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).
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Confidence interval (percentage points)
Same CI expressed in percentage points.
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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.
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Required response rate
Sample size as a share of the population.
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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))] )