Calibration of Polytomous Response Mathematics Achievement Test Using Generalized Partial Credit Model

Abstract

This study assessed the empirical comparability of item calibration in the developed essay (DEVessay-MAT) and (NECOessay-MAT) mathematics achievement test under the Generalized Partial Credit Model (GPCM). The instrumentation research approach of counterbalance design was employed. The sample consisted of 1080 senior secondary school students (SSS3) of 36 schools, who were drawn randomly from the Osun East senatorial district of Osun State, Nigeria. Two instruments were used and data obtained were subjected to Parallel Analysis (PA), Generalized Partial Credit Model (GPCM) and Independent sample t-test. Results showed that the test does not violate unidimensionality with the first Eigenvalue (2.05) from the experimental data was greater than the first random Eigenvalue (1.17) from PA, while other Eigenvalues from the experimental data were less than the rest of Eigenvalues under PA. Also, there existed a significant difference between the step difficulties/overall item difficulty and discrimination/slope index of the two instruments with (t = 3.52, df = 8, p < 0.05) and (t = 3.26, df = 8, p < 0.05) respectively. The authors’ concluded that the developed essay test produced better item statistics estimates compared to NECO-MAT (essay) test. Consequently, it was recommended that public examining bodies in sub-Sahara Africa should embrace an apt polytomous model for the calibration of their test items.