Sample Size Math Falls Apart at the Subgroup Level

There are a hundred sample size calculators on the internet. SurveyMonkey has one. Qualtrics has one. Every university statistics department has one. They all do the same thing: plug in confidence level, margin of error, population size, get a number. Done.

Here's the problem: that number tells you the total sample you need. It tells you nothing about your subgroups. And subgroups are where most analysis actually happens.

If you need n=1,000 total but you're cutting the data by four age groups, your smallest cell might have 80 people in it. The margin of error on n=80 at 95% confidence is ±11 points. Try presenting that to a client who wants to compare millennials versus boomers.

What's different about this one

You define your quota groups, set your desired margin of error for each group, and the tool calculates backward to tell you the total sample you need to ensure every subgroup hits the reliability threshold. It also applies finite population correction for smaller universes, which actually matters when you're studying niche B2B populations or specific geographies.

The FPC piece gets ignored constantly. If your total population is 5,000 people and you're sampling 500 of them, your effective margin of error is meaningfully tighter than the standard formula suggests. The correction factor kicks in once your sample exceeds about 5% of the population. Most online calculators skip this entirely.

Tech stack

React 18.2 + Babel CDN. Uses Cochran's sample size formula with continuity correction and FPC. The math isn't complicated. The value is having it all in one place with the subgroup planning layer on top, which is the part that saves you from embarrassing conversations three weeks into fieldwork.