Plan how many survey responses you need for target statistical precision.
Overview
Sample size planning answers: how many respondents do I need? For proportion estimates, a common formula is n = Z² p(1−p) / E², using critical value Z, guessed proportion p, and margin of error E.
Using p = 0.5 is conservative because p(1−p) is maximized at 0.5, yielding the largest n. If you expect a rare outcome, smaller n may suffice but carries risk if the guess is wrong.
Finite population correction reduces required n when sampling without replacement from small populations. Clustered sampling designs need design effect adjustments this simple formula omits.
Report confidence level (90%, 95%, 99%), margin of error, and assumed p when presenting sample size recommendations to stakeholders.
Steps
Sets Z such as 1.96 for 95%.
Maximum desired half-width of CI on proportion.
Use 0.5 if unknown for conservative n.
Apply formula and round up.
Adjust if population N is small.
Divide by expected completion rate to set invites.
Math
n = Z² p(1−p) / E²
Derived from normal approximation to binomial proportion confidence interval solved for n.
Worked cases
(1.96²×0.25)/0.0025 ≈ 384.16
n ≈ 385 after rounding up.
Error in denominator squared shrinks
Required n increases sharply.
p(1-p)=0.16 < 0.25
Smaller n than p=0.5 case.
Why use this
Questions