🎓 Statistics & Data • Inferential Statistics
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Sample Size Calculator (Cochran’s Formula)
Calculates minimum required sample size using Cochran’s formula with optional finite population correction.
Presets:
e.g. 3% margin
0.5 gives max n
Finite correction
Compensate loss
Recommended Minimum Sample Size (95% CL)
1,068 subjects
Required Sample Size across Margin of Error (Quadruple Law)Halving MOE quadruples n
Cochran Calculation Steps
Base formula (infinite population): n₀ = (z² × p × (1-p)) / E² = 1,068
Final recommended sample size: 1,068 subjects
Sample Size Determination
Determining the proper sample size ensures a study has sufficient statistical power to detect real effects without wasting resources.
Formula & Step-by-Step Calculation
n = (z² · p · (1 - p)) / E²
z = critical value, p = estimated proportion, E = desired margin of error.
Worked Step-by-Step Examples
Example 1
Calculate sample size for 95% confidence (z=1.96), 3% margin of error (E=0.03), and p=0.5
Solution: n = 1,068 respondents
• (1.96² × 0.5 × 0.5) / (0.03)² = (3.8416 × 0.25) / 0.0009 = 1,067.11 ⟹ 1,068
Common Real-World & Academic Use Cases
- ✓ Clinical drug trial patient recruitment planning
- ✓ National census survey sampling design
- ✓ Customer satisfaction Net Promoter Score research
How to Use the Sample Size Calculator (Cochran’s Formula)
1
Set Confidence Level & MOE
Choose 95% and enter desired ±% margin of error.
2
Optional Population Size
Leave blank for large populations or enter finite size.
3
Read Required n
Inspect total minimum respondents required.
Frequently Asked Questions
Q: Why assume p = 0.5 if unknown?
A proportion of 0.5 maximizes the product p(1-p) = 0.25, guaranteeing the most conservative (safe) maximum sample size.