Measurement, Evaluation, and Statistics
Program Description
The Measurement, Evaluation, and Statistics Program offers degree programs in Applied Statistics and in Measurement and Evaluation.
M.S. in Applied Statistics
The M.S. in Applied Statistics is a 32-point program that typically requires three semesters of full-time study. Students may complete the program on either a fall–spring–fall or fall–spring–summer schedule.
The program prepares students for positions in applied research settings, testing organizations, government agencies, and business organizations. In addition to satisfactorily completing the required coursework, students must complete an integrative project.
Ed.M. in Measurement and Evaluation
The Ed.M. in Measurement and Evaluation is a 60-point, two-year master’s degree program. It prepares students for positions in educational research, program evaluation, and testing organizations.
In addition to satisfactorily completing the required coursework, students must complete an integrative project.
Ph.D. in Measurement and Evaluation
The Ph.D. in Measurement and Evaluation prepares graduates for careers in a wide range of educational, research, testing, government, health care, and business settings. Students develop specialized knowledge and skills in test theory; test and instrument development and validation; program evaluation and causal inference; and the quantitative analysis of educational and psychological data.
Graduates pursue careers as college and university professors teaching measurement, evaluation, and statistics. Others work in city and state departments of education, where they plan and supervise testing programs and research and evaluation projects. Graduates are also employed by test publishers, licensure and certification boards, and government agencies, where they contribute to test development or manage large-scale testing programs. Still others work in evaluation, research design, and statistics for contract research firms, health care organizations, and businesses.
A Doctor of Philosophy degree is generally required for college and university teaching positions and for positions involving substantial professional responsibility in testing organizations, departments of education, and licensure and certification boards.
The 75-point Ph.D. program is appropriate for individuals with strong quantitative and technical skills who wish to study theoretical issues in measurement and evaluation. It is also appropriate for individuals with a strong background in a substantive area of psychology or education who wish to advance the development and application of measurement techniques in that area.
Academic Progress
Students must make satisfactory progress toward completion of their degree. A grade of C– or lower may result in dismissal from the program.
Program Degrees
Expand the accordion(s) to view the degree requirements:
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The master's degree in Applied Statistics offers preparation in applied statistics, data analysis and research methods, to prepare students for a number of research and applied positions in educational settings, testing bureaus, business, industry, and government.
The M.S. degree requires at least one year of study. In addition to the satisfactory completion of course work, a culminating project is required.
Statistics RequirementsApplied Statistics Core Courses (27 points):
The following courses are required (in special circumstances, substitute courses may be approved by an advisor.):
- HUDM 4125 Statistical inference (3)
- HUDM 5126 Linear models and regression analysis (3)*
- HUDM 5150 Statistical Careers, Communications and Capstone (3)**
- HUDM 6026 Computational statistics (3)
and at least one of:
- HUDM 5123 Linear models and experimental design (3)
- HUDM 6030 Multilevel and longitudinal data analysis (3)
and at least one of:
- HUDM 6055 Latent structure analysis (3)
- HUDM 6122 Multivariate analysis (3)
*Under special circumstances HUDM 5122 may be substituted for HUDM 5126; advisor approval is required.
**This should be taken in the last Fall semester of study. This course includes completion of a culminating project.
Statistics Electives:
Other advanced statistics courses offered by the Program or by other Departments/ Schools of Columbia University may be selected, in consultation with an advisor, to complete the 27-point requirement. Examples of candidate courses include: HUDM 5001, HUDM 5059, HUDM 5124, HUDM 5128, HUDM 5130, and HUDM 5133.
Breadth Requirement (6 points):
At least 6 points must be taken at Teachers College from outside the Program in Measurement, Evaluation, and Applied Statistics. (Non-HUDM)
Culminating Experience:
A special project that is conducted in consultation with an advisor.
Transfer Credit:
For the M.S. degree program, no transfer credit is granted for work completed at other universities.
Satisfactory Progress
Students must also make satisfactory progress towards completion of the degree. A grade of C- or lower may result in dismissal from the program.
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Measurement Core (15 points):
- HUDM 5059 Psychological measurement (3)
- HUDM 5124 Multidimensional scaling and clustering (3)
- HUDM 6051 Psychometric theory I (3)
- HUDM 6052 Psychometric theory II (3)
- HUDM 6055 Latent structure analysis (3)
Evaluation Core (12 points):
- HUDM 5130 Meta-analysis (3)
- HUDM 5133 Causal inference for program evaluation (3)
- ORLJ 5040 Research methods in social psychology (3)
with at least one Evaluation course selected from the following:
- HP8640 Methods in program evaluation (3) (at Mailman School of Public Health)
- P8705 Evaluation of health programs (3) (at Mailman School of Public Health)
Quantitative Methods Core (18 points):
- HUDM 4122* Probability and statistical inference (3)
- HUDM 5122* Applied regression analysis (3)
- HUDM 5123 Linear models and experimental design (3)
- HUDM 6026 Computational statistics (3)
- HUDM 6030 Multilevel and longitudinal data analysis (3)
- HUDM 6122 Multivariate analysis I (3)
*HUDM 4125 may be substituted for HUDM 4122 and HUDM 5126 may be substituted for HUDM 5122.
