.

Student Services      Career Services     Funding & Support

• Princeton University Doctoral Dissertations, 2011-2024
• Operations Research and Financial Engineering

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• Dissertation Areas and Joint PhD Programs
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• PhD in Accounting
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PhD in Econometrics and Statistics

• PhD in Microeconomics
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• Joint Program in Financial Economics
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• Joint PhD/JD Program

The Econometrics and Statistics Program provides foundational training in the science of learning from data towards solving business problems. Our students engage in extensive collaborative research on cutting-edge theory in Econometrics, Statistics and Machine Learning as well in applied research from a variety of fields within Booth (such as finance, marketing or economics).

Our program builds on a long tradition of research creativity and excellence at Booth.

Our PhD students become active members of the broad, interdisciplinary and intellectually stimulating Booth community. The program is ideal for students who wish to pursue an (academic) research career in data-rich disciplines, and who are motivated by applications (including but not limited to economics and business). As our PhD student, you will have a freedom to customize your program by combining courses at Booth (including business-specific areas such as marketing, finance or economics) with offerings at our partnering departments at the University of Chicago (Department of Statistics and Kenneth C. Griffin Department of Economics). You will acquire a solid foundation in both theory and practice (including learning theory, Bayesian statistics, causal inference or empirical asset pricing).

Our Distinguished Econometrics and Statistics Faculty

Chicago Booth’s Econometrics and Statistics faculty are committed to building strong collaborative relationships with doctoral students. We serve as research advisors and career mentors. Major areas of departmental research include: learning theory; causal inference; machine learning; Bayesian inference; decision theory; graphical models; high dimensional inference; and financial econometrics.

Bryon Aragam

Assistant Professor of Econometrics and Statistics and Robert H. Topel Faculty Scholar

Nabarun Deb

Assistant Professor of Econometrics and Statistics

Christian B. Hansen

Wallace W. Booth Professor of Econometrics and Statistics

Tetsuya Kaji

Associate Professor of Econometrics and Statistics and Richard Rosett Faculty Fellow

Mladen Kolar

Associate Professor of Econometrics and Statistics

Tengyuan Liang

Professor of Econometrics and Statistics and William Ladany Faculty Fellow

Nicholas Polson

Robert Law, Jr. Professor of Econometrics and Statistics

Veronika Rockova

Professor of Econometrics and Statistics, and James S. Kemper Foundation Faculty Scholar

Jeffrey R. Russell

Alper Family Professor of Econometrics and Statistics

Ekaterina (Katja) Smetanina

Assistant Professor of Econometrics and Statistics and Asness Junior Faculty Fellow

Panagiotis Toulis (Panos)

Associate Professor of Econometrics and Statistics, and John E. Jeuck Faculty Fellow

Dacheng Xiu

Professor of Econometrics and Statistics

A Network of Support

Booth’s Econometrics and Statistics group has been partnering with several (data science and interdisciplinary) research centers and institutes that facilitate the translation of research into practice. Through these venues, our PhD students can foster a strong research community and find additional resources including elective courses, funding for collaborative student work, and seminars with world-renowned scholars.

Data Science Institute at the University of Chicago The Data Science Institute executes the University of Chicago’s bold, innovative vision of Data Science as a new discipline by advancing interdisciplinary research, partnerships with industry, government, and social impact organizations. Center for Applied Artificial Intelligence The Center for Applied AI incubates transformative projects that fundamentally shape how humans use AI to interact with each other and the world. The Center’s innovative research uses machine learning and behavioral science to investigate how AI can best be used to support human decision-making and improve society. Toyota Technological Institute at Chicago Toyota Technological Institute at Chicago (TTIC) is a philanthropically endowed academic computer science institute, dedicated to basic research and graduate education in computer science. Its mission is to achieve international impact through world-class research and education in fundamental computer science and information technology. The Institute is distinctive to the American educational scene in its unique combination of graduate education and endowed research.

The Becker Friedman Institute for Economics With a mission of turning evidence-based research into real-world impact, the Becker Friedman Institute brings together the University of Chicago’s economic community. Ideas are translated into accessible formats and shared with world leaders tasked with solving pressing economic problems. Committee on Quantitative Methods in Social, Behavioral and Health Sciences This is an interdisciplinary community of faculty and students interested in methodological research in relation to applications in social, behavioral, and health sciences. The goals are to create an intellectual niche, exchange research ideas, facilitate research collaborations, share teaching resources, enhance the training of students, and generate a collective impact on the University of Chicago campus and beyond. The Institute for Data, Econometrics, Algorithms, and Learning The Institute for Data, Econometrics, Algorithms, and Learning (IDEAL) is a multi-discipline (computer science, statistics, economics, electrical engineering, and operations research) and multi-institution (Northwestern University, Toyota Technological Institute at Chicago, and University of Chicago) collaborative institute that focuses on key aspects of the theoretical foundations of data science. The institute will support the study of foundational problems related to machine learning, high-dimensional data analysis and optimization in both strategic and non-strategic environments.

The Fama-Miller Center for Research in Finance Tasked with pushing the boundaries of research in finance, the Fama-Miller Center provides institutional structure and support for researchers in the field. James M. Kilts Center for Marketing The Kilts Center facilitates faculty and student research, supports innovations in the marketing curriculum, funds scholarships for MBA and PhD students, and creates engaging programs aimed at enhancing the careers of students and alumni.

