This post is the home page to a collection of responses to the following video, which gives the relevant context.
This is response is substantially later than I had intended. Between life being busy and flip-flopping on whether to develop a response in video (which I started but did not complete) or a written form. Even in written form I had started it as a $\LaTeX$ document along with a bunch of notes in an Obsidian vault. Well, I’ve amalgamated these attempts to respond into a collection of blog posts that give some passing remarks on various aspects of Dustin’s video.
TL;DR: Neither Dustin or I think that nonparametric statistics are useless, but we still disagree on whether rank-based nonparametric statistics are useless.
Here they are, hopefully in some kind of coherent order:
- Actually Modelling the Data
- What Are Ranks?
- What are Nonparametric Statistics?
- Wilcoxon’s Heuristic
- What Is Useful Statistic?
- Rank-Based Statistics For Convergence Issues
- Just Plugging In Ranks
- Hacking The Data To Meet Assumptions
- Spearman Correlation Quantifies Comonotonicity
- A Rank-Based Mixed Effects Model
- A Rank-Based Structural Equation Model
- The Empirical Cumulative Distribution Function Is Rank-Based
- Are Rank-Based Statistics Bad For Incentives?
- Beyond Studying Order With Ranks
- The Ultimate Goal Of Research Is Not Parametric Models
- Nonparametric Statistics Don’t Model The Mathematical Structure Of Nature?
I have enjoyed trying to unpack Dustin’s video. It has given me an opportunity to think more thoroughly about how I understand a variety of concepts in Mathematics and Statistics. While I didn’t pull any punches, I hope that Dustin feels that I have ernestly attempted to consider his point of view.