Measurement, Evaluation, and Statistics Electives (18 points):
In consultation with an advisor, students choose 18 points of courses from the below list, or from advanced courses offered at Columbia University Statistics Department, Mailman School of Public Health, and Programs across Teachers College. The following are suggested but not required:
- HUDM 5058 Choice and decision making (3)
- P8120 Analysis of categorical data (3) (at Mailman School of Public Health)
- P8121 Generalized linear models (3) (at Mailman School of Public Health)
- W4640 Bayesian statistics (3) (at the Columbia Statistics Program)
- HUDM 5250 Research practicum in measurement and evaluation (0-4)
Psychology (18 points):
In consultation with an advisor, a group of courses aimed at substantive preparation in the field of psychology.
Related Courses (6 points):
Selected from the areas of curriculum development, guidance, applied human development, supervision, and administration, and in consultation with an advisor.
Dissertation Advisement and Seminar (minimum of 3 points):
HUDM 7500* Dissertation seminar (1-3 credits each for two semesters) required
HUDM 8900 Dissertation advisement (0)
Special Requirements:
The first two years require full-time study. In addition to the above coursework, an approved certification paper, successful performance on the certification examination, and completion of an approved doctoral dissertation are also required.
Transfer Credit
Of a planned program of 90 points, at least 45 points must be taken through Teachers College registration. A maximum of 45 points may be transferred from another university for the Ed.D. degree. Only completed graduate courses with earned grades of B or higher that appear on the student’s transcript from a regionally accredited institution may be considered for transfer credit.
The student files a “Request for an Allocation of Graduate Credit” with the Office of the Registrar. Once the Registrar's Office determines the eligibility of courses for transfer, final determination of transfer credit is awarded at the discretion of the faculty advisor after evaluation of the courses for content and relevance to program requirements. The Office of the Registrar notifies the student of the results.
Satisfactory Progress
Students must also make satisfactory progress towards completion of the degree. A grade of C- or lower may result in dismissal from the program.
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Degree Requirements - 60 Points
Measurement Core Courses (12 points):
- HUDM 5059 Psychological measurement (3)
- HUDM 6051-6052 Psychometric theory I and II (3 each)
- HUDM 6055 Latent structure analysis (3)
Evaluation Core (6 points): :
- HUDM 5133 Causal inference for program evaluation (3) (recommended)
- T6416 Program evaluation in social services (3) at School of Social Work
- P8582 Program evaluation design for health policy and management (3) at Mailman School of Public Health
- P8640 Methods in program evaluation (3) at Mailman School of Public Health
- P8705 Evaluation of health programs (3) at Mailman School of Public Health
- EDPS 5646 Evaluation of Education and Social Programs (3)
- EDPA 6002 Quantitative Methods for Evaluating Educational Policies and Programs (3)
Quantitative Methods (15 points):
- HUDM 4122 Probability and statistical inference (3)*
- HUDM 5122 Applied regression analysis (3)*
- HUDM 5123 Linear models and experimental design (3)
- HUDM 6030 Multilevel and longitudinal data analysis (3)
- HUDM 6122 Multivariate analysis (3)
*HUDM 4125 may be substituted for HUDM 4122 and HUDM 5126 may be substituted for HUDM 5122.
Psychology (12 points):
- Courses are taken in one or more of the following areas: developmental psychology, cognitive studies, counseling psychology, organizational psychology, or social psychology.
Research Methods (6 points):
- HUD 4120 Methods of empirical research (3)
- HUDM 5250 Research practicum in measurement and evaluation (0-4)
Other Aspects in Education (6 - 9 points):
One course in foundations of education and two courses in curriculum and teaching and/or educational leadership, chosen in consultation with an advisor.
Electives:
Chosen in consultation with an advisor and designed to strengthen and broaden the student’s professional preparation.
Culminating Experience:
A project that is conducted in consultation with an advisor.
