Keith Markus' Urban Sprawl:

  EPSY U73000 GC
Introduction to Psychometrics
CRN 48937
This course is equivalent to PSY U76000
Psychometric Methods

Course Information
American Educational Research Association
American Psychological Association

National Council on Measurement in Education
Psychometric Society
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Spring 2023

Time: Wednesday 6:30-8:30 PM
Graduate Center 3212

Contact Information:
Professor Keith A. Markus  (This is the best way to contact me.)
Office: 10.65.04  New Building, John Jay College
Address:  Psychology Department, 10th Floor
John Jay College of Criminal Justice, CUNY
524 W59th Street, New York, NY, 10019
Office Hours:
  Please contact me by email.  Most questions can be answered more quickly by email.  When that is not the case, we can use email to schedule an in-person appointment.

Course Description:
  The course offers a general introduction to psychometric methods primarily emphasizing classical test theory, test construction and validation, and test use.  The emphasis lies with developing a firm understanding of basic psychometric concepts.  This course lays a foundation for more advanced courses in specific topics introduced here. The course understands psychometrics and testing as applying broadly, not just to paper and pencil tests but also to performance assessments, behavioral observations, measured variables in experiments and quasi-experiments, surveys, and other forms of behavioral data collection. However, much of the material will emphasize measurement involving multiple indicators of a common construct.

Course Objectives: The course assumes a foundation in basic statistics and a healthy curiosity but little more. The more you put into the course, the more you will get out of the course. The course design reflects the following objectives.
1. Students will gain a basic understanding of the foundations of test theory that will prepare them to pursue more advanced topics (e.g., item response theory, structural equation modeling).
2. Students will gain the background and confidence to critically read technical manuals and other documentation in conjunction with use of published tests.
3. Students will gain facility with conceptual tools for thinking through issues of validity and reliability as applied to all measures from dependent variables in experiments to large scale testing programs.
4. Students will gain a level of comfort with algebraic representations of test scores and the use of these to think through applied problems related to test use and interpretation.
5. Students will gain an increased sensitivity to the fallibility of educational and psychological tests and the limits to their use and interpretation.
6. Students will gain exposure to the use of statistical software for conducting psychometric analyses and some experience with such analyses.

Text Book:
Bandalos, D. L. (2018). Measurement Theory and Applications for the Social Sciences.  New York:  Guildford.

Bandalos 2018 Book Cover
Additional Reading:
American Educational Research Association, American Psychological Association & National Council on Measurement in Education (2014).  Standards for educational and psychological testing.  Washington, DC:  AERA.
Standards Book Cover
Recommended Reading:
American Psychological Association (2020).  Publication manual of the American Psychological Association (7th ed.).  Washington, DC: Author.  (Project papers should be written in APA style and format.)

Markus, K. A. & Borsboom, D. (2013).  A theory of test score interpretation.  (from Markus, K. A. & Borsboom, D., 2013.  Frontiers of test validity theory.  New York:  Routledge.  A copy of the chapter will be provided.)

Course Flow:  Familiarize yourself with the reading material before the corresponding lecture.  Lectures will summarize and clarify the reading.  In general, I would rather answer your questions than lecture. I will use class time to illustrate and amplify particularly tricky points based on past experience. It is not possible to cover all the material in class.

I will illustrate psychometric concepts primarily using spreadsheets and R.  Familiarity with the software is not a course requirement. However, learning psychometrics simply by reading about it is akin to learning to swim, ski, or play a musical instrument simply by reading about it. Actual practice is a much more effective method. Whether you use a simple calculator, a spreadsheet, or advanced statistical software, it is a good habit to play around with the material by constructing concrete examples and taking a try-and-see attitude toward the material. If something seems puzzling, make up an example and try it out. If something seems counter-intuitive to you, try to construct a counterexample. The more concrete you make psychometrics, the more comfortable you will feel with the material, the better you will understand it, and the more skills you will develop that you can apply outside of the class. None of the this is required for the course, but it will make it more fun, more interesting, and more valuable at a practical level.

