GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 302 of 500
Build a confidence interval for a sample mean (Student t) or for a proportion (Wilson score interval) — the interval that quantifies how precisely a laboratory result is known.
Try sample values — fills the form with the worked example below.
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Lower limit
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Upper limit
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Margin of error
Equation: Mean: x̄ ± t(α/2, n−1) × s ÷ √n. Proportion (Wilson score): centre = (p̂ + z² ÷ 2n) ÷ (1 + z² ÷ n); half-width = z × √(p̂(1 − p̂) ÷ n + z² ÷ 4n²) ÷ (1 + z² ÷ n).
Method: Student t interval for a mean per ISO 16269-1; Wilson score interval for a proportion (Wilson, 1927), the interval recommended over the Wald interval because it stays inside 0–1 and behaves well for small samples. Critical values are computed from the t and normal distributions, not read from a table.
Assumptions: the mean interval assumes the data are approximately normally distributed (or n is large); the proportion interval assumes independent Bernoulli trials.
Limitations: a 95% interval does not mean there is a 95% chance the true value is inside this interval — it means 95% of intervals built this way contain the true value. The mean interval is unreliable for strongly skewed data with small n.
Rounding: limits and margin to 2 decimal places (proportion limits to 4 decimal places); intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Student t interval for a mean per ISO 16269-1; Wilson score interval for a proportion (Wilson, 1927), the interval recommended over the Wald interval because it stays inside 0–1 and behaves well for small samples. Critical values are computed from the t and normal distributions, not read from a table.
Assumptions: the mean interval assumes the data are approximately normally distributed (or n is large); the proportion interval assumes independent Bernoulli trials.
Limitations: a 95% interval does not mean there is a 95% chance the true value is inside this interval — it means 95% of intervals built this way contain the true value. The mean interval is unreliable for strongly skewed data with small n.
Rounding: limits and margin to 2 decimal places (proportion limits to 4 decimal places); intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Mean 50, SD 10, n = 25 at 95%: t(24) = 2.0639, margin = 4.13, interval 45.87 to 54.13.
Enter values above to see results.
Wider intervals mean less precision: to halve the width, quadruple the sample size. Tool 302 of 500 — GIFSQ