Transfer Credit:
For the Ed.M. degree, 30 points must be completed under the auspices of Teachers College, including 18 points in Teachers College courses. A maximum of 30 points of graduate credit may be transferred from other accredited institutions. Only completed graduate courses with earned grades of B or higher will be considered for transfer credit. For more information, please speak with the Transfer Credit Coordinator in the Office of the Registrar.
The student files a “Request for an Allocation of Graduate Credit” with the Office of the Registrar. Once the Registrar’s Office determines the eligibility of courses for transfer, final determination of transfer credit is awarded at the discretion of the Program Director after evaluation of the courses for content and relevance to program requirements. The Office of the Registrar notifies the student of the results.
Satisfactory Progress
Students must also make satisfactory progress towards completion of the degree. A grade of C- or lower may result in dismissal from the program.
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Degree Requirements - 75 Points
Measurement Core (15 points):
- HUDM 5059 Psychological measurement (3)
- HUDM 5124 Multidimensional scaling and clustering (3)
- HUDM 6051 Psychometric theory I (3)
- HUDM 6052 Psychometric theory II (3)
- HUDM 6055 Latent structure analysis (3)
Evaluation Core (9 points):
- HUDM 5130 Meta-analysis (3)
- HUDM 5133 Causal inference for program evaluation (3)
- ORLJ 5040 Research methods in social psychology (3)
- HBSS 6100 Measurement and Program Evaluation (3)
Quantitative Methods Core (21 points):
- MSTM 5030 Topics in probability theory (3)
- HUDM 4125 Statistical inference (3)
- HUDM 5123 Linear models and experimental design (3)
- HUDM 5126 Linear models and regression analysis (3)
- HUDM 6026 Computational Statistics (3)
- HUDM 6030 Multilevel and longitudinal data analysis (3)
- HUDM 6122 Multivariate analysis I (3)
Measurement, Evaluation, and Statistics Electives (18 points):
In consultation with an advisor, students select courses from the following list, as well as more generally from courses offered at other Departments and Schools at Columbia University:
- HUDM 5058 Choice and decision making (3)
- HUDM 5128 Applied Categorical Data Analysis
- HUDM 5100 Programming for Data Science (3)
- HUDM 5250 Research practicum in measurement and evaluation (0-4)
- P8121 Generalized linear models (3) (at Mailman School of Public Health)
- GU4224 Bayesian Statistics (3) (at the Columbia Statistics Program)
- P8640 Methods in program evaluation (3) (at Mailman School of Public Health)
- P8705 Evaluation of health programs (3) (at Mailman School of Public Health)
- EDPS 5646 Evaluation of Educational and Social Programs (3) Quantitative
- EDPA 6002 Methods for Evaluating Educational Policies and Programs (3)
Psychology (minimum of 9 points):
In consultation with an advisor, a group of courses aimed at substantive preparation in the field of psychology.
Dissertation Advisement and Seminar (minimum of 3 points):
HUDM 7500* Dissertation seminar (1-3 credits each for two semesters)
HUDM 8900 Dissertation advisement (0)
Special Requirements:
The first two years require full-time study. In addition to the above coursework, an approved empirical paper, an approved theoretical research paper, successful performance on the certification examination, and completion of an approved doctoral dissertation are required for the Ph.D degree.
M.Phil. Degree
The M.Phil. is an en passant degree awarded to those nearing the completion of the Ph.D. degree. Students contact the Office of Doctoral Studies (ODS) to file for the award of the degree.
To receive the M.Phil., the student must satisfactorily complete the following requirements:
- Complete at least six courses with evaluative grades under Teachers College registration
- Pass the Certification Examination (i.e., Research Methods Examination)
- Complete an approved empirical research paper
- Complete an approved theoretical research paper
- Complete all 75 points of coursework required for the degree
- Be recommended by the Program Advisor and Department Chair for the award of the M.Phil. degree, which signifies certification as a Ph.D. degree candidate who may continue the dissertation requirement under the auspices of the Teachers College faculty.
Candidates should provide copies of both research papers to the Department of Human Development for inclusion in the student’s records.
Transfer Credit
Relevant courses completed in other accredited graduate schools to a maximum of 30 points, or 45 points if completed in another Faculty of Columbia University, may be accepted toward the minimum point requirement for the degree.
Only completed graduate courses with earned grades of B or higher that appear on the student’s transcript from a regionally accredited institution may be considered for transfer credit.
The student files a “Request for an Allocation of Graduate Credit” with the Office of the Registrar. Once the Registrar's Office determines the eligibility of courses for transfer, final determination of transfer credit is awarded at the discretion of the faculty advisor after evaluation of the courses for content and relevance to program requirements. The Office of the Registrar notifies the student of the results.
Satisfactory Progress
Students must also make satisfactory progress towards completion of the degree. A grade of C- or lower may result in dismissal from the program.