Scholarly Publications

Our PhD students' research has been published in top journals including Econometrica, Journal of Royal Statistical Society, Journal of Econometrics, Neural Information Processing Systems and Journal of Machine Learning Research. Below is a recent list of publications and working papers authored by our PhD students. Modeling Tail Index with Autoregressive Conditional Pareto Model Zhouyu Shen, Yu Chen and Ruxin Shi, Journal of Business and Economic Statistics, (40) 2022 Online Learning to Transport via the Minimal Selection Principle Wenxuan Guo, YoonHaeng Hur, Tengyuan Liang, Chris Ryan, Proceedings of 35th Conference on Learning Theory (COLT), (178) 2022 FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting Boxin Zhao, Samuel Wang and Mladen Kolar, Journal of Machine Learning Research, (23) 2022 Approximate Bayesian Computation via Classification Yuexi Wang, Tetsuya Kaji and Veronika Rockova, Journal of Machine Learning Research (In press), 2022 Reversible Gromov-Monge Sampler for Simulation-Based Inference YoonHaeng Hur, Wenxuan Guo and Tengyuan Liang, Journal of the American Statistical Association (R&R). 2021. Data Augmentation for Bayesian Deep Learning Yuexi Wang, Nicholas Polson and Vadim Sokolov, Bayesian Analysis (In press), 2022 Pessimism Meets VCG: Learning Dynamic Mechanism Design via Offline Reinforcement Learning Boxiang Lyu, Zhaoran Wang, Mladen Kolar and Zhuoran Yang, In Proceedings of the 39th International Conference on Machine Learning (ICML), (162) 2022 Optimal Estimation of Gaussian DAG Models Ming Gao, Wai Ming Tai and Bryon Aragam, International Conference on Artificial Intelligence and Statistics (AISTATS), (151) 2022 Multivariate Change Point Detection for Heterogeneous Series Yuxuan Guo, Ming Gao, and Xiaoling Lu, Neurocomputing, (510) 2022 Disentangling Autocorrelated Intraday Returns Rui Da and Dacheng Xiu, Journal of Econometrics (R&R), 2021 When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility Rui Da and Dacheng Xiu, Econometrica, (89) 2021 Efficient Bayesian Network Structure Learning via Local Markov Boundary Search Ming Gao and Bryon Aragam, Advances in Neural Information Processing Systems (NeurIPS), (34) 2021 Structure Learning in Polynomial Time: Greedy Algorithms, Bregman Information, and Exponential Families Goutham Rajendran, Bohdan Kivva, Ming Gao and Bryon Aragam, Advances in Neural Information Processing Systems (NeurIPS), (34) 2021 Variable Selection with ABC Bayesian Forests Yi Liu, Yuexi Wang and Veronika Rockova, Journal of the Royal Statistical Association: Series B, (83) 2021  A Polynomial-time Algorithm for Learning Non-parametric Causal Graphs Ming Gao, Yi Ding, and Bryon Aragam, Advances in Neural Information Processing System (NeurIPS), (33) 2020 Uncertainty Quantification for Sparse Deep Learning Yuexi Wang and Veronika Rockova, International Conference on Artificial Intelligence and Statistics (AISTATS), (2018) 2020 Direct Estimation of Differential Functional Graphical Models Boxin Zhao, Samuel Wang and Mladen Kolar, Advances in neural information processing systems (NeurIPS), (32) 2019

The Effects of Economic Uncertainty on Financial Volatility: A Comprehensive Investigation Chen Tong, Zhuo Huang, Tianyi Wang, and Cong Zhang, Journal of Empirical Finance (R&R), 2022

Spotlight on Research

Econometrics and statistics research from our PhD students and faculty is often featured in the pages of Chicago Booth Review.

Is There a Ceiling for Gains in Machine-Learned Arbitrage?

In a recent paper by Chicago Booth’s Stefan Nagel and Dacheng Xiu and Booth PhD student Rui Da, findings suggest that there are limits to statistical arbitrage investment.

How (In)accurate Is Machine Learning?

Three Chicago Booth researchers quantify the likelihood of machine learning leading business executives astray.

Would You Trust a Machine to Pick a Vaccine?

"If we understand why a black-box method works, we can trust it more with our decisions, explains [Booth's] Ročková, one of the researchers trying to narrow the gap between what’s done in practice and what’s known in theory. "

Inside the Student Experience

Damian Kozbur, PhD ’14, says PhD students at Booth have the flexibility to work on risky problems that no one else has examined.

Video Transcript

Damian Kozbur, ’14: 00:01 I went to graduate school in order to develop econometrics tools in conjunction with machine-learning tools in conjunction with economic theory in order to do inference for economic parameters. When you work in high dimensional estimation and you're dealing with problems where the number of variables you're looking at can potentially be in the millions, there's no way to visualize what's going on. Demands now really require that you can handle huge datasets. There's something really satisfying about studying a problem and studying it well. I would say Booth is an excellent place to do it. You have the flexibility to work on really risky problems where you're trying to navigate this landscape that nobody's ever really looked at before. You have an opportunity to dig deeper. You have an opportunity to be rigorous. The faculty is there to help you. They're trying to figure out the same kinds of problems. Things that you figure out cannot always be visualized and it cannot always be easily understood. That doesn't necessarily mean that it's not practical or not useful.

Damian Kozbur, ’14: 01:08 There's an incredible explosion in terms of the amount of data we have on everything. There is an incredible explosion in terms of our understanding of high dimensional econometrics. If you're doing innovative work right now, it will have an impact.

Current Econometrics and Statistics Students

PhD students in econometrics and statistics apply statistical methods to a wide range of business problems, from the effectiveness of machine-learning tools to video-game preferences. Our graduates go on to work in high-profile institutions, generally in academia, finance, or data science.

Current Students

Y ifei Chen Rui Da

Chaoxing Dai

Wenxuan Guo

Shuo-Chieh Huang

Shunzhuang Huang So Won (Sowon) Jeong

Boxiang (Shawn) Lyu Edoardo Marcelli

Zhouyu Shen

Shengjun (Percy) Zhai

Current Students in Sociology and Business

Jacy Anthis

Program Expectations and Requirements

The Stevens Doctoral Program at Chicago Booth is a full-time program. Students generally complete the majority of coursework and examination requirements within the first two years of studies and begin work on their dissertation during the third year. For details, see General Examination Requirements by Area in the Stevens Program Guidebook below.

