Statistics Lab

A Bayesian graded-response model turns real votes into an axis of tendency to strike down, and a permutation test asks whether it lines up with the nominating president — a disciplined null, plus one collaboration-layer signal that is real

Where does the axis come from when we place a justice on a scale of tendency? Using the Taiwan Constitutional Court's official per-item vote records since 2022 as real votes, this piece estimates each justice's tendency to strike down (theta) with a Bayesian graded-response model, then tests whether that axis aligns with the nominating president. Nothing is detectable on four dimensions, and the null carries power, equivalence, and specification-curve discipline; per-justice credible intervals are wide and all adjacent ones overlap, so in this sparse-dissent term the justices are mostly indistinguishable. A second layer, the co-signing network of opinions since 1949 modelled with a hierarchical binomial, does find a moderate and robust same-nominee effect. The voting layer detects nothing; the collaboration layer detects something; the two speak to different things. No prior Taiwanese study has used official per-item real votes — this piece fills that gap, and reserves its novelty claim against one closely overlapping study whose full text remains unavailable.

2026-07-19 · 1 min read · ideal points, item response theory, graded response model, Bayesian estimation, permutation test, judicial behavior, non-significant result

Power and equivalence tests: turning "we found no difference" into "any difference is too small to matter"

A test returns p = 0.56, and you cannot conclude the two are the same — a non-significant result may just mean the study had no power to see the difference. This article uses drug bioequivalence to explain statistical power (how large an effect a study can see) and equivalence testing (TOST: bounding the effect inside a margin fixed in advance), and why "not significant" has to be split into "we can rule out any meaningful difference" and "we simply could not tell".

2026-07-18 · 6 min read · equivalence testing, TOST, statistical power, confidence interval, bioequivalence, non-significant result

A poll's '±4 points', and the question of whom that 95% is really about

A poll puts a candidate at 45% with a margin of error of ±4 points, and the paper writes that there is a 95% chance the true support lies between 41% and 49%. Almost everyone says this, and it is wrong. This piece derives a confidence interval by hand from a single mean, and watches the 95% lose its footing at the exact step where the observed numbers are plugged in. A submarine, a ratio interval, and a six-statement quiz then show that the experts fail at the same spot. The frequentist tool is not broken — it answers a well-defined question correctly. That question is just not the one you meant to ask.

2026-07-18 · 12 min read · confidence interval, margin of error, frequentist inference, Neyman, credible interval, misinterpretation

From a lady tasting tea to a signed statement: a short history of the p value quarrel

Null was never about nothingness. Fisher's null is the hypothesis that can be nullified — set up so the data have something to argue against. This piece follows one line: how a tea party produced the first p value, how Neyman and Pearson turned it into a decision rule, how textbooks welded the two together into something neither man designed, and where that weld cracks.

2026-07-13 · 7 min read · null hypothesis, p value, history of ideas, Fisher, Neyman-Pearson, replication crisis

Small-sample proportions and partial pooling in a Bayesian hierarchical model

Justice A files a separate opinion in 3 of 4 participating cases; justice B does so in 40 of 100. The two proportions describe the observed cases, but they do not justify a ranking. This article uses a binomial model, posterior distributions, and partial pooling to show how small-sample proportions can be estimated and reported.

2026-07-13 · 4 min read · Bayesian statistics, hierarchical models, partial pooling, small samples, Constitutional Court data, uncertainty