rwilson4

I think “mathematical maturity” is an important aspect of this discussion. Mathematical maturity is basically the ability to read a paper or textbook without assistance. It takes years to develop, and you still have to be familiar with the topic! For example, I feel comfortable reading statistics papers, but I would be totally lost reading number theory. As others have commented, familiarity with the foundational ideas is just as important as the notation.

So how do you get mathematical maturity? A bachelor’s in math, or equivalent. Meaning, approximately 4 years of focused, ideally guided, practice. I don’t think there are any faster ways.

Edit: Also important to know: most papers are poorly written, so that definitely doesn’t help. It’s especially important early on to identify who the leaders are in a field, and focus on their writings. In statistical Machine Learning, I recommend anything by Trevor Hastie, Rob Tibshirani, Bradley Efron, and Martin Wainwright.

Most statisticians work for people who are trying to sell something. Statistics is not always the best way of selling something.

In this particular example, the "treatment" is implementation of ergonomic practices, and the "response" is worker productivity.

If we divide a workplace into two segments, there almost certainly will be some difference in worker productivity between the segments, having nothing to do with implementation of ergonomic practices and just having to do with the inherit variance of individual productivity contributing to the group.

If the difference is productivity is large enough, you start thinking the ergonomic practices might have something to do with it. Statistics makes these principles more precise through concepts like statistical power, significance, and confidence intervals. Proper analysis of such an experiment would allow a company to compare the cost of the ergonomic processes with the benefit of the increased productivity attributable to those processes. This in turn would indeed allow them to make more money!

One of the desired outputs of an experiment analysis is an estimate of the size of the treatment effect, typically in the form of a confidence interval. Studies which only report statistical significance (and there are many of them) are of limited utility since you can have a tiny effect that is statistically significant, just as you can have a large effect that is not statistically significant!

I recently read Seber and Lee, Linear Regression Analysis, and highly recommend it.

https://www.amazon.com/Linear-Regression-Analysis-George-Seb...

Link to recent discussion on HN: https://news.ycombinator.com/item?id=17617825

In the context of experiment design, you do this because you want to know whether any apparent difference between the groups is plausibly an artifact of the random assignment of units to groups. You wouldn’t expect two groups to have identical behavior, but the goal of an experiment is to determine whether the difference is because of the treatment.

It just seems to me it is impossible to be surprised by a bounded random variable in this context. If the death sentence were carried out x days from now, where x is drawn from an exponential distribution, that would fulfill the surprising criterion. The source of the paradox is that the “surprising” aspect is fundamentally incompatible with the bounded nature of the sentence.