Concept

Reproducibility — where it appears

The property that repeating an analysis on the same data gives the same result. Seeded simulations have it by construction, and a randomised interval deliberately gives it up in exchange for exact coverage.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Twenty samples of 40, every one of them genuinely normal. Each panel is a quantile-quantile plot of 40 draws from a normal distribution. The worst point in the worst panel sits 0.87 standard deviations off the line. Anything a reader would reject here would be a false alarm.

The seed is part of the figure

Every other site in this fleet draws from a deterministic rule, so a figure either is or is not what it claims. Here the figures are samples, and a sample can be right by luck. That changes what a figure has to carry.

method · Seeds

Clopper–Pearson, mid-p and the randomised interval: coverage across the proportion, 20 trials. Clopper–Pearson never falls below 95% and runs up to 99.80%. The mid-p interval, which is the randomised interval with its coin fixed at one half, runs from 92.94% to 99.80%. The randomised interval covers 95% at every proportion, to within the 0.043% of the numerical integration over the coin.

The coin that makes it exact

Every interval for a proportion either covers less than 95% somewhere or more than 95% on average, because a count is discrete. One construction covers exactly 95% at every proportion: it adds a uniform random draw to the count. At thirty trials it is 0.9% wider than Wilson's interval and narrower than both exact ones — and two analysts with the same data report different intervals, and one study in forty that sees nothing reports an empty one.

discrete · Oscillation

Named alongside it

The objects these essays reach for when they reach for this one.

Coverage Clopper–Pearson Discreteness Fuzzy interval Mid-p Pseudorandom generator Randomised interval Seeding Spectral test Wilson interval

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