Sample Size Calculators

Estimate a population mean within a specified margin of error.

Compare one sample mean against a known or hypothesised value.

Compare means between two independent groups.

Compare two related measurements, such as before-and-after values.

Estimate a mean from a small, fixed population.

Compare means across more than two independent groups.

Plan a balanced study to test between-subject, within-subject, or group-by-measurement effects using univariate repeated-measures ANOVA.

Use for a two-arm trial with one baseline measurement and one primary follow-up, analysed using ANCOVA adjusted for baseline.

Use for a two-arm trial with one baseline, multiple follow-ups, and a common treatment effect averaged across follow-ups under compound symmetry.

Estimate a single population proportion with a desired margin of error.

Compare one observed proportion against a hypothesised value.

Compare proportions between two independent groups.

Compare paired binary outcomes.

Plan an omnibus Pearson chi-square comparison across three or more independent groups.

Plan a two-arm logistic-regression comparison adjusted for one binary baseline characteristic.

Estimate a proportion from a small, fixed population.

Plan approximate confidence-interval precision for one continuous population median.

Plan an exact one-sample sign test of a hypothesised population median.

Plan two independent groups using Noether’s large-sample Mann–Whitney approximation.

Plan paired observations using an exact sign test or a distribution-adjusted Wilcoxon signed-rank approximation.

Kruskal–Wallis omnibus planning under a Normal common-SD location-shift model.

Estimate a population correlation coefficient with desired precision.

Test whether a correlation differs from a specified value.

Compare correlation coefficients from two independent groups.

Plan a same-participant comparison of two Pearson correlations sharing one variable.

Plan a same-participant comparison of two Pearson correlations with no variables in common.

Plan a study to test an association using simple linear regression.

Plan a study powered to test one prespecified adjusted regression coefficient.

Plan an omnibus test of whether a prespecified multiple linear regression model explains outcome variance.

Plan a nested-model test of the R² increase contributed by a prespecified predictor block.

Plan a simple logistic-regression test for one continuous or binary predictor.

Plan a Wald test of one adjusted odds ratio for a continuous or binary primary predictor.

Plan an omnibus likelihood-ratio test for a prespecified multiple logistic-regression model.

Plan a likelihood-ratio test of a prespecified added predictor block in nested logistic models.

Estimate internal consistency reliability with desired precision.

Test whether Cronbach alpha meets a target reliability value.

Estimate intraclass correlation reliability with desired confidence-interval width.

Test whether ICC exceeds a minimum acceptable value.

Estimate two-rater kappa agreement with desired precision.

Test whether two-rater kappa exceeds a minimum acceptable value.

Estimate diagnostic-test sensitivity and specificity with a binary reference standard.

Test one diagnostic-test sensitivity against a fixed benchmark value.

Test one diagnostic-test specificity against a fixed benchmark value.

Estimate one ROC area under the curve with equal reference-standard-positive and reference-standard-negative groups.

Test whether a diagnostic test's anticipated ROC AUC is better than a prespecified minimum acceptable benchmark.

Compare ROC AUCs of two diagnostic tests evaluated in separate, independent participant samples.

Compare ROC AUCs of two diagnostic tests evaluated in the same participants.

Estimate a diagnostic test's positive or negative likelihood ratio with a prespecified clinically acceptable confidence bound.

Compare the sensitivity or specificity of two diagnostic tests evaluated in separate, independent participant samples.

Compare sensitivities or specificities of two diagnostic tests evaluated in the same participants.

Plan approximate confidence-interval precision for a Kaplan–Meier median survival estimate.

Plan precision for a Kaplan–Meier survival probability at one landmark time.

Plan a single-arm, one-sided test of a Kaplan–Meier survival probability at a prespecified landmark time.

Plan events and participants for a two-group log-rank comparison using median survival, landmark survival, or direct hazard-ratio assumptions.

Plan target events and participants to test one binary predictor in a Cox proportional-hazards model.

Plan target events and participants to test one continuous predictor in a Cox proportional-hazards model.

Plan a two-arm superiority trial with a continuous endpoint and a prespecified mean-difference margin.

Plan a two-arm non-inferiority trial with a continuous endpoint and a prespecified margin.

Plan a two-arm continuous-outcome equivalence trial with symmetric mean-difference limits.

Plan a two-arm superiority trial for an absolute risk-difference endpoint.

Plan a two-arm non-inferiority trial for an absolute risk-difference endpoint.

Plan a two-arm binary-outcome equivalence trial with symmetric risk-difference limits.

Plan a one-sided superiority comparison of two cluster-randomized arms with a continuous endpoint.

Plan a cluster-randomized non-inferiority trial with a continuous endpoint and prespecified margin.

Plan a cluster-randomized equivalence trial with continuous-outcome equivalence limits.

Plan a one-sided superiority comparison of two cluster-randomized arms with a binary endpoint.

Plan clusters and participants for a binary outcome using a justified absolute risk-difference non-inferiority margin.

Plan a cluster-randomized equivalence trial with binary-outcome risk-difference limits.

Plan a 2×2 AB/BA crossover superiority trial with a continuous outcome.

Plan a 2×2 AB/BA crossover non-inferiority trial with a continuous outcome.

Plan a 2×2 AB/BA crossover equivalence trial with a continuous outcome.

Plan a 2×2 AB/BA crossover superiority trial with a binary outcome.

Plan a 2×2 AB/BA crossover non-inferiority trial with a binary outcome.

Plan a 2×2 AB/BA crossover equivalence trial with a binary outcome.

Plan objective-specific pilot requirements for feasibility proportions, rates, progression criteria, or detecting important problems.

Plan a two-group longitudinal linear mixed model powered for a difference in mean linear slopes.

Plan a two-group linear mixed model powered for an average marginal mean difference across follow-up visits.

Plan a two-group linear mixed model powered for a marginal mean difference at one prespecified follow-up.

Plan an omnibus joint test of whether two longitudinal mean profiles differ across categorical follow-up visits.

Plan a two-group parallel trial using an MMRM superiority comparison at a prespecified follow-up visit.

Plan a two-group parallel trial using an MMRM non-inferiority comparison at a prespecified follow-up visit.

Plan a two-group parallel trial using MMRM and prespecified equivalence limits at a selected follow-up visit.

Plan a two-group parallel trial for a prespecified equal-weight average MMRM treatment contrast across selected follow-up visits.

Plan a population-averaged GEE joint test of whether two marginal mean profiles differ across categorical follow-up visits.

Plan a population-averaged GEE test of a two-group marginal mean difference at one prespecified follow-up.

Plan a population-averaged GEE test of an equally weighted mean difference across follow-up visits.

Plan a logistic GEE test of a common population-averaged odds ratio across repeated binary outcomes.

Plan a population-averaged GEE test of a difference between two linear longitudinal trends.

Plan an omnibus logistic-GEE test of whether a population-averaged odds-ratio profile changes across follow-ups.

Plan a logistic-GEE test of a population-averaged odds ratio at one prespecified follow-up.