Calculate confidence intervals for biological measurements and proportions with multiple statistical methods including Wald, Clopper-Pearson, Wilson, and Agresti-Coull approaches.
Confidence Interval
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Lower Bound
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Upper Bound
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Margin of Error
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Point Estimate
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A confidence interval is a range of values that likely contains the true population parameter. For example, a 95% confidence interval means we can be 95% confident that the true population value falls within that range.
In biology, confidence intervals help quantify uncertainty in your measurements. A narrower interval indicates more precise estimates, while a wider interval suggests more variability or smaller sample sizes.
Different methods handle edge cases differently. Wilson and Agresti-Coull methods perform better for small samples or extreme proportions, while Wald is simpler but can be inaccurate. Clopper-Pearson is exact but conservative.
The z-score for a 95% confidence interval is 1.96. This means the interval extends 1.96 standard errors on each side of the sample mean.
Confidence interval width increases with: higher confidence levels (99% vs 95%), larger standard deviations, and smaller sample sizes. Larger samples and lower variability produce narrower, more precise intervals.
Use proportion calculations for binary outcomes (success/failure, present/absent, alive/dead). Use mean calculations for continuous measurements like height, weight, concentration, or count data.
For small samples (n < 30), use exact methods like Clopper-Pearson for proportions or t-distribution for means. These methods account for the additional uncertainty in small sample estimates.