Empirical is defined in the oxford dictionary as something based on experience or observation rather than logic. For data to be considered empirical it does not need to be fact. It is often used interchangeably with first hand experience. Therein, one could say that empirical findings are extrapolated anecdotal data, as anecdotal is also defined as being based on personal experience rather than facts.
Theoretical evidence would explicitly oppose empirical evidence because it is based on calculation and cannot be opinionated. It is meant to be concise and eliminate ambiguity which empirical or anecdotal evidence can not.
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A theory
Empirical research is a way of gaining knowledge by means of direct observation or experience. Empirical evidence (the record of one's direct observations or experiences) can be analyzed quantitatively or qualitatively. Through quantifying the evidence or making sense of it in qualitative form, a researcher can answer empirical questions, which should be clearly defined and answerable with the evidence collected. Research design varies by field and by the question being investigated.Empirical evidence is gained by direct or indirect observation and experience.
"Empirical" evidence.
They obtain empirical evidence by undertaking research. Research includes doing experiments and running surveys.