According to the efficiency scores obtained by Data Envelopment Analysis (DEA), the main problem for inefficient decision-making units (DMU) is the factors that cause inefficiency. To deal with this problem, various studies have been handled, such as decomposing the total efficiency score, and two-stage DEA which can divide the whole process into two parts has been developed. In this study, independent models where the whole process is called a black box and related models where the series relationship is established in the whole process are discussed comparatively. These models are used to measure graduate education performances and scientific and technological research competency performances of state universities in Turkey. When the overall performances of universities are examined; Gebze Technical, Hacettepe, İstanbul Technical, İzmir Institute of Technology and Middle East Technical have been determined as efficient universities both in terms of overall performances of universities and in terms of independent model and related model. İstanbul, Ankara, Boğaziçi and Gazi, have been determined as efficient universities only in terms of independent model. Furthermore, this study is consistent with the research universities determined by the Council of Higher Education through certain criteria.