December 16, 2025
Circle back to chaos
I don't think Lindley's paradox supports p-circling
Red pens vs Bayes bros: comment section melts down over p-values
TLDR: A blogger argued that barely-significant results shouldn’t trigger “p-value circling” based on Lindley’s paradox. The comments exploded: some praised planning and effect sizes, others pushed Bayesian defenses, and one called a related page “astonishing bullshit.” It matters because this shapes how science decides what’s truly meaningful.
A stats blog dared to say Lindley’s paradox doesn’t back the habit of “p-value circling”—that move where you side-eye any result just barely under 0.05—and the comments instantly turned into a math fight club. The author’s gist: under the null (no effect), p-values are flatly random, so a 0.049 isn’t “more suspicious” than 0.001 in that strict frequentist world. Cue the red-ballpoint brigade vs the Bayesian believers. One fan, senkora, had an “aha” moment about planning studies by choosing a smallest meaningful effect and justifying your threshold, shouting “Huh, I’d never thought to do that before.” But then contravariant rolled in with a big-brain take: yes, you can justify circling weak p-values in a Bayesian world if you’ve got solid priors (aka assumptions before seeing data). Meanwhile, CrazyStat called out the post for mixing up what Lindley’s paradox even is, and gweinberg went full flamethrower, labeling a related explanation “astonishing bullshit.” The top popcorn moment? jeremysalwen claiming people don’t care about what p-values measure at all—they care if the idea is true. The memes basically wrote themselves: “Team Red Pen,” “Higgs-level alpha,” and “Bayes Bros assemble.” It’s not just math—it's a vibe war over how science decides what counts as real.
Key Points
- •The article challenges the practice of “p-value circling,” which treats p-values near 0.05 as suspect.
- •Fisher’s p < 0.05 convention remains widely used, despite critiques of arbitrariness.
- •The Neyman–Pearson framework requires a justified alpha level and defines decisions based on Type I/II errors.
- •Under the null hypothesis, p-values are uniformly distributed; an R simulation of 100,000 t-tests illustrates this.
- •Within NP frequentism, significance depends on p < alpha, not on how far below alpha the p-value falls.