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Confidence Calculator
Quick sample sizes and confidence intervals.
by Martin
Confidence Interval
Confidence interval from your actual sample.
Inputs
Total number of people in the group.
Number of completed responses.
Outputs
Confidence interval (proportion)
CI in proportion units (e.g. 0.12).
Confidence interval (percentage points)
Same CI expressed in percentage points.
Interpretation
For a proportion estimate of p, the interval is p ± CI. Here that's ± percentage points.
Detailed calculation
Uses a 95% confidence level with a conservative proportion of 0.5 and a finite population correction.
CI = 1.96 × √[(0.5 × (1 − 0.5)) / n] × √[(POP − n) / (POP − 1)], rounded to 3 d.p.
Sample Size
How many responses you need.
Inputs
Total number of people in the group.
As a proportion (e.g. 0.05 = ±5 percentage points).
Outputs
Required sample size
Number of responses needed.
Required response rate
Sample size as a share of the population.
Detailed calculation
Uses your chosen margin of error, confidence level and population proportion, with a finite population correction, then rounds up to the next whole case.
n = ROUNDUP( [Z² × p × (1 − p) / CI²] ÷ [1 + (Z² × p × (1 − p) / (CI² × POP))] )