Confidence intervals, in one sitting

Shape: From nothing
Plates: dropcap · quiz · dial · intervals · cheatsheet
Why: A unit is read alone, so it has to make the reader *do* something rather than watch. `quiz` comes before the explanation, and the wrong answer is the common intuition rather than a straw man. `dial` is the lesson: raise the sample size and watch the spread tighten. Told, that is a claim about sampling. Dragged, it is something they watched happen.

You poll forty people and forty-two per cent say yes. A colleague polls four hundred and gets forty-four. Somebody asks which is right, and the honest answer is that neither is a number — both are ranges, and one is much wider than the other.

Before the explanation

Quadruple the number of people you ask. How much narrower does the range get?

The width falls with the square root of the count, not the count.

Twice. Four times the people for half the width is why polls stop at about a thousand — the next halving costs four thousand more.

Raise the count. Watch the spread.

Wide enough that two honest pollsters disagree by twenty points.

People asked40people

noisysettled

Each bar is one poll. The true value is fixed; the bars are what you would have reported. Some miss, and that is what ninety-five per cent means.

The short version

1
A percentage without a range is not a measurement.
2
Four times the sample for half the width. Plan the budget around that, not around the sample.
3
Ninety-five per cent means one poll in twenty misses. Being wrong occasionally is the design.

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