Sample Size Calculator
Determine the required sample size for surveys, quality inspections, and statistical experiments
Sample Size Calculator
Use 50% if unknown (maximizes sample size)
Complete Guide to Sample Size Determination
Why Sample Size Matters
Too small a sample gives unreliable conclusions. Too large wastes time and money. The right sample size balances statistical confidence with practical resource constraints.
- Ensures statistically valid conclusions
- Optimizes inspection costs
- Required for AQL sampling plans
- Drives experiment design
Sample Size Formulas
For Proportions:
n = (Z² × p × (1-p)) / E²For Means:
n = (Z² × σ²) / E²Finite Population Correction:
n_adj = n / (1 + (n-1)/N)Z-Score by Confidence Level
| Confidence | Z-Score | α (significance) | Common Use |
|---|---|---|---|
| 80% | 1.282 | 0.20 | Preliminary studies |
| 90% | 1.645 | 0.10 | General screening |
| 95% | 1.960 | 0.05 | Standard (most common) |
| 99% | 2.576 | 0.01 | High-confidence |
| 99.9% | 3.291 | 0.001 | Critical applications |
FAQ
What proportion should I use if I don’t know the expected defect rate?
Use 50% (p = 0.5) which gives the maximum (most conservative) sample size. As the true proportion moves away from 50% in either direction, the required sample size decreases.
When should I use finite population correction?
Apply finite population correction when the sample is more than 5% of the total population. For large populations (over 100,000), the correction has negligible effect.
How do I estimate standard deviation for means?
Options: (1) Use data from a pilot study, (2) Use historical process data, (3) Estimate as range/4 if you can estimate the range, or (4) Use a conservative estimate and adjust after initial data collection.