Ah pardon me then. Yes, things like drawing conclusions from a few interviews, anecdotes and observations. The resulting data sets (video/audio-recording) tends to be non-numeric, not clearly generalizable and nowhere near identical between and within subjects, but by use of transcription, coding and analysis, it is possible to identify recurring broad themes. This empirical methodology is called qualitative research as opposed to quantitative research (i.e. simple statistics) and it has been used for decades now in many of the sciences, but particularly in market research, sociology, education and artificial intelligence (data mining from human experts in order to make expert systems).
You are misinterpreting what I am saying. I never claimed economic analysis is not based on empirical data. Reread what I said. I can however give you an example that premature and overt mathemization, in order to superficially resemble physics and so seem more scientific, can make and has clearly made economic analysis lead to axiomatic reasoning which is not just inaccurate but inappropriate altogether. Even worse taking the resulting calculations serious requires selectively ignoring empirical data or transforming it in such a way that it can be ignored.
Example: There has long been an assumption that risk follows a normal distrubution, i.e. Gaussian distribution. This has led to a systematic undervaluation of risks and gross underestimation of the frequency of crises. The reason for assuming normality of course is due to many factors, among others that it is mathematically more simple and partly a result of misapplying and/or misunderstanding the central limit theorem.
Many economic theoretical constructs, like volatility and risk, are nothing more than relabeled statistical concepts like variances and standard deviations in the setting of the normal distribution. Furthermore, much of financial theory is based on this same assumption of normality, most importantly the Black-Scholes equation (BSE), Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH).
Regarding the EMH, read this paper on arxiv, which shows that among other things that gauge theoretic methods can be used to study curvutare in economic markets and so make money through arbitrage:
https://arxiv.org/abs/0902.4274
Standard economic theory of course just claims arbitrage is impossible due to the EMH based on elegant but misleading proofs, which are mathematically sophisticated but have little to do with actual empirical economics (NB: this is analogous to von Neumann's proof of no hidden variables in QM, which is mathematically correct but physically unrealistic).
Like physics, it is posited that these theories (MPT, BSE, EMH) and equations describe economic phenomena, but unlike physics, these theories and their equations are not themselves based on empirical data. They are instead mathematical equations assumed a priori to be valid on the basis of simplicity and ignorance of alternatives, i.e. complete lack of understanding of higher mathematical probability theory. Data which is gathered is fitted to these equations, instead of finding equations which match data and discarding equations that don't, as is done in experimental science. Economists have no experience whatsover of doing experimental science outside of doing simple statistics and simple regression analysis; they will even tell you that that is all experiment is. Practically any undergraduate physics experiment course is far too complicated for them to even try analyzing, while these physical systems tend to be much simpler systems than the economic systems that economists claim to understand.
The result is that economic theory seems because of its mathematical form more scientific than it is, when its core concepts are treated as unquestionable principles when they are actually unjustifiable hypotheses in direct contradiction with experience. An example is the frequency of crises predicted on the basis of crisis frequency following a normal distribution opposed to empirical data of the frequency of crises. A correct analysis required a higher mathematical sophistication than what is taught in economics courses.
What economists should have done to prevent this catastrophe, but didn't do, is start out by actually learning graduate level higher stochastics and mathematical Probability Theory before constructing their theories. Instead it seems they just learned high school level statistics i.e. how to calculate probablities, means and variances using the normal distribution and then relabeled these things as key concepts in economic theory. (NB: this is comparable to physics prior to Newton, where statistical observation led to the mathematically precise Ptolemaic theory of epicycles in celestial mechanics, which in terms of physics was of course pure nonsense.)
Luckily things are starting to change, albeit slowly. Failures of standard economic and financial theory such as above, have crept into curricula and some quick fixes are cooked up for special scenarios, but these fixes tend to be fighting the symptoms, not fighting the disease. And since the late 20th century, at the forefront there are physicists and mathematicians who are trying to reform the entire science of economics completely from the ground up (they are the Complexity school of economics), simply because the problem is a dire one and it doesn't seem economists are willing or capable of solving it themselves. This is not purely an altruistic act on the part of these physicists and mathematicians: developing the correct mathematical theories of economics is almost guaranteed to solve the outstanding theoretical physics problem of open system non-equilibrium statistical mechanics.
The late mathematician Benoit Mandelbrot, discoverer of fractal geometry, has done much work on elucidating the correct mathematics needed for economics. It isn't an exaggeration to say that almost all of econophysics/complexity economics research carried out today are direct offshoots in some manner of Mandelbrot's work. Here is what late MIT economist Paul Cootner said about Mandelbrot's work:
