What is a margin of error?

When you measure a citation rate from a basket of prompts, you get one number, but that number is an estimate of a truer, unmeasurable rate, not the rate itself. The margin of error describes how far off that estimate could plausibly be, based purely on how many prompts you ran and how the result came out. A rate of 24% from twenty prompts carries a much wider margin than the same 24% from two thousand.

The practical failure mode is reading week-over-week movement as a trend when it sits inside the margin of error. If your basket is small enough that the margin is plus or minus ten points, a shift from 24% to 29% is not evidence of anything, it's the kind of jump you'd expect from noise alone on a fair number of re-runs. The fix isn't to distrust every number, it's to size the basket to the swing you actually care about detecting.

Margin of error and sample size move together, wider baskets narrow the margin, but the relationship isn't linear. Doubling your prompts does not halve your margin of error, which is why getting from a wide margin to a narrow one usually costs more prompts than people expect.