Download the 2023-2024 Guidebook!

How To Write The Results/Findings Chapter

For quantitative studies (dissertations & theses).

By: Derek Jansen (MBA) | Expert Reviewed By: Kerryn Warren (PhD) | July 2021

So, you’ve completed your quantitative data analysis and it’s time to report on your findings. But where do you start? In this post, we’ll walk you through the results chapter (also called the findings or analysis chapter), step by step, so that you can craft this section of your dissertation or thesis with confidence. If you’re looking for information regarding the results chapter for qualitative studies, you can find that here .

Overview: Quantitative Results Chapter

• What exactly the results chapter is
• What you need to include in your chapter
• How to structure the chapter
• Tips and tricks for writing a top-notch chapter
• Free results chapter template

What exactly is the results chapter?

The results chapter (also referred to as the findings or analysis chapter) is one of the most important chapters of your dissertation or thesis because it shows the reader what you’ve found in terms of the quantitative data you’ve collected. It presents the data using a clear text narrative, supported by tables, graphs and charts. In doing so, it also highlights any potential issues (such as outliers or unusual findings) you’ve come across.

But how’s that different from the discussion chapter?

Well, in the results chapter, you only present your statistical findings. Only the numbers, so to speak – no more, no less. Contrasted to this, in the discussion chapter , you interpret your findings and link them to prior research (i.e. your literature review), as well as your research objectives and research questions . In other words, the results chapter presents and describes the data, while the discussion chapter interprets the data.

Let’s look at an example.

In your results chapter, you may have a plot that shows how respondents to a survey  responded: the numbers of respondents per category, for instance. You may also state whether this supports a hypothesis by using a p-value from a statistical test. But it is only in the discussion chapter where you will say why this is relevant or how it compares with the literature or the broader picture. So, in your results chapter, make sure that you don’t present anything other than the hard facts – this is not the place for subjectivity.

It’s worth mentioning that some universities prefer you to combine the results and discussion chapters. Even so, it is good practice to separate the results and discussion elements within the chapter, as this ensures your findings are fully described. Typically, though, the results and discussion chapters are split up in quantitative studies. If you’re unsure, chat with your research supervisor or chair to find out what their preference is.

What should you include in the results chapter?

Following your analysis, it’s likely you’ll have far more data than are necessary to include in your chapter. In all likelihood, you’ll have a mountain of SPSS or R output data, and it’s your job to decide what’s most relevant. You’ll need to cut through the noise and focus on the data that matters.

This doesn’t mean that those analyses were a waste of time – on the contrary, those analyses ensure that you have a good understanding of your dataset and how to interpret it. However, that doesn’t mean your reader or examiner needs to see the 165 histograms you created! Relevance is key.

How do I decide what’s relevant?

At this point, it can be difficult to strike a balance between what is and isn’t important. But the most important thing is to ensure your results reflect and align with the purpose of your study .  So, you need to revisit your research aims, objectives and research questions and use these as a litmus test for relevance. Make sure that you refer back to these constantly when writing up your chapter so that you stay on track.

As a general guide, your results chapter will typically include the following:

• Some demographic data about your sample
• Reliability tests (if you used measurement scales)
• Descriptive statistics
• Inferential statistics (if your research objectives and questions require these)
• Hypothesis tests (again, if your research objectives and questions require these)

We’ll discuss each of these points in more detail in the next section.

Importantly, your results chapter needs to lay the foundation for your discussion chapter . This means that, in your results chapter, you need to include all the data that you will use as the basis for your interpretation in the discussion chapter.

For example, if you plan to highlight the strong relationship between Variable X and Variable Y in your discussion chapter, you need to present the respective analysis in your results chapter – perhaps a correlation or regression analysis.

Need a helping hand?

How do I write the results chapter?

There are multiple steps involved in writing up the results chapter for your quantitative research. The exact number of steps applicable to you will vary from study to study and will depend on the nature of the research aims, objectives and research questions . However, we’ll outline the generic steps below.

Step 1 – Revisit your research questions

The first step in writing your results chapter is to revisit your research objectives and research questions . These will be (or at least, should be!) the driving force behind your results and discussion chapters, so you need to review them and then ask yourself which statistical analyses and tests (from your mountain of data) would specifically help you address these . For each research objective and research question, list the specific piece (or pieces) of analysis that address it.

At this stage, it’s also useful to think about the key points that you want to raise in your discussion chapter and note these down so that you have a clear reminder of which data points and analyses you want to highlight in the results chapter. Again, list your points and then list the specific piece of analysis that addresses each point. 

Next, you should draw up a rough outline of how you plan to structure your chapter . Which analyses and statistical tests will you present and in what order? We’ll discuss the “standard structure” in more detail later, but it’s worth mentioning now that it’s always useful to draw up a rough outline before you start writing (this advice applies to any chapter).

Step 2 – Craft an overview introduction

As with all chapters in your dissertation or thesis, you should start your quantitative results chapter by providing a brief overview of what you’ll do in the chapter and why . For example, you’d explain that you will start by presenting demographic data to understand the representativeness of the sample, before moving onto X, Y and Z.

This section shouldn’t be lengthy – a paragraph or two maximum. Also, it’s a good idea to weave the research questions into this section so that there’s a golden thread that runs through the document.

Step 3 – Present the sample demographic data

The first set of data that you’ll present is an overview of the sample demographics – in other words, the demographics of your respondents.

For example:

• What age range are they?
• How is gender distributed?
• How is ethnicity distributed?
• What areas do the participants live in?

The purpose of this is to assess how representative the sample is of the broader population. This is important for the sake of the generalisability of the results. If your sample is not representative of the population, you will not be able to generalise your findings. This is not necessarily the end of the world, but it is a limitation you’ll need to acknowledge.

Of course, to make this representativeness assessment, you’ll need to have a clear view of the demographics of the population. So, make sure that you design your survey to capture the correct demographic information that you will compare your sample to.

