Sample Size Calculator

This calculator computes Required Sample Size as n = z² × p × (1−p) ÷ e² (line 73), where z is looked up from a fixed table for 90%, 95%, or 99% confidence (lines 14-18) and e is Margin of Error converted to a decimal. Switching Confidence Level end to end actually moves Required Sample Size more than any other input: at the default Margin of Error and Expected Response Rate, 90% confidence needs 271 responses and 99% needs 664 — more than double — because z is squared in the numerator and 99%'s z-score (2.576) is well over 90%'s (1.645). Margin of Error is a different kind of lever: it's the input you drag smoothly rather than pick from three fixed options, and among Confidence Level and Expected Response Rate, it's the only one that moves Required Sample Size at all under a small, symmetric nudge — raising it always lowers the required sample size, since e sits in the denominator, squared.

Expected Response Rate (p) showing no effect from a symmetric 10% nudge at its default of 0.5 is not evidence that it's irrelevant — it's the opposite kind of trap. p × (1−p) is maximized exactly at p = 0.5 (its derivative, 1 − 2p, is zero there), so a symmetric nudge to 0.45 and 0.55 lands on the identical value, 0.2475, on both sides — that reads as zero effect only because it straddles a peak, not because the term is flat everywhere; moving p to 0.3 instead changes p(1−p) to 0.21, a real and substantial shift. When Population Size is between 0 and 1,000,000, a finite-population correction shrinks the required sample further (line 78-80), and the reported Effective Margin of Error is recomputed against that adjusted sample size rather than simply echoing the target Margin of Error back. This calculator does not account for expected non-response or attrition beyond the response-rate proportion itself, and it silently falls back to the 95% z-value (1.96) if an unrecognized Confidence Level ever reaches the engine (line 20), though the UI only ever offers 90, 95, or 99.