2026 (Current Year) Faculty Courses Liberal arts and basic science courses Teacher education courses
Mathematical Statistics and Test Theory
- Academic unit or major
- Teacher education courses
- Instructor(s)
- Kentaro Nagahara
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue (M-B45(H105))
- Class
- -
- Course Code
- LAT.A417
- Number of credits
- 100
- Course offered
- 2026
- Offered quarter
- 2Q
- Syllabus updated
- Mar 5, 2026
- Language
- Japanese
Syllabus
Course overview and goals
As the importance of data science and AI education continues to grow, teachers are increasingly required to develop statistical literacy and to apply it appropriately in educational practice. This course takes “statistical inference” as taught in the high school mathematics curriculum as its starting point and provides a systematic introduction to the fundamentals of statistical inference, with a particular emphasis on Bayesian methods.
Building on this foundation, the course introduces major frameworks for educational measurement—Classical Test Theory (CTT) and Item Response Theory (IRT)—and develops the basic knowledge needed to analyze and interpret test data. Students will also conduct hands-on IRT analyses using R, examining model fit, item characteristics, and ability estimation, in order to understand the full workflow of measurement and analysis in educational assessment.
Course description and aims
(A) Understand the fundamentals of statistical inference and solve standard introductory problems.
(B) Answer standard questions about the frameworks of test theory, including Classical Test Theory (CTT) and Item Response Theory (IRT).
(C) Analyze real test data and interpret the results appropriately.
Keywords
Statistical inference, Bayesian methods, properties of point estimators, Classical Test Theory (CTT), Item Response Theory (IRT)
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The course will be conducted primarily in a lecture format using the blackboard. Since we will periodically carry out hands-on exercises in data analysis using R—an open-source software environment and programming language specialized for statistical computing and data visualization—students are required to bring a laptop computer to each class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Fundamentals of Statistical Inference |
Assignments will be announced as needed during class. |
| Class 2 | Fundamentals of Bayesian Methods |
Assignments will be announced as needed during class. |
| Class 3 | Classical Test Theory |
Assignments will be announced as needed during class. |
| Class 4 | Models in Item Response Theory |
Assignments will be announced as needed during class. |
| Class 5 | Parameter Estimation in Item Response Theory |
Assignments will be announced as needed during class. |
| Class 6 | Test Equating |
Assignments will be announced as needed during class. |
| Class 7 | Item Response Theory Analysis Using R Packages |
Submit a written report. |
Study advice (preparation and review)
Textbook(s)
Kato, K.; Yamada, T.; and Kawahashi, I. (2014). Item Response Theory with R (in Japanese). Ohmsha.
Reference books, course materials, etc.
Instructions will be provided as needed during class.
Evaluation methods and criteria
Evaluation will be based on overall performance, consider
Related courses
- SHS.D445 ： Instructional-Design Theories and Models
Prerequisites
There are no specific prerequisites; however, it is recommended that students review “statistical inference” covered in the high school mathematics curriculum (Mathematics B) in advance.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
stat-test[at]te.ila.isct.ac.jp
Office hours
Make an appointment by email.