Public Health Research Toolkit

Plan Your Study With Confidence

Evidence-based sample size and power calculations for public health, epidemiology, clinical, and health research.

Explore Study Designs

9 Available calculators

PH Public-health focused

R Statistical engine

CALCULATORS

Choose Your Study Design

Select the statistical objective or epidemiologic design that best matches your research question.

Single Proportion

Estimate prevalence, coverage, risk, or another population proportion.

Available

Single Mean

Estimate a population mean with a predefined level of precision.

Available

Two Proportions

Compare proportions between two independent populations.

Available

Two Means

Compare continuous outcomes between two independent study groups.

Available

Case-Control

Estimate sample size using exposure prevalence and an expected odds ratio.

Available

Cohort Study

Compare outcome risks between exposed and unexposed populations.

Available

Cluster Survey

Account for clustering using cluster size and intra-cluster correlation.

Available

Diagnostic Accuracy

Estimate sample size for sensitivity, specificity, and diagnostic accuracy.

Available

Correlation

Calculate sample size required to detect a correlation coefficient.

Available

Regression

Planning for linear and logistic regression models.

Coming soon

Survival Analysis

Power and required events for time-to-event studies.

Coming soon

Non-Inferiority

Sample size for non-inferiority and equivalence studies.

Coming soon

Evidence-based

Each calculator documents the underlying statistical method, assumptions, formula, and methodological reference.

Designed for Researchers

Results include interpretation, intermediate calculations, and important adjustments rather than only a final number.

Public Health Oriented

Modules are designed around common epidemiologic and public-health research designs.

ESTIMATION

Sample Size for a Single Proportion

Use this calculator to estimate the sample size required to measure a population proportion such as prevalence, coverage, or risk with a specified level of precision.

Study Parameters

Confidence level

Expected proportion / prevalence (%)

Margin of error (%)

Population size (optional)

Design effect

Expected non-response (%)

Statistical Method

For a simple random sample, the initial sample size is calculated from the expected population proportion, the selected confidence level, and the desired absolute precision.

$$ n_0 = \frac{Z_{1-\alpha/2}^{2}p(1-p)}{d^2} $$

Where: p = expected proportion, d = absolute precision, and Z = critical value corresponding to the selected confidence level.

Adjustments

Finite population correction, when a population size is specified.
Design effect for complex or clustered sampling designs.
Inflation for expected non-response.

Key References

Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies: A Practical Manual. World Health Organization; 1991.
Cochran WG. Sampling Techniques. 3rd ed. Wiley; 1977.

ESTIMATION

Sample Size for a Single Mean

Estimate the sample size required to estimate a population mean with a specified confidence level and absolute precision.

Study Parameters

Confidence level

Expected standard deviation

Absolute margin of error

Population size (optional)

Design effect

Expected non-response (%)

Statistical Method

$$ n_0 = \frac{Z_{1-\alpha/2}^{2}\sigma^2}{d^2} $$

σ represents the expected population standard deviation and d is the desired absolute precision.

Key References

Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies. WHO; 1991.
Cochran WG. Sampling Techniques. 3rd ed. Wiley; 1977.

COMPARISON

Sample Size for Two Independent Proportions

Calculate sample size for comparing two independent population proportions.

Study Parameters

Expected proportion in Group 1 (%)

Expected proportion in Group 2 (%)

Significance level

Statistical power

Group 2 : Group 1 allocation ratio

Expected loss / non-response (%)

Statistical Method

The calculation uses the normal approximation for comparing two independent proportions with the requested allocation ratio.

The displayed sample size is calculated separately for Group 1 and Group 2.

Key References

Fleiss JL, Levin B, Paik MC. Statistical Methods for Rates and Proportions.
Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies. WHO; 1991.

COMPARISON

Sample Size for Two Independent Means

Calculate sample size for comparing mean outcomes between two independent study groups.

Study Parameters

Expected mean difference

Standard deviation in Group 1

Standard deviation in Group 2

Significance level

Statistical power

Group 2 : Group 1 allocation ratio

Expected loss / non-response (%)

Statistical Method

$$ n_1 = \frac{(Z_{1-\alpha/2}+Z_{1-\beta})^2(\sigma_1^2+\sigma_2^2/r)}{\Delta^2} $$

Here r is the Group 2 to Group 1 allocation ratio and Δ is the minimum mean difference to be detected.

EPIDEMIOLOGIC DESIGN

Sample Size for an Unmatched Case-Control Study

Estimate the number of cases and controls required based on exposure prevalence among controls and the expected odds ratio.