But what if I’m not interested in generalisability?

Well, even if your purpose is not necessarily to extrapolate your findings to the broader population, understanding your sample will allow you to interpret your findings appropriately, considering who responded. In other words, it will help you contextualise your findings . For example, if 80% of your sample was aged over 65, this may be a significant contextual factor to consider when interpreting the data. Therefore, it’s important to understand and present the demographic data.

 Step 4 – Review composite measures and the data “shape”.

Before you undertake any statistical analysis, you’ll need to do some checks to ensure that your data are suitable for the analysis methods and techniques you plan to use. If you try to analyse data that doesn’t meet the assumptions of a specific statistical technique, your results will be largely meaningless. Therefore, you may need to show that the methods and techniques you’ll use are “allowed”.

Most commonly, there are two areas you need to pay attention to:

#1: Composite measures

The first is when you have multiple scale-based measures that combine to capture one construct – this is called a composite measure .  For example, you may have four Likert scale-based measures that (should) all measure the same thing, but in different ways. In other words, in a survey, these four scales should all receive similar ratings. This is called “ internal consistency ”.

Internal consistency is not guaranteed though (especially if you developed the measures yourself), so you need to assess the reliability of each composite measure using a test. Typically, Cronbach’s Alpha is a common test used to assess internal consistency – i.e., to show that the items you’re combining are more or less saying the same thing. A high alpha score means that your measure is internally consistent. A low alpha score means you may need to consider scrapping one or more of the measures.

#2: Data shape

The second matter that you should address early on in your results chapter is data shape. In other words, you need to assess whether the data in your set are symmetrical (i.e. normally distributed) or not, as this will directly impact what type of analyses you can use. For many common inferential tests such as T-tests or ANOVAs (we’ll discuss these a bit later), your data needs to be normally distributed. If it’s not, you’ll need to adjust your strategy and use alternative tests.

To assess the shape of the data, you’ll usually assess a variety of descriptive statistics (such as the mean, median and skewness), which is what we’ll look at next.

Step 5 – Present the descriptive statistics

Now that you’ve laid the foundation by discussing the representativeness of your sample, as well as the reliability of your measures and the shape of your data, you can get started with the actual statistical analysis. The first step is to present the descriptive statistics for your variables.

For scaled data, this usually includes statistics such as:

• The mean – this is simply the mathematical average of a range of numbers.
• The median – this is the midpoint in a range of numbers when the numbers are arranged in order.
• The mode – this is the most commonly repeated number in the data set.
• Standard deviation – this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average).
• Skewness – this indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph (this is called a normal or parametric distribution), or do they lean to the left or right (this is called a non-normal or non-parametric distribution).
• Kurtosis – this metric indicates whether the data are heavily or lightly-tailed, relative to the normal distribution. In other words, how peaked or flat the distribution is.

A large table that indicates all the above for multiple variables can be a very effective way to present your data economically. You can also use colour coding to help make the data more easily digestible.

For categorical data, where you show the percentage of people who chose or fit into a category, for instance, you can either just plain describe the percentages or numbers of people who responded to something or use graphs and charts (such as bar graphs and pie charts) to present your data in this section of the chapter.

When using figures, make sure that you label them simply and clearly , so that your reader can easily understand them. There’s nothing more frustrating than a graph that’s missing axis labels! Keep in mind that although you’ll be presenting charts and graphs, your text content needs to present a clear narrative that can stand on its own. In other words, don’t rely purely on your figures and tables to convey your key points: highlight the crucial trends and values in the text. Figures and tables should complement the writing, not carry it .

Depending on your research aims, objectives and research questions, you may stop your analysis at this point (i.e. descriptive statistics). However, if your study requires inferential statistics, then it’s time to deep dive into those .

Step 6 – Present the inferential statistics

Inferential statistics are used to make generalisations about a population , whereas descriptive statistics focus purely on the sample . Inferential statistical techniques, broadly speaking, can be broken down into two groups .

First, there are those that compare measurements between groups , such as t-tests (which measure differences between two groups) and ANOVAs (which measure differences between multiple groups). Second, there are techniques that assess the relationships between variables , such as correlation analysis and regression analysis. Within each of these, some tests can be used for normally distributed (parametric) data and some tests are designed specifically for use on non-parametric data.

There are a seemingly endless number of tests that you can use to crunch your data, so it’s easy to run down a rabbit hole and end up with piles of test data. Ultimately, the most important thing is to make sure that you adopt the tests and techniques that allow you to achieve your research objectives and answer your research questions .

In this section of the results chapter, you should try to make use of figures and visual components as effectively as possible. For example, if you present a correlation table, use colour coding to highlight the significance of the correlation values, or scatterplots to visually demonstrate what the trend is. The easier you make it for your reader to digest your findings, the more effectively you’ll be able to make your arguments in the next chapter.

Step 7 – Test your hypotheses

If your study requires it, the next stage is hypothesis testing. A hypothesis is a statement , often indicating a difference between groups or relationship between variables, that can be supported or rejected by a statistical test. However, not all studies will involve hypotheses (again, it depends on the research objectives), so don’t feel like you “must” present and test hypotheses just because you’re undertaking quantitative research.

The basic process for hypothesis testing is as follows:

• Specify your null hypothesis (for example, “The chemical psilocybin has no effect on time perception).
• Specify your alternative hypothesis (e.g., “The chemical psilocybin has an effect on time perception)
• Set your significance level (this is usually 0.05)
• Calculate your statistics and find your p-value (e.g., p=0.01)
• Draw your conclusions (e.g., “The chemical psilocybin does have an effect on time perception”)

Finally, if the aim of your study is to develop and test a conceptual framework , this is the time to present it, following the testing of your hypotheses. While you don’t need to develop or discuss these findings further in the results chapter, indicating whether the tests (and their p-values) support or reject the hypotheses is crucial.

