# Should we trust statistics? [closed]

My mathematical statistics theory professor, an expert in the field, said today he doesn't trust statistics enough to use it in practice. He just likes the beauty of the math. He said he would never be able to teach applied statistics in good conscience. Do you trust statistics? If so, why?

The more statistics I learn, the more I realize how much of it is founded on assumptions. We specify assumptions, and then use rigorous mathematics to generate conclusions. Why is this any better than not using advanced statistics? After all, we do not know our assumptions are true. How can we justify hypothesis testing, for example, when we don't know the true distribution? (I ignore descriptive statistics here, which are clearly useful.)

The more I learn, the less confidence I have in statistics and the more faith I have in machine learning, which is not bold enough to make claims like causality.

• You think machine learning does not need assumptions? Feb 9, 2019 at 1:06
• Of course it requires assumptions, but there is a clear out-of-sample testing process. Model quality is evaluated based on test error. The same is not commonly done for causal analysis in classical statistics, for example. Feb 9, 2019 at 1:08
• I think that comment is superprovocative which to me just show how opinionated any answer to this question is going to be. Feb 9, 2019 at 1:45
• It is absurd to discard a (statistical) model only because it is not entirely correct (no model, also a machine learned pattern, is ever entirely correct). In this way your question asking for convincing fact-focused arguments for the use of statistics is a loaded question (it is wrong to assume/expect complete rigour). You are right however that the mathematical rigour in the methods/models used by statistics can be misleading regarding the degree of rigour in the conclusions that are made based on the use of a certain method/model. Feb 9, 2019 at 6:57
• Re causality: recently ML / deep learning moved into the causality field. Also statistics and ML (aka nonparametric statistics) are here to solve real world problems. Understanding / estimating causality is at the core most real world problems that we face. So the fact that statistics tries to answer those questions , rather than just say "we can't do cross validation for it, so we 'll not try to answer these important questions" is good! Besides nonparametric stats / ML is actively working on validation and assumption testing for causal inference Feb 9, 2019 at 13:18