stats.ts

1	/** Mean and a 95% confidence interval's half-width, for paired differences and plain samples. */
2	export interface Estimate {
3	mean: number
4	/** Half the 95% interval: the true mean is within mean ± ci, 19 times in 20. */
5	ci: number
6	n: number
7	}
8
9	export function estimate(xs: number[]): Estimate {
10	const n = xs.length
11	if (!n) return { mean: 0, ci: 0, n }
12	const mean = xs.reduce((a, b) => a + b, 0) / n
13	const variance = n > 1 ? xs.reduce((a, x) => a + (x - mean) ** 2, 0) / (n - 1) : 0
14	return { mean, ci: 1.96 * Math.sqrt(variance / n), n }
15	}
16
17	/** "+1.2 ± 0.3", or "+1.2 ± 0.3 ✱" when the interval leaves out 0 (a real difference). */
18	export function signed(e: Estimate, digits = 2): string {
19	const sign = e.mean > 0 ? '+' : e.mean < 0 ? '−' : ' '
20	const real = e.n > 1 && Math.abs(e.mean) > e.ci ? ' ✱' : ''
21	return `${sign}${Math.abs(e.mean).toFixed(digits)} ± ${e.ci.toFixed(digits)}${real}`
22	}