Abstract
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.
Highlights
Due to the advancement of technology and information, conventional tests using papers or Paper Based Test (PBT) has been replaced with tests using computers or Computer Based Testing (CBT)
This model is developed by implementing joint distribution concept, that is a multiplication of conditional ditribution model of response accuracy with response time, which is the two-parameter logistic model with marginal distribution model of the response time
Data used in analyzing the simultaneous model between response accuracy and response time is the score of correct answers (1) - wrong answers (0) and the test taker’s response time taking quiz of statistics, descriptive statistics materials using Computer-Based Testing (CBT) provided by the lecturers in Institut Agama Islam Negeri Ponorogo that consist of 10 multiple choice questions
Summary
Due to the advancement of technology and information, conventional tests using papers or Paper Based Test (PBT) has been replaced with tests using computers or Computer Based Testing (CBT). This study aim to develop twoparameter logistics model with random variable of response time for power test, whose chosen parameters are limited to the difference of the questions (aj), the difficulty level of the questions (bj), the ability of the test takers (Ɵi), the delay due to the questions (di) and response time (tij). This model is simultaneously developed using joint distribution concept with lognormal marginal distribution. The method used to test the suitability is Posterior Predictive Model Checking (PPMC) by comparing the difference between the data from observation and the result of model prediction
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