Confidence interval

Editorial approval scope: The team checked current source fidelity, scope boundaries, dates, arithmetic, reader usefulness, practical workflow, and general-information limitations.

Start with the quantity being estimated

A confidence interval can surround a mean, mean difference, proportion, risk ratio, odds ratio, regression coefficient, effect size, or another estimand. The endpoints have meaning only with that quantity and unit.

Write the comparison, population, time point, scale, and direction before interpreting the numbers.

Confidence describes the method

Under a common frequentist interpretation, a 95% confidence procedure would produce intervals containing the true parameter in 95% of repeated samples under the model and assumptions. The parameter is treated as fixed; the interval changes across samples.

The observed interval is not automatically a 95% probability distribution for the parameter. Bayesian credible intervals use another framework and assumptions.

Width communicates precision

A narrow interval supplies a more precise estimate on its scale than a wide interval, assuming the method is appropriate. Sample size, event count, variability, clustering, missing data, model choice, and measurement reliability can affect width.

Precision does not establish low bias. A precise estimate can still be wrong because of design, confounding, selection, measurement, or analysis problems.

Look beyond the null value

For a difference, the null may be zero. For a ratio, it may be one. If an interval crosses the null, the data may be compatible with effects in more than one direction under the model.

Also compare the range with a prespecified clinically important threshold. An interval can exclude the null while including only trivial effects, or include both meaningful benefit and harm.

Confidence, prediction, and tolerance intervals differ

NIST's interval overview distinguishes a confidence interval for a population parameter from intervals intended to cover future observations or a proportion of a population.

Read the label and method. A confidence interval for a group mean does not predict every client's future response.

A fictional study result

A fictional caregiver-training study estimates an 8-point mean difference with a 95% confidence interval from 2 to 14 points. The interval excludes zero under the stated model.

If a 5-point difference was defined beforehand as clinically important, the range includes effects below and above that threshold. The result supports a positive average difference with remaining uncertainty about magnitude. It does not promise an individual outcome.

Assumptions belong beside the interval

Check randomization or sampling, independence, clustering, distributional assumptions, variance method, missing-data handling, model specification, and whether the chosen interval works for small samples or rare events.

The NIH Research Methods Resources provides general methods material. The original study and statistical analysis plan should identify the actual procedure.

Multiplicity can change interpretation

Many outcomes, time points, subgroups, and unplanned analyses increase the opportunity for striking results. Determine whether the interval was prespecified and whether the analysis adjusted for multiple comparisons where appropriate.

Give primary outcomes more weight than an isolated favorable subgroup found after looking at the data.

Single-case graphs need different care

Group-study confidence intervals do not automatically transfer to single-case experimental designs. Visual analysis, repeated measurement, design logic, overlap, level, trend, variability, and replication answer different questions.

Use methods suited to the design and report any interval's derivation and unit.

A compact reading checklist

• What parameter, population, comparison, time, and unit are estimated?
• What is the point estimate and interval width?
• Which values represent no effect, meaningful benefit, or harm?
• Were the method and assumptions appropriate?
• Were outcomes and analyses prespecified?
• What design bias remains outside the interval?
• Does the evidence apply to this person and context?

Compare intervals across studies carefully

Two intervals can overlap even when a formal comparison suggests a difference, and they can fail to overlap for reasons unrelated to a meaningful clinical contrast. Use a model that directly estimates the comparison of interest rather than judging significance from visual overlap alone.

When reading a synthesis, check whether studies use the same outcome scale, time point, population, comparator, and direction. Standardized effects may improve comparability while making the units less intuitive. Transformations can create asymmetric intervals after returning to the original scale.

For ratios, explain whether the interval is presented on a ratio or logarithmic scale. For proportions near zero or one, verify that the method respects the possible range. For clustered or repeated observations, confirm that dependence was handled.

Record the estimate and both endpoints instead of reporting only whether the interval crossed a threshold. Pair statistical uncertainty with study limitations, applicability, client priorities, burden, harms, and cost. A precise group estimate can still be a poor guide for a person whose context differs from the studied sample.

Before acting, write the smallest and largest effects compatible with the interval in plain language and state which decisions would differ across that range. If those decisions conflict, gather better evidence or choose a reversible step with monitoring. Avoid converting a wide interval into a confident treatment ranking.