Why or why not?
How do you prove your theory without tests?
Statistics gives you the framework of measurement of your results. Technically, you don't need formal statistics. But you won't be able to measure the certainty of the results as well. This can fall victimđ” to many đ unconscious biases. https://data36.com/statistical-bias-types-explained/
In my opinion, no: Why? I think that science is fundamentally different from a field like mathematics. In math, you list a set of axioms, a format set of rules, and you can prove statements directly from them. Once you have a proof, you are guaranteed to know that it holds forever. In science, a âproofâ is different to the concept in mathematics. The model is as follows: you make a theory, and then you test the universe against your theory. The more you test something, the more confident you can be that it is correct, but you can never âproveâ it in the same way as mathematics. You might think you understand gravity, and the apple falls down the first billion times you try, but you are not necessary guaranteed that it will behave the same way on try 1 billion and one [at least, not in the same way we know there are, say, infinitely many primes]. Similarly, we may think we understand things like the standard model, or genetics- but all of these facts are in essence (good) theories we have based on our observations. For the statisticians or ML people out there, this type of thinking can be thought of as fundamentally bayesian. Science can be thought of as the the art of building models of our world based off of observations/evidence. These models are likely true given what we know, but the more we probe into the universe, the better these models become. In my opinion, this is why science is fundamentally statistical. Since we canât prove anything about our world in the same way as mathematics, we are forced to make models of our world, given the evidence of experiment. This is process is why science inherently uses statistics.
How did newton come up with this in the first place? By observing the world, and building a model that fit his observations. But what if tomorrow F = d(mv)/dt stopped describing the world around us? It probably wonât, but we do not know for sure- at least not in the same way we know iron clad mathematical truths. Itâs a theory that fits data we gathered about our world- the equation might not be statistical, but the method through which we came to it sure is. [That being said, my liberal use of the word statistics here doesnât really line up with say: statistical mechanics- it more lines up with model fitting- ie computing P(model | observations)]
Thatâs fair- and youâre right that there is a difference. In statistics proper, there are mathematical rules you apply (what is the maximum likelihood model given observation) vs in science creating a model given observation isnât so simple or formal. I bucket the second category into statistics. You donât- and I totally respect that.
No. Science doesnât exist without data. Statistics doesnât exist without data. Correlation, no causation.
Correlation does not imply causation, is not relevant to this question. Improper use of this argument. đ
Sure, many measurements have very low deviations, so statistical variations are negligible, so you can still have data and use the scientific method, just a lot more unknowns will occur with inferior analysis that doesn't use statistics. For example, deciding whether an item is flammable or not near STP, what phase an item is around STP (ignore Mercury), length of day, year, lunar month, keplerian orbital mechanics, etc. There will be some issues with borderline cases, like Mercury above, but a lot of progress can be made.
Technically science can exist without statistics but it would be rudimentary. You can do basic science by testing a hypothesis and making inferences. This doesnt require any math only basic reasoning and logic. In modern science nowadays things must be expressed with statistical mechanisms to be considered good science
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How do you define science?