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sci.confidence-interval-proportion Calculator
Calculates 95% confidence interval for a proportion using the Wilson score method: CI = (p̂ + z²/2n ± z√(p̂(1−p̂)/n + z²/4n²))/(1 + z²/n). Wilson interval is recommended over normal approximation — it remains accurate near p = 0 and p = 1 where the normal approximation fails.
Inputs
N Sample
Number of data points collected. Larger samples give narrower confidence intervals. Rule of thumb: 30+ for most statistical tests.
P Hat Pct
Reference formula or conversion factor shown for context.
Confidence Pct
How certain you want to be that the interval contains the true value. 95% is standard. Going to 99% widens the interval.
Results
point estimate p̂
The value at the specified point or condition.
standard error SE
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
margin of error (±)
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
confidence interval (lower)
Range within which the true population value lies at the stated probability. A 95% CI means: if you repeated the study 100 times, 95 of those intervals would contain the true value.
confidence interval (upper)
Range within which the true population value lies at the stated probability. A 95% CI means: if you repeated the study 100 times, 95 of those intervals would contain the true value.
CI = p̂ ± z·SE
Reference formula or conversion factor shown for context.