Step 8 – Provide a chapter summary

To wrap up your results chapter and transition to the discussion chapter, you should provide a brief summary of the key findings . “Brief” is the keyword here – much like the chapter introduction, this shouldn’t be lengthy – a paragraph or two maximum. Highlight the findings most relevant to your research objectives and research questions, and wrap it up.

Some final thoughts, tips and tricks

Now that you’ve got the essentials down, here are a few tips and tricks to make your quantitative results chapter shine:

• When writing your results chapter, report your findings in the past tense . You’re talking about what you’ve found in your data, not what you are currently looking for or trying to find.
• Structure your results chapter systematically and sequentially . If you had two experiments where findings from the one generated inputs into the other, report on them in order.
• Make your own tables and graphs rather than copying and pasting them from statistical analysis programmes like SPSS. Check out the DataIsBeautiful reddit for some inspiration.
• Once you’re done writing, review your work to make sure that you have provided enough information to answer your research questions , but also that you didn’t include superfluous information.

If you’ve got any questions about writing up the quantitative results chapter, please leave a comment below. If you’d like 1-on-1 assistance with your quantitative analysis and discussion, check out our hands-on coaching service , or book a free consultation with a friendly coach.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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Thank you. I will try my best to write my results.

Awesome content 👏🏾

this was great explaination

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Mathematics PhD theses

A selection of Mathematics PhD thesis titles is listed below, some of which are available online:

2022   2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Melanie Kobras –  Low order models of storm track variability

Ed Clark –  Vectorial Variational Problems in L∞ and Applications to Data Assimilation

Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes  

Chiara Cecilia Maiocchi –  Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems

Samuel R Harrison – Stalactite Inspired Thin Film Flow

Elena Saggioro – Causal network approaches for the study of sub-seasonal to seasonal variability and predictability

Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions  

Jennifer E. Israelsson –  The spatial statistical distribution for multiple rainfall intensities over Ghana

Giulia Carigi –  Ergodic properties and response theory for a stochastic two-layer model of geophysical fluid dynamics

André Macedo –  Local-global principles for norms

Tsz Yan Leung  –  Weather Predictability: Some Theoretical Considerations

Jehan Alswaihli –  Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations

Jemima M Tabeart –  On the treatment of correlated observation errors in data assimilation

Chris Davies –  Computer Simulation Studies of Dynamics and Self-Assembly Behaviour of Charged Polymer Systems

Birzhan Ayanbayev –  Some Problems in Vectorial Calculus of Variations in L∞

Penpark Sirimark –  Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation

Adam Barker –  Path Properties of Levy Processes

Hasen Mekki Öztürk –  Spectra of Indefinite Linear Operator Pencils

Carlo Cafaro –  Information gain that convective-scale models bring to probabilistic weather forecasts

Nicola Thorn –  The boundedness and spectral properties of multiplicative Toeplitz operators

James Jackaman  – Finite element methods as geometric structure preserving algorithms

Changqiong Wang - Applications of Monte Carlo Methods in Studying Polymer Dynamics

Jack Kirk - The molecular dynamics and rheology of polymer melts near the flat surface

Hussien Ali Hussien Abugirda - Linear and Nonlinear Non-Divergence Elliptic Systems of Partial Differential Equations

Andrew Gibbs - Numerical methods for high frequency scattering by multiple obstacles (PDF-2.63MB)

Mohammad Al Azah - Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF-913KB)

Katarzyna (Kasia) Kozlowska - Riemann-Hilbert Problems and their applications in mathematical physics (PDF-1.16MB)

Anna Watkins - A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF-2.46MB)

Niall Arthurs - An Investigation of Conservative Moving-Mesh Methods for Conservation Laws (PDF-1.1MB)

Samuel Groth - Numerical and asymptotic methods for scattering by penetrable obstacles (PDF-6.29MB)

Katherine E. Howes - Accounting for Model Error in Four-Dimensional Variational Data Assimilation (PDF-2.69MB)

Jian Zhu - Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF-1.69MB)

Tommy Liu - Stochastic Resonance for a Model with Two Pathways (PDF-11.4MB)

Matthew Paul Edgington - Mathematical modelling of bacterial chemotaxis signalling pathways (PDF-9.04MB)

Anne Reinarz - Sparse space-time boundary element methods for the heat equation (PDF-1.39MB)

Adam El-Said - Conditioning of the Weak-Constraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF-2.64MB)

Nicholas Bird - A Moving-Mesh Method for High Order Nonlinear Diffusion (PDF-1.30MB)

Charlotta Jasmine Howarth - New generation finite element methods for forward seismic modelling (PDF-5,52MB)

Aldo Rota - From the classical moment problem to the realizability problem on basic semi-algebraic sets of generalized functions (PDF-1.0MB)

Sarah Lianne Cole - Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF-2.84MB)

Alexander J. F. Moodey - Instability and Regularization for Data Assimilation (PDF-1.32MB)

Dale Partridge - Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF-3.19MB)

Joanne A. Waller - Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF-6.75MB)

Faez Ali AL-Maamori - Theory and Examples of Generalised Prime Systems (PDF-503KB)

Mark Parsons - Mathematical Modelling of Evolving Networks

Natalie L.H. Lowery - Classification methods for an ill-posed reconstruction with an application to fuel cell monitoring

David Gilbert - Analysis of large-scale atmospheric flows

Peter Spence - Free and Moving Boundary Problems in Ion Beam Dynamics (PDF-5MB)

Timothy S. Palmer - Modelling a single polymer entanglement (PDF-5.02MB)

Mohamad Shukor Talib - Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF-2.49MB)

Cassandra A.J. Moran - Wave scattering by harbours and offshore structures

Ashley Twigger - Boundary element methods for high frequency scattering

David A. Smith - Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF-1.05MB)

Stephen A. Haben - Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF-3.51MB)

Jing Cao - Molecular dynamics study of polymer melts (PDF-3.98MB)

Bonhi Bhattacharya - Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF-4.06MB)

Tamsin E. Lee - Modelling time-dependent partial differential equations using a moving mesh approach based on conservation (PDF-2.17MB)

Polly J. Smith - Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF-3Mb)

Corinna Burkard - Three-dimensional Scattering Problems with applications to Optical Security Devices (PDF-1.85Mb)

Laura M. Stewart - Correlated observation errors in data assimilation (PDF-4.07MB)

R.D. Giddings - Mesh Movement via Optimal Transportation (PDF-29.1MbB)

G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB)

C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.

