What is the best way to improve Statistical Thinking?

[R_cubed]

@ChristopherTong

I once thought that probabilistic thinking would help all of us improve our reasoning skills. I no longer believe that. In many cases probabilities are presented with incredible (false) precision that are arrived at by simply ignoring major sources of error/uncertainty that cannot be easily quantified.

I’m not sure what you mean by “probabilistic thinking”, but distinguishing thinking within a proposed mathematical model vs. thinking about a model in a rigorous way is the essential feature of “probabilistic thinking”, which is an application of tools from mathematical logic and computability theory.

Related thread:

Significance tests, p-values, and falsificationism

I think the questions being discussed are now more fruitfully addressed using the techniques of computational theory as Paul Thagard discussed in A Computational Philosophy of Science. It is also discussed in this link on computational epistomology. If we translate “falsification” to “computable” the “scientific method” becomes a decision procedure (aka. algorithm) that can be examined rigorously with mathematical methods. I like to think of “computational theory” as simply applied logic. …