Sample size for estimating a proportion
How many participants are needed to estimate a single proportion to a stated precision, with optional finite population and dropout adjustments.
Open resources
Research tools
Calculators for the statistics that come up most often in clinical research. Each one states its formula, its assumptions and its limitations, and cites the literature the method comes from. They are free to use, and nothing you enter leaves your browser.
Study design
Sample size for comparing two proportions
How many participants per group are needed to detect a difference between two independent proportions at a given significance level and power.
Estimation
Confidence interval for a proportion
Wilson score and Wald intervals for an observed proportion, showing why the two disagree near zero and one.
Epidemiology
2 × 2 table: odds ratio, risk ratio, ARR and NNT
Odds ratio, risk ratio, risk difference, absolute risk reduction and number needed to treat, each with a confidence interval.
Diagnostics
Diagnostic accuracy
Sensitivity, specificity, predictive values and likelihood ratios, with predictive values projected onto any prevalence you choose.
Effect size
Cohen's d effect size
Standardised mean difference between two independent groups, with Hedges' small-sample correction and a confidence interval.
A note on accuracy
Every formula on these pages is covered by an automated test against a worked example with a published answer. That does not make a calculator a substitute for statistical advice — choosing the right method for a particular study is the harder problem, and these tools cannot do it for you.