This calculator estimates how many responses or observations a study needs to reach a chosen confidence level and margin of error.
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Enter the confidence level, acceptable margin of error, expected proportion, and population size if it is finite. If the expected proportion is unknown, use 50%, which produces the most cautious sample-size estimate.
For a proportion, the initial sample size is n0 = z² × p × (1 - p) / e². For a finite population N, adjust it with n = n0 / [1 + (n0 - 1) / N], then round up.
For a large population, 95% confidence, a 5% margin of error, and p = 0.50 give n0 = 1.96² × 0.50 × 0.50 / 0.05² = 384.16. Round up to 385 completed responses, and recruit more people if some will not respond.
A 50% proportion creates the greatest variability and therefore the largest required sample. It is the safer planning value when prior evidence is thin.
Yes. Divide the required completed sample by the expected response rate, so 385 completed responses at a 70% response rate requires inviting about 550 people.
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