This study determined the mean ability estimates of students in public and private secondary schools when their scores are equated through linear equating, and it examined which of the equating methods is more efficient. This study adopted a descriptive research design. The population for the study comprised 24,874 candidates that registered and sat for the 2016 June/July National Examinations Council (NECO) mathematics examination in Ogun State. A sample of 1139 candidates were selected from both public and private schools using the multi-stage sampling procedure. The research instruments used for the study were secondary data sources. The data was analyzed using Multidimensional Item Response Theory (MIRT), Separate and Linear Equation. The results showed that private school candidates’ ability score (x̅ = -0.001, SD = 0.961), (x̅= -0.001, SD = 0.961) was higher than public school candidates’ ability score (x̅= -0.865, SD = 1.058), (x̅= -0.626, SD = 0.970) when equated using separate calibration and linear equating methods respectively and that the difference observed in the ability estimate of examinees from public school and private school were significant  (t 1138 = - 14.431, p 0.05) and (t 1138 = -10.876, p 0.05) when their scores were equated with each of the equating methods. However, the results showed that the linear equating method was more efficient.