P. Jelfs - A C-property satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF-11.7MB)

L. Bennetts - Wave scattering by ice sheets of varying thickness

M. Preston - Boundary Integral Equations method for 3-D water waves

J. Percival - Displacement Assimilation for Ocean Models (PDF - 7.70MB)

D. Katz - The Application of PV-based Control Variable Transformations in Variational Data Assimilation (PDF- 1.75MB)

S. Pimentel - Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF-5.9MB)

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• Published: 08 May 2024

Measurement and analysis of change in research scholars’ knowledge and attitudes toward statistics after PhD coursework

• Mariyamma Philip 1  

BMC Medical Education volume  24 , Article number:  512 ( 2024 ) Cite this article

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Knowledge of statistics is highly important for research scholars, as they are expected to submit a thesis based on original research as part of a PhD program. As statistics play a major role in the analysis and interpretation of scientific data, intensive training at the beginning of a PhD programme is essential. PhD coursework is mandatory in universities and higher education institutes in India. This study aimed to compare the scores of knowledge in statistics and attitudes towards statistics among the research scholars of an institute of medical higher education in South India at different time points of their PhD (i.e., before, soon after and 2–3 years after the coursework) to determine whether intensive training programs such as PhD coursework can change their knowledge or attitudes toward statistics.

One hundred and thirty research scholars who had completed PhD coursework in the last three years were invited by e-mail to be part of the study. Knowledge and attitudes toward statistics before and soon after the coursework were already assessed as part of the coursework module. Knowledge and attitudes towards statistics 2–3 years after the coursework were assessed using Google forms. Participation was voluntary, and informed consent was also sought.

Knowledge and attitude scores improved significantly subsequent to the coursework (i.e., soon after, percentage of change: 77%, 43% respectively). However, there was significant reduction in knowledge and attitude scores 2–3 years after coursework compared to the scores soon after coursework; knowledge and attitude scores have decreased by 10%, 37% respectively.

The study concluded that the coursework program was beneficial for improving research scholars’ knowledge and attitudes toward statistics. A refresher program 2–3 years after the coursework would greatly benefit the research scholars. Statistics educators must be empathetic to understanding scholars’ anxiety and attitudes toward statistics and its influence on learning outcomes.

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A PhD degree is a research degree, and research scholars submit a thesis based on original research in their chosen field. Doctor of Philosophy (PhD) degrees are awarded in a wide range of academic disciplines, and the PhD students are usually referred as research scholars. A comprehensive understanding of statistics allows research scholars to add rigour to their research. This approach helps them evaluate the current practices and draw informed conclusions from studies that were undertaken to generate their own hypotheses and to design, analyse and interpret complex clinical decisions. Therefore, intensive training at the beginning of the PhD journey is essential, as intensive training in research methodology and statistics in the early stages of research helps scholars design and plan their studies efficiently.

The University Grants Commission of India has taken various initiatives to introduce academic reforms to higher education institutions in India and mandated in 2009 that coursework be treated as a prerequisite for PhD preparation and that a minimum of four credits be assigned to one or more courses on research methodology, which could cover areas such as quantitative methods, computer applications, and research ethics. UGC also clearly states that all candidates admitted to PhD programmes shall be required to complete the prescribed coursework during the initial two semesters [ 1 ]. National Institute of Mental Health and Neurosciences (NIMHANS) at Bangalore, a tertiary care hospital and medical higher education institute in South India, that trains students in higher education in clinical fields, also introduced coursework in the PhD program for research scholars from various backgrounds, such as basic, behavioral and neurosciences, as per the UGC mandate. Research scholars undertake coursework programs soon after admission, which consist of several modules that include research methodology and statistical software training, among others.

Most scholars approach a course in statistics with the prejudice that statistics is uninteresting, demanding, complex or involve much mathematics and, most importantly, it is not relevant to their career goals. They approach statistics with considerable apprehension and negative attitudes, probably because of their inability to grasp the relevance of the application of the methods in their fields of study. This could be resolved by providing sufficient and relevant examples of the application of statistical techniques from various fields of medical research and by providing hands-on experience to learn how these techniques are applied and interpreted on real data. Hence, research methodology and statistical methods and the application of statistical methods using software have been given much importance and are taught as two modules, named Research Methodology and Statistics and Statistical Software Training, at this institute of medical higher education that trains research scholars in fields as diverse as basic, behavioural and neurosciences. Approximately 50% of the coursework curriculum focused on these two modules. Research scholars were thus given an opportunity to understand the theoretical aspects of the research methodology and statistical methods. They were also given hands-on training on statistical software to analyse the data using these methods and to interpret the findings. The coursework program was designed in this specific manner, as this intensive training would enable the research scholars to design their research studies more effectively and analyse their data in a better manner.

