Qualitative Research underlying philosophy of Constructivism (also known as Idea

Qualitative Research
underlying philosophy of Constructivism (also known as Idealism)
considers knowledge (reality) to be constructed (i.e., shared meaning or interpretation of the nature of being in the world)
constructions are subjective (i.e., subject to individual interpretation)
uses inductive reasoning (research-then-theory approach) where 1. categories/themes emerge from the data during analysis, and 2. categories/themes play an active role in development of theory 
Quantitative Research
underlying philosophy of Positivism (also known as Naturalism)
considers knowledge to be created by application of natural science methods
knowledge is objective based on: 1. empiricism (knowledge based on empirical observation); 2. testing and verification of theories, and 3. development of universal laws
uses deductive reasoning (theory-then-research approach) where: 1. research design is tightly structured and 2. research questions are highly specific (usually formulated as hypotheses)
I am one of those nurse researchers who has conducted research using both Qualitative and Quantitative methodologies, as well as a third methodology called Mixed Methods.  Read a bit about the philosophy of this Mixed Methods research method below.
Mixed Methods Research
does not adhere to particular approaches based on philosophical underpinnings
combines Quantitative and Qualitative research methods
requires a pragmatic approach to research where research design is seen as a choosing of methods that best facilitate understanding of a problem
Ref:
UKEssays. (November 2018). Comparison of Qualitative and Quantitative Research Methods. Retrieved from https://www.ukessays.com/assignments/qualitative-quantitative-research-methods

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