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This study investigated dimensionality of Binary Response Items through a non-parametric technique of Item Response Theory measurement framework. The study used causal comparative research type of nonexperimental design. The sample consisted of 5,076 public senior secondary school examinees (SSS3) between the age of 14-16 years from 45 schools, which were drawn randomly from three senatorial districts of Osun State, Nigeria. Instrument used for this study was 2018 Osun State unified multiple-choice mathematics achievement test items with empirical reliability coefficient of 0.82. Data obtained were analysed using Non-linear factor analysis, Stout's Test of Essential Unidimensionality (STEU), Factor Analysis (FA), Full Information Factor Analysis (FIFA) and Bootstrap Modified Parallel Analysis Test (BMPAT). Results showed that both the BMPAT and STEU ascertained violation of unidimensionality assumption of the test items (the observed difference in the second eigenvalue of the observed data and that of second eigenvalue of the simulated data was statistically significant, p = 0.0099; Stout's test rejected the assumption of essential unidimensionality, T = 10.6260, p<0.05). Non-linear factor analysis and full information factor analysis revealed that four dimensions embedded in the test items and loadings of the items showed within-item multidimensionality respectively. The authors' concluded that modeling examinees' performance with unidimensional model when it was actually multidimensional in nature would affect performance of examinees adversely and could lead to blur judgment. Consequently, it is recommended that unidimensional scoring method of Osun State unified mathematics achievement test implicit in Classical Test Theory should be jettisoned and an appropriate scoring model (multidimensional) should be embraced.