It is important to study attitudes toward statistics because attitudes are known to impact the learning process. Also, most importantly, these scholars are expected to utilize the skills in statistics and research methods to design research projects or guide postgraduate students and research scholars in the near future. Several authors have assessed attitudes toward statistics among various students and examined how attitudes affect academic achievement, how attitudes are correlated with knowledge in statistics and how attitudes change after a training program. There are studies on attitudes toward statistics among graduate [ 2 , 3 , 4 ] and postgraduate [ 5 ] medical students, politics, sociology, ( 6 – 7 ) psychology [ 8 , 9 , 10 ], social work [ 11 ], and management students [ 12 ]. However, there is a dearth of related literature on research scholars, and there are only two studies on the attitudes of research scholars. In their study of doctoral students in education-related fields, Cook & Catanzaro (2022) investigated the factors that contribute to statistics anxiety and attitudes toward statistics and how anxiety, attitudes and plans for future research use are connected among doctoral students [ 13 ]. Another study by Sohrabi et al. (2018) on research scholars assessed the change in knowledge and attitude towards teaching and educational design of basic science PhD students at a Medical University after a two-day workshop on empowerment and familiarity with the teaching and learning principles [ 14 ]. There were no studies that assessed changes in the attitudes or knowledge of research scholars across the PhD training period or after intensive training programmes such as PhD coursework. Even though PhD coursework has been established in institutes of higher education in India for more than a decade, there are no published research on the effectiveness of coursework from Indian universities or institutes of higher education.

This study aimed to determine the effectiveness of PhD coursework and whether intensive training programs such as PhD coursework can influence the knowledge and attitudes toward statistics of research scholars. Additionally, it would be interesting to know if the acquired knowledge could be retained longer, especially 2–3 years after the coursework, the crucial time of PhD data analysis. Hence, this study compares the scores of knowledge in statistics and attitude toward statistics of the research scholars at different time points of their PhD training, i.e., before, soon after and 2–3 years after the coursework.

Participants

This is an observational study of single group with repeated assessments. The institute offers a three-month coursework program consisting of seven modules, the first module is ethics; the fifth is research methodology and statistics; and the last is neurosciences. The study was conducted in January 2020. All research scholars of the institute who had completed PhD coursework in the last three years were considered for this study ( n  = 130). Knowledge and attitudes toward statistics before and soon after the coursework module were assessed as part of the coursework program. They were collected on the first and last day of the program respectively. The author who was also the coordinator of the research methodology and statistics module of the coursework have obtained the necessary permission to use the data for this study. The scholars invited to be part of the study by e-mail. Knowledge and attitude towards statistics 2–3 years after the coursework were assessed online using Google forms. They were also administered a semi structured questionnaire to elicit details about the usefulness of coursework. Participation was voluntary, and consent was also sought online. The confidentiality of the data was assured. Data were not collected from research scholars of Biostatistics or from research scholars who had more than a decade of experience or who had been working in the institute as faculty, assuming that their scores could be higher and could bias the findings. This non funded study was reviewed and approved by the Institute Ethics Committee.

Instruments

Knowledge in Statistics was assessed by a questionnaire prepared by the author and was used as part of the coursework evaluation. The survey included 25 questions that assessed the knowledge of statistics on areas such as descriptive statistics, sampling methods, study design, parametric and nonparametric tests and multivariate analyses. Right answers were assigned a score of 1, and wrong answers were assigned a score of 0. Total scores ranged from 0 to 25. Statistics attitudes were assessed by the Survey of Attitudes toward Statistics (SATS) scale. The SATS is a 36-item scale that measures 6 domains of attitudes towards statistics. The possible range of scores for each item is between 1 and 7. The total score was calculated by dividing the summed score by the number of items. Higher scores indicate more positive attitudes. The SAT-36 is a copyrighted scale, and researchers are allowed to use it only with prior permission. ( 15 – 16 ) The author obtained permission for use in the coursework evaluation and this study. A semi structured questionnaire was also used to elicit details about the usefulness of coursework.

Statistical analysis

Descriptive statistics such as mean, standard deviation, number and percentages were used to describe the socio-demographic data. General Linear Model Repeated Measures of Analysis of variance was used to compare knowledge and attitude scores across assessments. Categorical data from the semi structured questionnaire are presented as percentages. All the statistical tests were two-tailed, and a p value < 0.05 was set a priori as the threshold for statistical significance. IBM SPSS (28.0) was used to analyse the data.

One hundred and thirty research scholars who had completed coursework (CW) in the last 2–3 years were considered for the study. These scholars were sent Google forms to assess their knowledge and attitudes 2–3 years after coursework. 81 scholars responded (62%), and 4 scholars did not consent to participate in the study. The data of 77 scholars were merged with the data obtained during the coursework program (before and soon after CW). Socio-demographic characteristics of the scholars are presented in Table  1 .

The age of the respondents ranged from 23 to 36 years, with an average of 28.7 years (3.01), and the majority of the respondents were females (65%). Years of experience (i.e., after masters) before joining a PhD programme ranged from 0.5 to 9 years, and half of them had less than three years of experience before joining the PhD programme (median-3). More than half of those who responded were research scholars from the behavioural sciences (55%), while approximately 30% were from the basic sciences (29%).

General Linear Model Repeated Measures of Analysis of variance was used to compare the knowledge and attitude scores of scholars before, soon after and 2–3 after the coursework (will now be referred as “later the CW”), and the results are presented below (Table  2 ; Fig.  1 ).

Comparison of knowledge and attitude scores across the assessments. Later the CW – 2–3 years after the coursework

The scores for knowledge and attitude differed significantly across time. Scores of knowledge and attitude increased soon after the coursework; the percentage of change was 77% and 43% respectively. However, significant reductions in knowledge and attitude scores were observed 2–3 years after the coursework compared to scores soon after the coursework. The reduction was higher for attitude scores; knowledge and attitude scores have decreased by 10% and 37% respectively. The change in scores across assessments is evident from the graph, and clearly the effect size is higher for attitude than knowledge.

The scores of knowledge or attitude before the coursework did not significantly differ with respect to gender or age or were not correlated with years of experience. Hence, they were not considered as covariates in the above analysis.

A semi structured questionnaire with open ended questions was also administered to elicit in-depth information about the usefulness of the coursework programme, in which they were also asked to self- rate their knowledge. The data were mostly categorical or narratives. Research scholars’ self-rated knowledge scores (on a scale of 0–10) also showed similar changes; knowledge improved significantly and was retained even after the training (Fig.  2 ).

Self-rated knowledge scores of research scholars over time. Later the CW – 2–3 years after the coursework

The response to the question “ How has coursework changed your attitude toward statistics?”, is presented in Fig.  3 . The responses were Yes, positively, Yes - Negatively, No change – still apprehensive, No change – still appreciate, No change – still hate statistics. The majority of the scholars (70%) reported a positive change in their attitude toward statistics. Moreover, none of the scholars reported negative changes. Approximately 9% of the scholars reported that they were still apprehensive about statistics or hate statistics after the coursework.

How has coursework changed your attitude toward statistics?

Those scholars who reported that they were apprehensive about statistics or hate statistics noted the complexity of the subject, lack of clarity, improper instructions and fear of mathematics as major reasons for their attitude. Some responses are listed below.

“The statistical concepts were not taught in an understandable manner from the UG level” , “I am weak in mathematical concepts. The equations and formulae in statistics scare me”. “Lack of knowledge about the importance of statistics and fear of mathematical equations”. “The preconceived notion that Statistics is difficult to learn” . “In most of the places, it is not taught properly and conceptual clarity is not focused on, and because of this an avoidance builds up, which might be a reason for the negative attitude”.

Majority of the scholars (92%) felt that coursework has helped them in their PhD, and they were happy to recommend it for other research scholars (97%). The responses of the scholars to the question “ How was coursework helpful in your PhD journey ?”, are listed below.

“Course work gave a fair idea on various things related to research as well as statistics” . “Creating the best design while planning methodology, which is learnt form course work, will increase efficiency in completing the thesis, thereby making it faster”. “Course work give better idea of how to proceed in many areas like literature search, referencing, choosing statistical methods, and learning about research procedures”. “Course work gave a good idea of research methodology, biostatistics and ethics. This would help in writing a better protocol and a better thesis”. “It helps us to plan our research well and to formulate, collect and plan for analysis”. “It makes people to plan their statistical analysis well in advance” .

This study evaluated the effectiveness of the existing coursework programme in an institution of higher medical education, and investigated whether the coursework programme benefits research scholars by improving their knowledge of statistics and attitudes towards statistics. The study concluded that the coursework program was beneficial for improving scholars’ knowledge about statistics and attitudes toward statistics.

Unlike other studies that have assessed attitudes toward statistics, the study participants in this study were research scholars. Research scholars need extensive training in statistics, as they need to apply statistical tests and use statistical reasoning in their research thesis, and in their profession to design research projects or their future student dissertations. Notably, no studies have assessed the attitudes or knowledge of research scholars in statistics either across the PhD training period or after intensive statistics training programs. However, the findings of this study are consistent with the findings of a study that compared the knowledge and attitudes toward teaching and education design of PhD students after a two-day educational course and instructional design workshop [ 14 ].

Statistics educators need not only impart knowledge but they should also motivate the learners to appreciate the role of statistics and to continue to learn the quantitative skills that is needed in their professional lives. Therefore, the role of learners’ attitudes toward statistics requires special attention. Since PhD coursework is possibly a major contributor to creating a statistically literate research community, scholars’ attitudes toward statistics need to be considered important and given special attention. Passionate and engaging statistics educators who have adequate experience in illustrating relatable examples could help scholars feel less anxious and build competence and better attitudes toward statistics. Statistics educators should be aware of scholars’ anxiety, fears and attitudes toward statistics and about its influence on learning outcomes and further interest in the subject.

Strengths and limitations

Analysis of changes in knowledge and attitudes scores across various time points of PhD training is the major strength of the study. Additionally, this study evaluates the effectiveness of intensive statistical courses for research scholars in terms of changes in knowledge and attitudes. This study has its own limitations: the data were collected through online platforms, and the nonresponse rate was about 38%. Ability in mathematics or prior learning experience in statistics, interest in the subject, statistics anxiety or performance in coursework were not assessed; hence, their influence could not be studied. The reliability and validity of the knowledge questionnaire have not been established at the time of this study. However, author who had prepared the questionnaire had ensured questions from different areas of statistics that were covered during the coursework, it has also been used as part of the coursework evaluation. Despite these limitations, this study highlights the changes in attitudes and knowledge following an intensive training program. Future research could investigate the roles of age, sex, mathematical ability, achievement or performance outcomes and statistics anxiety.

The study concluded that a rigorous and intensive training program such as PhD coursework was beneficial for improving knowledge about statistics and attitudes toward statistics. However, the significant reduction in attitude and knowledge scores after 2–3 years of coursework indicates that a refresher program might be helpful for research scholars as they approach the analysis stage of their thesis. Statistics educators must develop innovative methods to teach research scholars from nonstatistical backgrounds. They also must be empathetic to understanding scholars’ anxiety, fears and attitudes toward statistics and to understand its influence on learning outcomes and further interest in the subject.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

The author would like to thank the participants of the study and peers and experts who examined the content of the questionnaire for their time and effort.

This research did not receive any grants from funding agencies in the public, commercial, or not-for-profit sectors.

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This study used data already collected data (before and soon after coursework). The data pertaining to knowledge and attitude towards statistics 2–3 years after coursework were collected from research scholars through the online survey platform Google forms. The participants were invited to participate in the survey through e-mail. The study was explained in detail, and participation in the study was completely voluntary. Informed consent was obtained online in the form of a statement of consent. The confidentiality of the data was assured, even though identifiable personal information was not collected. This non-funded study was reviewed and approved by NIMHANS Institute Ethics Committee (No. NIMHANS/21st IEC (BS&NS Div.)

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Philip, M. Measurement and analysis of change in research scholars’ knowledge and attitudes toward statistics after PhD coursework. BMC Med Educ 24 , 512 (2024). https://doi.org/10.1186/s12909-024-05487-y

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Received : 27 October 2023

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DOI : https://doi.org/10.1186/s12909-024-05487-y

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