Program Faculty
Faculty
- Chia-Yi Chiu
Associate Professor Applied Statistics - James E Corter
Professor of Statistics and Education - Lawrence T DeCarlo
Professor of Psychology and Education - Bryan Sean Keller
Associate Professor of Practice in Applied Statistics - Young-Sun Lee
Associate Professor of Psychology and Education - Youmi Suk
Assistant Professor of Applied Statistics
Professors of Teaching
- Jie Gao
Assistant Professor of Teaching
Program Courses
HUD4120 Methods of empirical research
An introduction to the methods of scientific inquiry, research planning, and techniques of making observations and analyzing and presenting data.
HUDM4050 Introduction to measurement
An introduction to basic concepts and issues in measurement. Descriptive statistics, scales of measurement, norms, reliability, validity. Advantages and limitations of measurement techniques are discussed and illustrated.
HUDM4120 Basic concepts in statistics
Designed as a one‑semester introduction to statistical concepts and methods. An overview of data analysis techniques, including organizing, graphing, analyzing, reporting, and interpreting data. Both descriptive and inferential techniques will be introduced. Use of statistical software is discussed.
HUDM4122 Probability and statistical inference
An introduction to statistical theory, including elementary probability theory; random variables and probability distributions; sampling distributions; estimation theory and hypothesis testing using binomial, normal, T, chi square, and F distributions. Calculus not required.
HUDM4125 Statistical inference
Prerequisite: Course in Calculus. Calculus-based introduction to mathematical statistics. Topics include an introduction to calculus-based probability; continuous and discrete distributions; point estimation; method of moments and maximum likelihood estimation; properties of estimators including bias and mean squared error; large sample properties of estimators; hypothesis testing including the likelihood ratio test; and interval estimation.
HUDM4901 Research and independent study: Measurement and evaluation
Permission required.
HUDM4902 Research and independent study: Applied statistics
Permission required.
HUDM5000 Statistics Lab
Students in this lab must also be enrolled in HUDM 5122 or HUDM 5123.
HUDM5001 Programming for Data Science
This course is an introduction to essential programming concepts, structures, and techniques for data science. Topics covered include data types, data structures, control statements, and functions, using the NumPy and Pandas libraries in the programming language Python. The course also covers version control using GitHub and database management using SQLite. Additionally, the course includes content on data visualizations and coding practices using AI.
HUDM5026 Intro to Data Analysis in R
Prerequisite: HUDM 4122 or HUDM 4125. This course provides an introduction to the R language and environment for statistical computing with an emphasis on the application of fundamental graphical and statistical techniques. While some theory will be presented (for example, when discussing regression models), the focus will be on implementation and interpretation as opposed to study of the statistical properties of the methods.
HUDM5058 Choice and decision making
Surveys research on psychological judgment and decision making, including historical and modern versions of utility theory, Tversky and Kahneman's influential Prospect Theory, emotion and decision making, decisions from experience, and decisions in a social context. The focus is on psychological or descriptive models of how people make decisions, although methods for decision analysis are briefly discussed.
HUDM5059 Psychological measurement
A previous course in statistics or measurement is recommended. An in-depth examination of measurement and associated techniques, norms, classical test theory, reliability, validity, item response theory, issues, and applications.
HUDM5122 Applied Regression Analysis
Prerequisite: HUDM 4122, HUDM 4125, HUDM 4120 or equivalent. This course is an introduction to regression with emphasis on the practical aspects. Topics include: simple linear regression, multiple linear regression, regression with categorical independent variables and/or interactions, role of assumptions, model diagnostics, and generalized linear models. Class time includes lab time devoted to applications with IBM SPSS.
HUDM5123 Linear Models Experimentl Dsgn
Prerequisite: HUDM 5122 or HUDM 5126. This course provides an overview of experimental design and analysis from the perspective of the general linear modeling framework. Topics include the incremental F test for model comparisons, dummy and effect coding, single and multiple factor ANOVA and ANCOVA, analysis of categorical outcome data via generalized linear models, and repeated measures. The course includes lab time devoted to computer applications.
HUDM5124 Multidimensional scaling and clustering
An introduction to exploratory multivariate data analysis techniques, known in machine learning contexts as "unsupervised learning" methods, for analyzing multivariate profiles or proximity data (similarities, correlations, etc.). The surveyed methods include multidimensional scaling, which represents similarities among items by plotting the items into a geometric space, and cluster analysis for grouping items or entities. Graph and network models will also be discussed. Applications in psychology, marketing, education. Familiarity with R recommended.
