Want half the margin of error? Prepare for 4x the data

Question

A dashboard reports an estimate with a 95% margin of error of $\pm 2\%$ from 2,500 observations. A stakeholder asks: "Can we get that down to $\pm 1\%$ ? And how about $\pm 0.5\%$ ?"

Explain how margin of error scales with sample size, and compute the sample sizes needed to hit $\pm 1\%$ and $\pm 0.5\%$ .

Accepted Answer

The scaling law. The margin of error is proportional to the standard error, which shrinks like 1/\sqrt{n}: 	ext{margin} = z \cdot \frac{\sigma}{\sqrt{n}} \ \propto\ \frac{1}{\sqrt{n}}. The square root is the whole story. To halve the margin you must divide 1/\sqrt{n} by 2, which means multiplying n by 2^2 = 4. To cut it to a third, multiply n by 9. Precision is expensive: every additional digit of accuracy costs a hundredfold more data. The numbers. Starting from \pm 2\% at n = 2{,}500: - To reach \pm 1\% (half the margin): n 	o 2{,}500 	imes 4 = 10{,}000. - To reach \pm 0.5\% (a quarter o…

Want half the margin of error? Prepare for 4x the data

Your answer

More Statistics questions