Sample Size & Power Calculator

An intuitive tool for researchers to calculate sample sizes and statistical power for various study designs and analyses.

Study Design

Cohort/RCT: Compare proportions in cohort studies or RCTs
One Sample Proportion: Test single proportion against null
Two Sample Proportion: Compare independent group proportions
Population Proportion (CI): Calculate confidence intervals
Two Means: Compare means using t-tests

Specialized Tests

RNA Seq: Sample size for RNA sequencing analysis
Success Run: Consecutive successes for reliability
Seq Success: Sample size for variant detection
Diagnostic Test: Calculate diagnostic metrics

Quick Start Tutorial

Frequently Asked Questions

What is a sample size calculator?

A sample size calculator helps researchers determine the number of subjects needed for a study to achieve statistical significance. It ensures studies are neither underpowered nor waste resources.

Why use this calculator?

Our calculator is free, comprehensive, and designed specifically for medical research. It includes specialized calculators for RCTs, RNA-seq, diagnostic tests, and more.

How accurate is this calculator?

This calculator uses established statistical methods and formulas published in peer-reviewed literature. All calculations are based on widely accepted statistical principles.

Have a suggestion or need a specific test? Email us

Cohort/RCT Sample Size Calculator

This calculator helps determine sample size requirements for comparing two proportions in a cohort study or randomized controlled trial (RCT).

Uses method of Fleiss, Tytun, and Ury (without continuity correction) to estimate:

Power - given a sample size
Sample size - to achieve a desired power

For a two-sided test comparing the difference between two proportions.

*Reference: Fleiss JL, Tytun A, Ury HK (1980): A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics 36:343–6.

Data Table

One Sample Proportion Test Calculator

Calculate sample size or power for testing a single proportion against a null hypothesis value.

Common uses include:

Testing if a population proportion differs from a specified value
Determining if a new treatment success rate exceeds a threshold
Evaluating if an adverse event rate is below an acceptable level

*Reference: Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.

Data Table

Two-sample proportion test

This calculator helps determine sample size or power when comparing proportions between two independent groups.

Common applications include:

Comparing treatment success rates between two groups
Testing if proportions differ between populations
Evaluating differences in event rates

Data Table

Population Proportion Calculator

Calculate confidence intervals and sample size requirements for estimating population proportions.

Useful for:

Prevalence studies
Survey research
Population characteristic estimation

Currently not working!

Disease Prevalence and Sample Size

*Buderer, N. M. F. (1996). Statistical methodology: I. Incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity. Academic Emergency Medicine.

Two Means Calculator

Calculate sample size or power for comparing means between groups using t-tests.

Supports:

One sample t-test (comparing to a known mean)
Two independent sample t-test
Paired t-test

Data Table

RNA-Seq Sample Size Calculator

Calculate sample size or power for RNA sequencing differential expression analysis.

Key parameters to consider:

FDR (False Discovery Rate) threshold
Minimum fold change of interest
Expected read counts and dispersion

This is quite a slow calculation

Data Table

Success Run Calculator

Results

Required Success Run Length:

Interpretation:

About Success Run Analysis

Success run analysis is used to determine the required number of consecutive successes (n) needed to demonstrate reliability (p).

Confidence Level: How certain you want to be about your conclusion (e.g., 95%)
Target Reliability: The minimum acceptable reliability level (e.g., 95% reliable)

Applications include:

Medical device validation
Quality control testing
Process reliability assessment

Example Application

Consider testing a medical device where you need to be 95% confident that it is at least 95% reliable:

Set confidence interval to 0.95 (95%)
Set reliability to 0.95 (95%)
The calculator will tell you how many consecutive successful tests you need

This approach is particularly useful for:

Validation testing where failures are costly or time-consuming
Safety-critical applications requiring high reliability
Quality assurance in manufacturing processes

Sequencing Success Calculator

Determine sample size requirements for detecting genetic variants through sequencing.

Key considerations:

Expected variant allele frequency
Background sequencing error rate
Required detection confidence

Results (if any cell contains a value less than 5, Fishers Exact test is performed as opposed to Persons Chi Square)

Overview of calculations

Still need to edit this text Power is the probability of not making a Type II error (1 – beta).

Type II error is the probability of wrongly failing to reject the null (i.e. you dont see a difference in you test but there is actually a difference).

Thus, simply put, power is the probability that the test rejects the null hypothesis (H0) when, in fact, it is false. You want power to be as large as possible.

What affects power?

Significance level (alpha)

Sample size

Variability, or variance, in the measured response variable

Magnitude of the effect

p-value: How likley our sample results are under our assumption of the truth. Put another way, what is the probability of being this far or further from the null in either direction (two sided test).

So for example, our H0 when comparing two means would be H0=u1-u2=0. Type I error is to falsely infer the existence of something that is not there.

It is the likelihood that you will report a difference as significant when, in reality, it is not. You want this to be as small as possible.

How to Report Sample Size and Power Calculations

General Guidelines

When reporting sample size and power calculations, include:

The statistical test that will be used
The significance level (α)
The desired power (1-β)
The expected effect size or difference to detect
Any assumptions made about variability or standard deviations

Clinical Trial Example

Example 1: RCT comparing two treatments

Sample text: 'Sample size was calculated using a two-sided test with α=0.05 and 80% power to detect a 15% absolute difference in treatment success rate between groups (60% vs 75%). Assuming a 10% dropout rate, we need to recruit 164 participants (82 per group).'

Example 2: Diagnostic test study

Sample text: 'To estimate sensitivity with a precision of ±5% (95% CI), assuming an expected sensitivity of 85% and disease prevalence of 30%, we calculated a required sample size of 200 participants.'

Basic Science Example

Example 1: RNA-seq study

Sample text: 'Sample size calculations for RNA-seq were performed assuming a fold-change threshold of 2.0, FDR of 5%, average read depth of 20 million reads per sample, and biological coefficient of variation of 0.4. To achieve 80% power, we determined that 5 biological replicates per group were needed.'

Example 2: Laboratory experiment

Sample text: 'Power analysis indicated that 8 samples per group would provide 90% power to detect a 1.5-fold difference in protein expression (α=0.05), assuming a standard deviation of 0.4 based on preliminary data.'

Common Mistakes to Avoid

Not stating the effect size or difference you're trying to detect
Omitting key assumptions that went into the calculation
Not accounting for multiple comparisons when relevant
Failing to justify the chosen effect size or power level
Not mentioning adjustments for anticipated dropout/attrition

Additional Resources

For more detailed guidance, consult: