Confidence Interval Calculator
Confidence intervals for a mean or a proportion, with margin of error and standard error shown.
Mean 100 ± 5.6011 (t = 2.045, df = 29, SE = 2.7386)
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- Deterministic math, shown in the open
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Method notes
Means use the t distribution with n−1 degrees of freedom. Proportions show both the normal-approximation interval and the Wilson score interval, which behaves better near 0% and 100%.
Reading a confidence interval
What the interval says
It is a range of values compatible with your data at the chosen confidence level. A wider interval means less precision, usually from a small sample or high variability.
Margin of error
Half the interval width. It scales with 1/√n, so quadrupling the sample size halves the margin of error — a useful sanity check when planning studies.
t versus z
With an estimated standard deviation, the t distribution widens the interval to account for that extra uncertainty. The difference matters most below about n = 30.
Wilson intervals
For proportions near 0% or 100%, the normal approximation can produce impossible bounds. The Wilson score interval stays inside 0–100% and is the safer default to report.
What Quandra v8 adds
These calculators give you one number at a time. Quandra v8 writes the statistical analysis plan, generates R/SAS code, cross-checks assumptions against a locked reference corpus, and keeps an audit trail for regulated work.