Quantitative Psychology

Quantitative psychology is the study of methods and techniques for the measurement of human attributes, the statistical and mathematical modeling of psychological processes, the design of research studies and the analysis of psychological data.

Quantitative psychology is central to all aspects of psychology: science, education, public interest and practice. This essential role of quantitative psychology is reflected in the fact that Division 5 — Evaluation, Measurement and Statistics — is one of the Charter Divisions of the APA.

Quantitative psychology includes research and development in a number of broad areas: measurement, research design and statistical analysis (see Aiken, West, Sechrest, & Reno, 1990), as well as mathematical and statistical modeling of psychological processes. Within each of these areas, quantitative psychologists develop new methodologies; they also evaluate existing methodologies to examine their behavior under conditions that exist in psychological data (e.g., with small samples). This work supports the substantive research of all areas within psychology.

Doctoral Programs in Quantitative Psychology and Related Programs, for review by program members. See below for an explanation of how this list was formed.

University	Program Name
PROGRAMS OFFERING A PHD IN QUANTITATIVE PSYCHOLOGY
Arizona State University	Quantitative Research Methods in Psychology
University of British Columbia	Quantitative Methods
University of California, Davis	Quantitative Psychology
University of California, Los Angeles	Quantitative Psychology
Fordham University	Psychometrics
Georgia Institute of Technology	Quantitative Psychology
University of Illinois, Champaign	Quantitative Psychology
University of Kansas	Quantitative Training Program
McGill University	Quantitative Psychology
University of Minnesota	Quantitative and Psychometric Methods
University of Missouri	Quantitative Psychology
University of New Mexico	Quantitative/Methodology
University of North Carolina	Quantitative Psychology
University of Notre Dame	Quantitative Psychology
Ohio State University	Quantitative Psychology
University of Oklahoma	Quantitative Psychology
Purdue University	Quantitative Psychology
University of Rhode Island	Research Methods
Simon Fraser	Theory and Methods
University of Southern California	Quantitative
Vanderbilt University	Quantitative Methods and Evaluation
University of Virginia	Quantitative
University of Western Ontario	Personality and Measurement
PROGRAMS WITH A CONCENTRATION IN QUANTITATIVE METHODS IN COMBINATION WITH SUBSTANTIVE AREAS
Michigan State University	Concentration in Quantitative Methods and Evaluation Science Concentration
New York University	Minor in Quantitative Psychology
Ohio University	Applied Quantitative
University of Washington	Quantitative
DEVELOPMENTAL PROGRAMS OFFERING METHODOLOGY CONCENTRATION
Pennsylvania State University	Department of Human Development and Family Studies, Developmental Research Methodology Concentration

Following our definition of quantative psychology, we began our resource analysis by developing a list of the PhD concentrations in quantitative psychology that are housed in departments of psychology. We used a number of sources to develop the list:

A list of training programs in quantitative methods developed by APA Division 5, Evaluation, Measurement and Statistics. In March, 2005, Division 5 undertook the project of creating a list of training programs in quantitative methods, to include programs in psychology and education. Division 5 made a call for program identification from the email list of its members.
"Graduate Study in Psychology, 2007." The Task Force received an advance copy of in July 2006. From this we culled all programs indexed under “Quantitative Psychology/Psychometrics.” A number of well recognized quantitative PhD programs were not listed in the index. We reviewed the actual narratives of individual departments in the book to determine whether these departments listed a quantitative concentration.
Departmental websites. We reviewed websites of departments that historically had had a quantitative concentration but were not identified by the above sources.
Self-identified programs in a survey by Aiken, West and Millsap (2007). Aiken et al (2007) had carried out a survey of the quantitative curriculum of all PhD programs in North America, with data collection completed in 1999 and with an 86 percent response rate. In that survey departments were asked whether they had PhD programs in any area of quantitative methods. In fall, 2006, we reviewed the websites of all programs that had answered affirmatively to determine whether the quantitative programs still existed. We also contacted quantitative faculty in those departments to determine whether the programs were still functioning.

Once a student has decided that quantitative psychology may be an area of possible doctoral study, the APA Task Force for Increasing the Number of Quantitative Psychologists advises students to consider the following academic and research experiences to prepare for the doctoral programs in North America. It is important to note that doctoral programs in quantitative psychology vary in the background and experience that they require for their applicants, so it is important to visit individual program websites for specific requirements.

Wherever possible, it is useful to identify a faculty member who has quantitative interests to supervise and mentor during the preparation for graduate school. At many schools this may be difficult because there are no faculty whose primary focus is on quantitative methods. If this is the case, it is useful to align oneself with a faculty mentor who is an active researcher from whom one can receive advice and gain experience as a research apprentice.