Course Project:

The course project is broken into four parts: topic, and Parts 1 to 3.  Details of the assignment along with R scripts will be provided through Blackboard.  Due dates are listed below on the course schedule.

Grading:  The course project is the only graded assignment. The topic is worth 10%, Part 1 25%, Part 2 30% and Part 3 35%.  Letter grades will be assigned as indicated below.

Letter Grade
Percent Grade

Special Needs:
To request accommodations please contact the Office of the Vice President for Student Affairs (Room 7301 Graduate Center; (212) 817-7400). Information about accommodations can be found in the Graduate Center Student Handbook 05-06, pp. 51-52).

Academic Honesty:    
The Graduate Center of The City University of New York is committed to the highest standards of academic honesty. Acts of academic dishonesty include—but are not limited to—plagiarism, (in drafts, outlines, and examinations, as well as final papers), cheating, bribery, academic fraud, sabotage of research materials, the sale of academic papers, and the falsification of records. An individual who engages in these or related activities or who knowingly aids another who engages in them is acting in an academically dishonest manner and will be subject to disciplinary action in accordance with the bylaws and procedures of The Graduate Center and the Board of Trustees of The City University of New York.  

Each member of the academic community is expected to give full, fair, and formal credit to any and all sources that have contributed to the formulation of ideas, methods, interpretations, and findings. The absence of such formal credit is an affirmation representing that the work is fully the writer’s. The term “sources” includes, but is not limited to, published or unpublished materials, lectures and lecture notes, computer programs, mathematical and other symbolic formulations, course papers, examinations, theses, dissertations, and comments offered in class or informal discussions, and includes electronic media. The representation that such work of another person is the writer’s own is plagiarism.

Care must be taken to document the source of any ideas or arguments. If the actual words of a source are used, they must appear within quotation marks. In cases that are unclear, the writer must take due care to avoid plagiarism.

The source should be cited whenever:
(a) a text is quoted verbatim
(b) data gathered by another are presented in diagrams or tables
(c) the results of a study done by another are used
(d) the work or intellectual effort of another is paraphrased by the writer

    Because the intent to deceive is not a necessary element in plagiarism, careful note taking and record keeping are essential in order to avoid unintentional plagiarism.

    For additional information, please consult “Avoiding and Detecting Plagiarism,” available in the Office of the Vice President for Student Affairs, the Provost’s Office, or at

(From The Graduate Center Student Handbook 05-06, pp. 36-37)

Reading Due
Assignments Due
Week 1 W 1/25
Course overview & Models of test scores
"R in an Hour"
Bandalos Ch. 1(B1)
Week 2 W 2/1
Scale development
B3 & Standards Ch. 4 (S4)
Week 3 W 2/8
Norms and standard scores
B2 & S5 Post Choice of Project Topic
Week 4 W 2/15
Cognitive items
Week 5 W 2/22
Non-cognitive items
Week 6 W 3/1
Item analysis
B6 & S7 Project Part 1
Week 7 W 3/8
Reliability (part one)
B7 & S2
Week 8 W 3/15
Reliability (part two)

Week 9 W 3/22
Validity (part one)

B11 (pp. 254-265) & S1

Week 10 W 3/29
Validity (part two)
B11 (pp. 265-297)

Week 11 W 4/19
(Class Does Not Meet 4/5 or 4/12)

Exploratory Factor Analysis
Project Part 2
Week 12 W 4/26
Item Response Theory

Week 13 W 5/3
Test equating
B18 (recall S5)
Week 14 W 5/10
Test bias & Test fairness
B16 & S3
Week 15 W 5/17
(no meeting)
Open office hours for project questions (virtual)

5/23 (no meeting)
(Last day of final exam week)
Project Part 3

Created 27 January 2008
Updated 24 January 2023
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