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Although mixed methods research becomes increasingly popular, the issue that to what extent qualitative and quantitative research methods can be combined is insufficiently explored. To fill this gap, this critical literature review revisits the qualitative-quantitative debate between proponents and opponents of mixed methods research, examines the underlying philosophical assumptions held by two sides, and provides a new perspective to evaluate research combining qualitative and quantitative approaches. A brief review of the origin and development of mixed methods research is provided, followed by a presentation of the divergent opinions of proponents and opponents of mixed methods research and an illustration of why grounded theory, classified as a qualitative research method, can work well with quantitative studies. These ideas contribute to the conclusion rendered here: paradigmatic differences cannot be reduced to the simplistic duality of qualitative-quantitative debate, and the use of compatible paradigms is the key to mixing different research methods.