Sample Size Calculator and Budget Horizon/ERC
Calculate sample size for clinical studies (Fleiss two-proportion formula) and estimate Horizon Europe/ERC budget. Deterministic calculations in the browser - no AI, no data sent.
The sample size is one of the fundamental calculations in the design of clinical and preclinical studies. The formula by Fleiss (1981/2003) for the two-proportion test allows determining the minimum number of participants per group (N) needed to detect a clinically relevant difference between two proportions (p1, p2) with a given statistical power (1-β) and significance level (α), in a design involving two independent samples.
The implemented formula is: n = [z_α/2 × √(2·p̄·q̄) + z_β × √(p₁q₁+p₂q₂)]² / (p₁-p₂)², where p̄ is the pooled proportion. The Z values are hardcoded from standard normal distribution tables (D-53-10/SC4), with no external dependencies. Rounding always occurs by ceiling to ensure nominal power.
The second module estimates the budget Horizon Europe / ERC divided by eligible categories (personnel, overhead, indirect costs, equipment, consumables, travel) according to the Annotated Grant Agreement (AGA) EC 2021. The values are a starting point - the final budget requires verification with your organization’s administrative office and the project financial consultant.
Formula: Fleiss JL, Levin B, Paik MC. Statistical Methods for Rates and Proportions, 3rd ed., Wiley, 2003. Budget: EC Annotated Grant Agreement 2021 [ASSUMED - verify eligibility rules AGA before submission].
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Sample size (Fleiss)
Budget Horizon Europe/ERC (€)
Result
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Enter values and press the button to calculate.
Calculation example
CRO Study: Phase III clinical trial comparing an experimental drug to placebo. Expected remission rate in control group: p1=0.30 (30%). Expected rate in treatment group: p2=0.50 (50%). α=0.05 two-tailed, power=80%.
- Average rating: 0.4/1
- z_α/2 = 1.960 (α=0.05); z_β = 0.842 (power=80%)
- n = [1.96×√(2×0.4×0.6) + 0.84×√(0.21+0.25)]² / (0.2)² → N per group approximately 94
- Total: about 188 participants (94 per arm) → always round up
[Fleiss formula (2003) without continuity correction. Consult a biostatistician for regulatory studies. Z values from standard tables [VERIFIED].]
Glossary
- Statistical power (1-β)
- Probability of detecting a real effect when it exists. The complement β is the risk of type II error (false negative). Standard accepted: 80% (0.80) for most studies; 90% for studies with critical primary endpoints.
- Significance level (α)
- Probability threshold below which the null hypothesis is rejected. α=0.05 means accepting a 5% chance of falsely concluding there is a difference (type I error). Regulators (EMA, FDA) require α=0.05 for superiority studies; α=0.025 for non-inferiority studies.
- Fleiss' Formula (1981/2003)
- Standard method for calculating sample size in studies with two independent proportions. Uses the normal distribution approximation (z values) and pooled proportion. The continuity correction alternative increases N by about 5-10% for greater conservatism.
- European Research Council
- Horizon Europe is the main EU research program (2021-2027, budget 95.5 billion EUR). ERC funds fundamental research with individual grants (Starting, Consolidator, Advanced). A project’s budget must comply with eligible cost categories defined in the Annotated Grant Agreement (AGA).
Frequently Asked Questions
What is sample size and why is it crucial in a clinical study?
The sample size is the minimum number of participants needed to detect a clinically relevant difference between two groups with a certain probability (statistical power) and an acceptable risk of error (α). An underpowered study fails to detect real effects (error β); an overpowered one wastes resources. A priori calculation is required by all ethics committees and ICH E9 protocols.
What does "80% power" and "α=0.05" mean?
Statistical power (1-β) is the probability of detecting a real effect when it exists. 80% power means that, if the difference between groups is real, the study will detect it in 80% of cases. α=0.05 is the significance threshold: the probability of falsely concluding there is a difference (type I error). Common combinations are 80% power + α=0.05 (standard) or 90% power + α=0.01 (regulatory studies).
What is the difference between two-tailed and one-tailed testing?
A two-tailed test (default) checks if the two groups differ in any direction (superiority or inferiority). A one-tailed test verifies only if the treatment group is better than the control. The two-tailed test is always more conservative (requires more participants) and is preferred by regulators (EMA, FDA) for efficacy studies. Use a one-tailed test only if justified beforehand in the protocol.
What are indirect costs (overhead) in a Horizon Europe budget?
In Horizon Europe, indirect costs are a flat percentage applied to eligible direct costs, excluding equipment. Most beneficiaries use the standard rate of 25% or a certified rate by the agency. Overhead costs included in the budget cover infrastructure, administrative management, and shared services not directly attributable to the project.
Does this tool use AI or send data to servers?
No. All calculations occur locally in the browser, without server connection and artificial intelligence. The Fleiss formula and Z values are implemented in pure TypeScript in the frontend. No personal, clinical, or financial data is transmitted or stored.
Can I use these results directly in an ERC Advanced Grant proposal?
The results serve as a useful starting point for power analysis and financial planning. Before submission, the sample size should be verified by an expert biostatistician (some institutes offer specific consultation for ERC proposals) and the budget should be adjusted to fit the program's rules and the grant call's maximum budget.
How is it used?
- Configure the statistical test
Enter the expected event rate in the control group (p1) and the treatment group (p2), the significance level α, and the desired statistical power. Fleiss's formula calculates the number of participants needed to detect a difference.
- Estimate Horizon/ERC Budget
Enter project cost items (staff, overhead, indirect costs, equipment, supplies, travel) to get the total eligible amount according to the Annotated Grant Agreement (AGA) EC guidelines.
- Interpret the results
The tool shows the number of participants per group, total, and used Z values. For the budget, it displays the total and percentage for personnel. All calculations happen in the browser - no data is sent to servers.
- Document in project proposal
Use the results as a starting point for the power analysis section and the financial table of the proposal. Always have the estimates reviewed by an expert biostatistician before submission.
Do you need a custom analysis?
This tool is free and informative. For in-depth analysis with AI on-prem - private data, zero cloud - contact Federico.