For years I thought I had to do it the way the big boys do, studying university text books and referencing papers in the field and putting a bunch of mathematical notation in my designs and emails. While also knowing all the foundations underneath. Unsurprisingly, that didn't really go anywhere, except hours lost fiddling with Word's equation editor (or worse, Latex).

What did help me was reading a few (really a few - just 2 or 3) simple, applied books; a 'statistics for dummies' (literally, the 'for dummies' book), a textbook used in undergrad business courses ('<something something> business analytics' I think?) and a book that applied all the stats to the field I was working on at the time (transportation modeling). Just being able to apply a linear regression (as in, actually being able to estimate the parameter on a single regressor in a simple data set) got me much further than all the times I thought 'whoops, getting into optimization now, better put this aside and first get a graduate level understanding of linear algebra'. And in a week instead of 2 years, too - quite important to keep your motivation up when you're not a full time student any more.

So while the above is not 'advice', it is my personal experience that when learning applied maths at a later age, it was better for me to focus on application and taking shortcuts even if that meant not fully knowing or understanding what was happening underneath - as intellectually unsatisfying and 'dirty' that felt at the time.

Understanding the distributions helped me the most. My favorite class was something like ‘single point estimates’ because it covered a lot about why mean and std dev are so powerful, but also sometimes so broken at conveying meaning.

Depends on the context for trying to catch up; both where you're at in life and what you're wanting to get out of it.

If you want to connect, feel free to reach out to the email in my profile. I may not be the best resource for best places to go next depending on what you're after, but may be able to help out.

A few general points though:

- Every field has it's own flavor of statistics. Supply chain, marketing, industrial engineering, business operations, finance, etc. Most practitioners will bastardize a technique or methodology common in their field before reaching out to another one for something more appropriate. Keep this in mind when looking at things, as you can find a lot of cases where the general premise for a technique is no longer valid, but practitioners are still going on momentum. You can also find some really neat nuggets/advancements that can be generalized and applied to another field. Although this can be difficult to suss out, as every industry tends to develop their own vernacular to refer to a particular set of base statistical techniques.

- Focus less on the math and more on the applicability of a particular technique or methodology to a situation. Generally speaking, statistical techniques are nothing more than sophisticated heuristics. Their validity, applicability, and actionability are entirely dependent on the situation they're applied in and the particular heuristics (statistical techniques) chosen. Understanding the techniques that are out there, what their applications are, and what their limitations are is far more useful than focusing purely on the math. The math can always be looked up once you know what to look up.

- Design of experiments[1] is a critical and often overlooked concept. It's rarely done in practice, and even when it is it's rarely more than a superficial attempt. But is a hugely important concept to understand how to approach a problem space.

- The output of a statistical analysis ranges from "checks the box of measuring something but so disconnected from observed reality that it'll otherwise be ignored" to "interesting but not robust enough to make decision on" to "directionally accurate" to "willing to make decisions based on confidence intervals". Understanding where your analysis stands on that scale, and where it needs to stand to meet your needs, is critical. Align your efforts with your needs, and set expectations accordingly.

[1] https://www.jmp.com/en_ch/applications/design-of-experiments...