Sizing a poll for a yes/no split is one thing; pinning down an average ā wait time, basket size, blood pressure ā is another. Here the lever isn't the proportion, it's the spreadThe standard deviation of the individual values: how spread out they are. Wider spread needs a bigger sample to average out to the same precision. of the values. Feed in how varied they are and how tight a band you want, and read off the sample it takes ā or run it backwards.
Your average of 100 is really somewhere between 97.92 and 102, with 95% confidence ā from 200 measurements.
| Measurements | Margin |
|---|---|
| 50 | Ā±4.16 |
| 100 | Ā±2.94 |
| 250 | Ā±1.86 |
| 500 | Ā±1.31 |
| 1,000 | Ā±0.93 |
| 2,500 | Ā±0.59 |
The margin shrinks with the square root of the sample, so each halving of the band needs four times the measurements. Past a few thousand, more data barely moves the band.
Aiming for a target instead? See how many it needs ā