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In the last two decades computer-based assessment has become an important part in support of teaching and learning. It is seen as a solution to implement assessment for learning in school and provide immediate feedback on students’ performance in real-time. Research literature on computer-based assessment suggests that every measurement instrument developer before implementation of a test has to provide evidence that computer-based and paper-based versions are equivalent and provide consistent measures. There is a risk that properties of computer-based assessment including unfamiliarity with the system and proficiency level of digital skills can seriously affect students’ performance. This paper focuses on computer-based diagnostic assessment system designed to support numeracy and literacy teaching and learning. The aim of this study is to confirm that literacy and numeracy learning measurement instruments elaborated in diagnostic assessment system provide consistent results as paper-based versions of both instruments. Data were collected administering four tests. Two of the assessments were computer-based literacy and numeracy diagnostic assessments and two were paper-based versions. By analyzing both versions of assessments using various statistical techniques we explore differences in students’ performance. Our results showed that at this development phase of the computer-based diagnostic assessment system the students who completed computer-based test versions showed similar or better performance than their counterparts who completed paper-based versions.