Maybe-Mathematical Musings
Math, Teaching, Literature, and Life
May 24, 2022
This is the second-part of a three-part series on hypothesis testing.
Today we'll look at the way we do hypothesis testing in practice, and how it tends to fail. Modern researchers use hypothesis testing as a tool to develop knowledge, but it's really a tool for making decisions, and so it encourages us to draw strong conclusions from weak evidence. It also encourages us to view studies that don't reject the null hypothesis as failures, which leads even honest and dedicated researchers to do shoddy research, producing "statistically significant" results that can't be reproduced.
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March 31, 2022
This is the first part of a three-part series explaining what hypothesis testing is and how it works. In this essay I'll talk about the way hypothesis testing developed historically, in two rival schools of thought. I'll explain how these two methodologies were originally supposed to work, and why you might (or might not) want to use them.
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February 02, 2022
The replication crisis is a major problem in medicine and social science; we know that a huge fraction of the published literature is outright wrong. But in math we don't seem to have a similar crisis, despite reasonably frequent minor errors in published papers. Why not, and what can this tell us about the fields that are in crisis?
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November 28, 2021
A back-of-the-envelope cost-benefit analysis tells us that taking ivermectin for covid might have positive expected value. If we follow that logic to its conclusion, we wind up taking twenty different supplements and this seems like it can't be wise. Resolving this apparent conflict exposes some of the deep flaws in how we often think about rationality and Bayesian reasoning.
A response to a piece by Scott Alexander at Astral Codex Ten.
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July 28, 2021
I got a lot of good, interesting comments on my recent post on the axiom of choice (both on the post itself, and in this very good Hacker News thread). I wanted to answer some common questions and share the most interesting thing I learned.
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