Enter a sample mean, standard deviation, sample size, and confidence level to estimate the margin of error and interval.
Audit interval width and relative margin, then estimate the sample size needed for a target margin at the selected confidence level.
Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.
The summary-input calculator above remains authoritative for its modes. This workspace uses the same WTAStats distribution functions to calculate a raw-data t interval, a known-σ z interval, or a proportion from successes and trials.
Raw-data mode recomputes n, mean and sample SD locally.
Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.
Use the tool first, then apply these checks to verify the inputs, interpret the result, and hand it off without displacing the primary workflow.
A t interval for a mean uses a sample standard deviation, while a z interval with known sigma assumes a population standard deviation is genuinely known. A proportion interval starts from counts or a sample proportion. Do not choose the model only because one version produces a narrower interval.
When the original observations are available, recomputing n, the sample mean, and the sample standard deviation removes a common transcription error between a dataset and a summary-statistic calculator. Keep the pasted values with the report when another person needs to reproduce the interval.
A 95% confidence interval does not mean there is a 95% probability that a fixed population parameter lies inside this one realized interval. The confidence level describes the long-run coverage of the interval-building procedure under its assumptions. Sampling design and model assumptions still matter.
A narrow interval can still center on an effect too small to matter, and a wide interval can include both important and unimportant values. Report the estimate, interval, sample size, and units together rather than presenting the confidence level or margin of error alone.
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