Coursework in mathematics and statistics in undergraduate school

Among the frequently asked questions of undergraduate students who are considering the field of quantitative psychology is what level of mathematics training is required. In fact, this answer varies widely by quantitative program. Quantitative programs do not typically state minimum mathematics and statistics requirements for admission. Yet, admissions committees carefully review transcripts for evidence that the applicant has studied mathematics and/or statistics and has talent in this area. It is useful, and for admission to some quantitative programs essentially mandatory, that students have successfully completed a college-level calculus series. A course in linear algebra is also often useful.

A sustained interest in mathematics and/or statistics is important. Many undergraduates place out of college mathematics courses through advanced placement tests and coursework completed during high school. It is also possible that students have pursued majors during college that require few mathematics requirements. If this is the case, it is still important show evidence that there is an adequate interest and good performance in mathematics.

Coursework in mathematics in graduate school

Some quantitative graduate programs will encourage applicants, once accepted to the doctoral program, either to brush up or strengthen their math abilities by taking courses in the math, statistics or biostatistics departments. In addition to calculus and linear algebra, math courses might include advanced calculus and multivariate calculus. Statistics courses might include introduction to statistics, statistical methods and theory, numerical methods, statistical linear models or probability.

Undergraduate coursework in quantitative methodology in psychology

There are courses in the psychology department that would be very useful to take prior to applying to a quantitative doctoral program. The number of these courses available within the department of psychology varies widely across universities. They may consist of courses covering introductory statistics, advanced undergraduate statistics, tests and measurement, and research methods. Sometimes these courses are offered in other departments as well. Quantitative admissions committees will expect students to show excellent performance in the following types of psychology courses: Statistics for the behavioral sciences, research methods, tests and measurements (psychometric theory) and any advanced psychological statistics course that is offered.

Taking graduate methodology courses as an undergraduate

Some psychology departments will allow (with permission) qualified undergraduates to enroll in graduate-level statistics courses such as a two-semester first year doctoral sequence or upper-level quantitative courses (e.g., multivariate analysis, structural equation modeling and psychometric theory). These experiences are extremely valuable and demonstrate to an admissions committee a student’s ability to perform as a graduate student.

Independent research project

If there is an opportunity to conduct an honors thesis, capstone experience or master’s thesis, this independent research is an excellent way to demonstrate the ability to conceptualize a research problem, select an appropriate design, obtain data, conduct analyses and report findings. Honors theses that involve data-intensive experiences involving statistical/quantitative modeling are strongly encouraged.

Data-intensive research experience

Another important experience that can help an undergraduate or master’s student prepare for a quantitative program is simply joining a professor’s laboratory where there is a chance for significant involvement in a research project (e.g., as a research assistant). While research participation is always useful, for a doctoral program in quantitative a student’s involvement should ideally be focused on the data component of the research, including assisting with research design, item writing, data management, planning for statistical analyses, conducting analyses using common and specialized statistical software and reporting findings.

Other valuable experience

The following additional activities are useful ways to help an admissions committee see a student’s commitment to quantitative. Sometimes there are opportunities to participate in additional educational experiences, such as multiday workshops in quantitative methods, that are offered either at one’s own institution, prior to a national conference or in some other forum. These workshops do not substitute for a course, but they provide a valuable overview of quantitative area. Students are encouraged to present their research (preferably with a quantitative emphasis) at a professional conference and/or publish their research. Most often, it is expected that these professional activities will be conducted under the supervision of a mentor or research advisor. Some students have the opportunity to be a paid (or unpaid) teaching assistant for a research methods course, a statistics course or other related course.

Mathematical psychology is an approach to scientific research across multiple subdisciplines of psychology that “is broadly defined to include work of a theoretical character that uses mathematical methods, formal logic, or computer simulation” (Society for Mathematical Psychology website, accessed Nov. 7, 2012). Scholarly work involving approaches of mathematical psychology includes research in such areas as complex decision making, neural networks and brain mechanisms, models of perception, psycholinguistics and computational models of language, learning, subjective probability, game theory, psychophysics, problem solving and beyond. In fact, quantitative programs in some departments of psychology include tracks in both traditional areas of quantitative psychology (measurement, research design and statistical analysis) and in mathematical and statistical modeling. In other programs, quantitative methods training for the PhD is focused on the traditional areas; mathematical psychology exists as a separate concentration that may or may not exist in the same programs as those that house the more traditional foci. In all, only a handful of psychology departments identify a distinct mathematical psychology concentration.

