Normal Distribution
nothing is called 95% until it has been counted
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The thread: One run is an anecdote

A figure showing a single simulation is showing one draw from a distribution of figures. Where the claim is about behaviour rather than about one dataset, the figure runs across many seeds and reports what held for all of them — and where it shows one run, it shows twenty of them side by side.
00.1000.2000.3000.400-2024standardised sumdensityskew 0.7472/√n = 0.70740,000 sums, one seed eachthe rate is predicted, not just the shape The distribution itself

Sums of almost anything

The theorem says sums converge on one shape whatever they are sums of, which is remarkable and true. Watching it happen from a one-sided skewed source, with the rate of convergence predicted in advance, is more convincing than watching the shape appear.

 20 independent samples, 40 points eachall twenty are normalthis is what the noise looks like What makes it checkable

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.

 20 independent samples, 40 points eachall twenty are normalthis is what the noise looks like The distribution itself

What normal actually looks like

A single quantile plot of forty normal points wanders enough to look suspicious. Twenty of them, all genuinely normal, show what the noise looks like — and any single panel a reader would have rejected is in there.

 the truth, 0.350.00.20.40.60.80 of 20 missedthe 95% belongs to the procedure, not to one interval Intervals, counted

Twenty intervals and one expected miss

The 95% belongs to the procedure, not to the interval in front of you. Twenty intervals from twenty samples make that visible in a way no definition does, and the one that misses is not a mistake.

 first measurementsecond+0.55-0.59predicted 0.64 from the correlation alonenobody was treated Reversals that are not errors

Regression to the mean

Select the worst performers, measure them again, and they improve. Select the best and they decline. No intervention is required for either, the size of the apparent effect is predictable from the correlation alone, and it is the reason so many things appear to work.

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