Field note · June 17, 2026
3.0%, plus or minus what?
A point estimate of 3.0%, the interval around it, and what a tighter one would cost.
is_holiday on grid-energy-load is true in 3.0% of 8,760 rows. That is a point estimate, and on its own it is half a sentence.
The standard error on a proportion is sqrt(p(1-p)/n). Here that is 0.18 percentage points, so the 95% interval runs 2.7% to 3.4% — a width of 0.7 points.
import math
n, k = 8760, 264
p = k / n
se = math.sqrt(p * (1 - p) / n)
print(f"{p:.3%} [{p - 1.96*se:.3%}, {p + 1.96*se:.3%}]")That interval is tight, which is what 8,760 rows buys you. It is worth knowing why it is tight, so you recognise the cases where it is not.
Getting the interval down to ±0.5 points would need about 4,492 rows. Precision costs sample size quadratically — halving the width costs four times the data — which is the single most useful fact for anyone about to promise a more precise answer next week.
Normal approximation, and it starts lying at small counts or proportions near the boundaries; the Wilson interval behaves there. The pattern has both.