Sample Size Calculator
Calculate Required Sample Size with Step-by-Step Derivation
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Sample Size Formulas
Proportion: n = z² × p̂(1 - p̂) / E²
Mean: n = (z × σ / E)²
Always round up to next integer for sample size!
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Use p̂ = 0.5 for maximum sample size when no prior estimate exists.
What is Sample Size Calculation?
Sample size calculation determines how many participants are needed in a study to reliably detect an effect of a given size.
Confidence Level
Typically 95% (α = 0.05)
Margin of Error
Acceptable error in estimate
Estimate
Proportion or standard deviation
Round Up
Always round up to integer
💡 Example: For 95% confidence, margin of error 0.05, p̂ = 0.5: n = (1.96)² × 0.5 × 0.5 / 0.05² = 384.16 → 385
Applications
Research
Clinical Trials
Surveys
Quality Control
Market Research
Frequently Asked Questions
What is sample size calculation?▼
Sample size calculation determines how many participants needed for study to detect effect, considering alpha, power, and effect size.
Why is sample size important?▼
Too small: low power, false negatives. Too large: wasteful, ethical issues. Right size balances precision, cost, ethics.
What factors affect sample size?▼
Alpha (significance level), power, effect size, population variance (for means), or proportion (for binary outcomes).
What is power in statistics?▼
Power = 1 - β = probability of correctly rejecting false null hypothesis. Typical power = 0.80 or 0.90.
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