Equating and Linking Scores in National Exams

Document Type : Original Article


1 Research Expert of National Organization of Educational Testing (NOET), Iran

2 Associate Professor, Faculty of Psychology and Education, University of Tehran, Tehran, Iran



Objective: According to the approval of the Supreme Council of Cultural Revolution the National Organization of Educational Testing is supposed to hold a national exam twice a year and the score of each test would have credit for two years. The purpose of this research is to introduce and implement appropriate methods of equating in the framework of the classical test theory in order to compare the test scores of different courses to choose applicants in a fair way.
Methods: Based on common-item nonequivalent groups design three test forms X, Y and Z of differential calculus were experimentally implemented on the group of 600, 1111 and 2200 examinees. The number of test items were 21, 21 and 20 with six common item in total. Data were analyzed in R software with the package equate (Albano & Albano, 2018). The equipercentile function was used to equate the test forms; The pre-smoothing process with linear logarithmic transformations were done so that the parameters were estimated with less standard error and scores with more accuracy.
Results: The average difficulty of these test forms were 9.03, 7.61 and 7.79 respectively. Also, all three forms have different skewness 0.203, 0.518 and 0.392, respectively.
Conclusion: Due to the different difficulty and right skewness of the distribution of the tests scores, it is suggested to equate them with the equipercentile function in a nonequivalent anchor test design. The tests for which common item cannot be developed, it is recommended to link their scores by the same equipercentile function.


Main Subjects


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