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Assess your innovation's Technology Readiness Level across Horizon Europe, NASA, and DeepTech frameworks with gap analysis and grant eligibility.
How It Works
The Sample Size Calculator determines the minimum number of completed observations needed to achieve statistical significance. It accepts your desired confidence level (typically 95% or 99%), acceptable margin of error (e.g., 5%), expected population size, and statistical power (1 - β, typically 80% or 90%). It computes both the unadjusted sample size and the Cochran finite population correction when applicable.
Formula & Technical Methodology
For survey proportions: n = (Z² · p · (1 - p)) / e² where Z is the standard normal quantile (1.96 for 95% confidence), p is the expected proportion (default 0.5 for maximum variance), and e is the margin of error. For finite populations N: n_adj = n / (1 + (n - 1) / N). For two-sample mean comparisons: n = 2 · ((Z_α/2 + Z_β)² · σ²) / Δ², where Δ is the detectable difference (Cohen's d = Δ / σ).
When Should You Use This Tool?
Use this tool before commencing field research, academic theses, clinical interventions, or product A/B tests to prevent underpowered studies (type II errors) or wasteful over-sampling.
Practical Example
For a population of 50,000 customers, with 95% confidence level and 5% margin of error: base sample is 384. Applying the finite population correction yields 382 completed respondents. If expecting a 20% dropout rate, the recommended recruitment target is 478 participants.
Frequently Asked Questions
- Why is 95% confidence level and 5% margin of error the standard?
- A 95% confidence level corresponds to an alpha (type I error rate) of 0.05, which is the peer-reviewed scientific benchmark. A 5% margin of error balances precision with manageable participant recruitment costs.
- What is the Finite Population Correction (FPC)?
- When your sample size exceeds 5% of the total population (n/N > 0.05), the finite population correction reduces the required sample size because sampling without replacement captures a significant proportion of total population variance.
- How does statistical power affect sample size?
- Statistical power (1 - beta) is the probability of detecting a real effect if one exists. Increasing power from 80% to 90% typically increases the required sample size by approximately 30% to 40%.
- Can I export calculation steps for grant proposals or IRB approval?
- Yes. The tool generates an itemized methodology breakdown including equations, z-scores, effect sizes, and attrition adjustments ready to copy into your ethics protocol or grant application.