HUDM5126 Linear models and regression analysis
Prerequisite: HUDM 4125 or HUDM 4122. Introduction to the theory and application of linear regression using calculus and matrix algebra. Focus on multiple regression models including dummy variables and polynomial models, regression diagnostics, and advanced methods such as weighted least squares, multilevel models, and an introduction to the generalized linear model.
HUDM5128 Applied Categorical Data Analysis
Prerequisite: HUDM 5122 or HUDM 5126. This course provides an introduction to basic concepts and common statistical models and analyses for categorical data. It includes enough theory, examples of applications, and practice using categorical techniques so that students can use these methods in their own research, as well as critically read research papers that use such methods. Topics include description and inference for binomial and multinomial; analysis of contingency tables; generalized linear models for discrete data; logistic regression; multicategory logit models; inference for matched pairs and correlated clustered data; and loglinear models.
HUDM5133 Causal inference for program evaluation
This course will prepare students to start research in causal inference. It will provide an introduction to the theoretical and practical aspects of causal inference methods, along with real-world applications in education. Topics include: the Neyman-Rubin potential outcomes framework, Pearl’s directed acyclic graphical models, single-world intervention graphs, non-equivalent control group designs using both traditional methods (e.g., matching, weighting, regression) and machine learning methods, optimal treatment regimes, regression discontinuity designs, and sensitivity analysis.
HUDM5150 Statistical Careers, Communication, and Capstone
This is a capstone course for the M.S. degree in Applied Statistics. In this course we will discuss best practices in statistical analyses, including the role of a consultant and ethical issues encountered in analyses. Students will also study best practices for effective communication of statistics, including verbal, written, and graphical means of communication. Students will produce a capstone paper integrating the methods and skills they have learned across the M.S. degree. Internships that align with the goals of the M.S. program are recommended as opportunities for students to develop and apply statistical skills through practical experience in relevant professional and industry settings.
HUDM5250 Research practicum in measurement and evaluation
Permission required. Students enrolled are expected to spend a semester involved in a research project, either assisting a faculty member or in an applied setting. A formal report will be submitted.
HUDM6026 Computational statistics
Prerequisite: HUDM 4125 and either HUDM 5122 or HUDM 5126. Provides an introduction to computationally intense methods in applied statistics, taught in R. Topics include methods of evaluating statistical estimators; design, implementation, and reporting of Monte Carlo simulation studies; resampling and reordering methods; and nonparametric and data mining approaches to regression.
HUDM6030 Multilevel longitudinal data analysis
Multilevel models include a broad range of models called by various names, such as random effects models, multi-level models, and growth curve models. This course introduces the background and computer skills needed to understand and utilize these models.
HUDM6051 Psychometric Theory I
Permission required. Prerequisites: Both HUDM 5059 and HUDM 5122 or 5126. Classical test theory, and test/instrument development and validation.
HUDM6052 Psychometric theory II
Prerequisite: HUDM 6051 or equivalent. Item response theory & applications, and cognitive diagnostic models.
HUDM6053 Cognitive Diagnosis in Psychometrics
To equip our students with the cutting-edge methods for analyzing educational data, the course provides an in-depth introduction to cognitive diagnosis models and methods, a novel psychometric framework for developing educational and psychological tests and analyzing item-response data. This course covers the rationale, bases and frameworks for analyzing cognitive diagnosis data, as well as the most recent developments in the area. Specific topics include parametric and nonparametric methods for cognitive diagnosis, algorithms for model estimation and procedures for model comparison, theories on skill and item associations and their validations, and computerized adaptive testing. These topics are taught through lectures, discussions, inquiry-based strategies, and hands-on data analysis.
HUDM6055 Latent structure analysis
Prerequisite: HUDM 5122. Recommended: HUDM 6122. Study of latent structure analysis, including measurement models for latent traits and latent classes, path analysis, factor analysis, structural equations, and categorical data analysis.
HUDM6122 Multivariate analysis I
An introduction to multivariate statistical analysis, including matrix algebra, general linear hypothesis and application, profile analysis, principal components analysis, discriminant analysis, and classification methods.
HUDM6900 Advanced research and independent study
Permission required.
HUDM7500 Dissertation seminar
Permission required. Development of doctoral dissertations and presentation of plans for approval. Registration limited to two terms. Ph.D & Ed.D students must complete 3 points over 2 semesters prior to proposing their dissertation.
HUDM8900 Dissertation advisement
Individual advisement on doctoral dissertation. Fee to equal 3 points at current tuition rate for each term. See section in catalog on Continuous Registration for Ed.D./ Ph.D. degrees. Ed.D & Ph.D students must register for this every semester while completing their dissertation.