Study Parameters

Exposure prevalence among controls (%)

Expected odds ratio

Significance level

Statistical power

Controls per case

Expected loss / incomplete data (%)

Statistical Method

The expected exposure prevalence among cases is derived from the exposure prevalence among controls and the anticipated odds ratio.

$$ P_1 = \frac{OR \times P_0}{1-P_0 + OR \times P_0} $$

Key References

Fleiss JL, Levin B, Paik MC. Statistical Methods for Rates and Proportions.
Kelsey JL et al. Methods in Observational Epidemiology.

EPIDEMIOLOGIC DESIGN

Sample Size for a Cohort Study

Compare outcome incidence between exposed and unexposed groups using an expected risk ratio.

Study Parameters

Outcome risk in unexposed group (%)

Expected risk ratio

Significance level

Statistical power

Unexposed per exposed participant

Expected loss to follow-up (%)

Statistical Method

Expected outcome risk in the exposed group is derived from the outcome risk in the unexposed group and the anticipated risk ratio.

Key References

Fleiss JL, Levin B, Paik MC. Statistical Methods for Rates and Proportions.
Kelsey JL et al. Methods in Observational Epidemiology.

CLUSTER SAMPLING

Sample Size for a Cluster Survey

Estimate sample size for a prevalence or proportion survey using cluster sampling, accounting for intra-cluster correlation and average cluster size.

Study Parameters

Confidence level

Expected prevalence (%)

Margin of error (%)

Average cluster size

Intra-cluster correlation (ICC)

Population size (optional)

Expected non-response (%)

Statistical Method

The calculation first estimates the sample size required under simple random sampling.

$$ n_0 = \frac{Z_{1-\alpha/2}^{2}p(1-p)}{d^2} $$

The sample size is then multiplied by a design effect derived from the average cluster size and intra-cluster correlation coefficient.

$$ DEFF = 1 + (m-1)\rho $$

Where m is the average cluster size and ρ is the intra-cluster correlation.

Key References

Cochran WG. Sampling Techniques. 3rd ed. Wiley; 1977.
Kerry SM, Bland JM. The intracluster correlation coefficient in cluster randomisation. BMJ.
Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies. WHO; 1991.

DIAGNOSTIC ACCURACY

Sample Size for Diagnostic Accuracy

Estimate the total sample required to achieve specified precision for sensitivity and specificity, taking expected disease prevalence into account.

Study Parameters

Confidence level

Expected sensitivity (%)

Expected specificity (%)

Expected disease prevalence (%)

Desired precision for sensitivity (%)

Desired precision for specificity (%)

Expected non-response / unusable data (%)

Statistical Method

The required number of participants with the condition is calculated from the anticipated sensitivity.

$$ n_{disease} = \frac{Z_{1-\alpha/2}^{2}Se(1-Se)} {d_{Se}^{2}} $$

The required number without the condition is similarly calculated from the anticipated specificity.

$$ n_{non-disease} = \frac{Z_{1-\alpha/2}^{2}Sp(1-Sp)} {d_{Sp}^{2}} $$

Expected disease prevalence is then used to determine the total number of participants required to satisfy both sensitivity and specificity precision targets.

Key Reference

Buderer NMF. Statistical methodology: I. Incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity. Academic Emergency Medicine. 1996.

ASSOCIATION

Sample Size for Correlation

Calculate the sample size required to detect a Pearson correlation coefficient with a specified statistical power.

Study Parameters

Expected correlation coefficient

Significance level

Statistical power

Expected non-response / incomplete data (%)

Statistical Method

The calculation uses Fisher's z transformation of the anticipated Pearson correlation coefficient.

$$ Z_{\rho} = \frac{1}{2} \ln \left( \frac{1+\rho}{1-\rho} \right) $$

$$ n = \left( \frac{ Z_{1-\alpha/2} + Z_{1-\beta} }{ Z_{\rho} } \right)^2 + 3 $$

The current implementation assumes a two-sided hypothesis test.

Key References

Fisher RA. On the probable error of a coefficient of correlation.
Hulley SB et al. Designing Clinical Research. Sample-size methods for correlation and association.

COMING SOON

Regression Models

Sample-size planning for linear regression, multiple regression, and logistic regression will be available in a future release.

Module under development

This calculator is planned for a future release. The statistical method, assumptions, interpretation, and methodological references will be documented.

COMING SOON

Survival Analysis

Sample-size and event requirements for time-to-event studies.

Module under development

This calculator is planned for a future release. The statistical method, assumptions, interpretation, and methodological references will be documented.

COMING SOON

Non-Inferiority & Equivalence

Sample-size calculations for non-inferiority and equivalence studies.

Module under development

This calculator is planned for a future release. The statistical method, assumptions, interpretation, and methodological references will be documented.