Two Parameter Logistics Model with Lognormal Response Time for Computer-based Testing


  • Andhita Dessy Wulansari Universitas Negeri Yogyakarta Institut Agama Islam Negeri Ponorogo
  • Kumaidi Kumaidi Universitas Muhammadiyah Surakarta
  • Samsul Hadi Universitas Negeri Yogyakarta



Logistics Model, Response Time, Lognormal, Joint Distribution, CBT.


In addition to the information on response pattern/accuracy, Computer-Based Testing (CBT) can also generate information on response time. This research contributes to develop two-parameter logistics model with random variables of response time for CBT power test. Based on that model, the probability of the test taker answering the test questions correctly is influenced by the test taker’s ability, the test question’s discriminating power, the question’s level of difficulty, the delay due to the test question’s factors and response time. The development of this model aims to improve the parameter estimation of the logistics model on Item Response Theory (IRT) which does not consider the response time of the model. This model is simultaneously developed using joint distribution concept, by multiplying the conditional distribution of response accuracy (two-parameter logistics model) by response time with marginal distribution of response time. The marginal distribution chosen in this study is lognormal distribution because it has positive value in the form of positive skewed according to the characteristics of the response time. To prove the model is suitable for power test, is tested using CBT data. The study found that the simultaneous model generated from the multiplication between the two-parameter logistics model integrated with response time and the lognormal response time model is an appropriate model for CBT power test.

Author Biographies

Andhita Dessy Wulansari, Universitas Negeri Yogyakarta Institut Agama Islam Negeri Ponorogo

Andhita Dessy Wulansari, received her Bachelor of Statistics (S.Si) at Sepuluh Nopember Institute of Technology in 2006 and earned her Master of Statistics (M.Si) in 2009. Now, she’s studying for a Doctoral Education (Dr.) at Department of Educational Research and Evaluation, Yogyakarta State University. She has published several research papers in national journals in the area of Statistics and Educational Measurement. She has also authored books, Parametric Statistics and Research Methods in Education.

Kumaidi Kumaidi, Universitas Muhammadiyah Surakarta

Kumaidi, male, 67 years old, who is a Professor at Department of Psychology, Mu-hammadiyah University of Surakarta.

Samsul Hadi, Universitas Negeri Yogyakarta

Samsul Hadi, male, 58 years old, who is a Doctor and lecturer at Department of Electronics Engineering Education, Yogyakarta State University.




How to Cite

Wulansari, A. D., Kumaidi, K., & Hadi, S. (2019). Two Parameter Logistics Model with Lognormal Response Time for Computer-based Testing. International Journal of Emerging Technologies in Learning (iJET), 14(15), pp. 138–158.