University	Program Name
University of California, Irvine	Department of Cognitive Sciences
Indiana University	Concentration in Mathematical Psychology
Ohio State University	Quantitative Psychology/Judgment and Decision making
University of Illinois, Champaign	Quantitative Psychology
Purdue University	Quantitative/Mathematical

Departments of educational psychology often house concentrations in quantitative methods. There is a strong tradition of methodological training in educational psychology, with research focused toward educational issues (e.g., educational measurement). Individuals trained in quantitative methods in education “bridge the gap between the theoretical statistician/psychometrician and the educational researcher. They teach, act as consultants to the educational researcher, and conduct their own research on statistics and psychometrics as applied to education” (University of Wisconsin, Department of Educational Psychology website, Feb. 6, 2007).

University	Program Name
Arizona State University	Measurement, Statistics and Methodological Studies
University of California, Los Angeles	Social Research Methodology
University of Colorado	Research and Evaluation Methodology
University of Northern Colorado	Applied Statistics and Research Methods
Columbia University	Measurement, Evaluation and Statistics
University of Connecticut	Measurement, Evaluation and Assessment
Florida State University	Measurement and Statistics
University of Florida	Research and Evaluation Methodology
University of South Florida	Educational Measurement and Research
University of Georgia	Research, Evaluation, Measurement and Statistics
University of Illinois	Queries Division: Studies in interpretive, statistical, measurement and evaluative methodologies for education
Indiana University	Inquiry Methodology
University of Iowa	Educational Measurement and Statistics
University of Maryland	Measurement, Statistics, and Evaluation
University of Massachusetts	Research and Evaluation
Michigan State	Measurement and Quantitative Methods
University of Minnesota	Quantitative Methods in Education
University of Nebraska, Lincoln	Qualitative and Quantitative Methods in Education
City University of New York	Quantitative, Educational Policy
University of North Carolina, Greensboro	Educational Research Methodology
University of Pittsburgh	Research Methodology
University of South Carolina	Educational Psychology and Research
University of Texas	Quantitative Methods
Texas A&M	Research, Measurement, and Statistics
James Madison University, Virginia	Quantitative Methods
University of Wisconsin, Madison	Quantitative Methods Area

Disclaimer. We have attempted to capture as many methodology programs housed in Departments of Educational Psychology as possible. We do not claim that this list is complete. Visit the National Council on Measurement in Education (NCME) for a list of programs in educational measurement.

We thank members of the Educational Psychology community, including Deborah Bandalos, University of Georgia, David Kaplan, University of Wisconsin, and David Rindskopf, the Graduate Center, CUNY, for their help in generating this list.

Table 1. Number of job advertisements in various areas of Psychology in 1991-1996 versus number of earned doctorates in these areas during the same 6 years.

Area	Number of Job Advertisements	Number of Earned Doctorates	Job Advertisements per Earned Doctorate
Cognitive	413	674	.61
Developmental	401	1040	.39
Experimental	408	844	.48
Industrial Organizational	349	876	.40
Physiological	135	446	.30
Social	553	877	.63
TOTAL OF ABOVE	2259	4757	.47

Quantitative	292	122	2.40

Note: Counts of Job Ads taken from Bell and Gordie (1997).

Counts of Earned Doctorates taken from NSF Survey of Earned Doctorates, as compiled by the APA Office of Research, January, 2006.

Links to related articles

Too few in quantitative psychology
by Rebecca Clay in the Monitor

As Test-Taking Grows, Test-Makers Grow Rarer
by David Herszenhorn in the NY Times

Links to other web resources

Society for Mathematical Psychology

Acknowledging the fact that the number of quantitative psychologists is dwindling at the same time that there is a pressing need for training and education in all aspects of quantitative methods, the APA Council of Representatives authorized a special task force in 2006. Members of the task force were selected by the APA Board of Scientific Affairs (BSA) and the APA Board of Educational Affairs (BEA). The Task Force for Increasing the Number of Quantitative Psychologists was charged with addressing both the pipeline of qualified students and opportunities for training in quantitative psychology (with an emphasis on early undergraduate education through postdoctoral training). One of the goals of the task force was the development of strategies for increasing representation of minorities and women in the field of quantitative psychology. The task force submitted its final report to the Council of Representatives in 2009. The report details approaches for making qualified students aware of the discipline of quantitative psychology. It also contains an analysis of sources of students (within and beyond psychology), and includes strategies to inform those who mentor undergraduate students into graduate disciplines about the field of quantitative psychology.

Task Force Members

Chair, Leona S. Aiken, PhD, Arizona State University
Herman Aguinis, PhD, University of Colorado, Denver
Mark Appelbaum, PhD, University of California San Diego
Gwyneth M. Boodoo, PhD, GMB Enterprises
Michael C. Edwards, PhD, Ohio State University
Richard D. Gonzalez, PhD, University of Michigan
Abigail Panter, PhD, University of North Carolina
Debra Park, West Deptford High School
Thanos Patelis, PhD, The College Board