What This Calculator Measures
Estimate sample size for power using effect size, alpha, and power targets.
By combining practical inputs into a structured model, this calculator helps you move from vague estimation to clear planning actions you can execute consistently.
This calculator estimates sample size for power-based studies.
How to Use This Well
- Enter effect size, alpha, and power target.
- Add standard deviation and allocation ratio.
- Set dropoff percent.
- Review total sample size.
- Adjust effect size assumptions.
Formula Breakdown
n = 2 x (zα + zβ)^2 x σ^2 / d^2Total: n x (1 + ratio).
Adjusted: total / (1 - dropoff).
Group 1: total / (1 + ratio).
Worked Example
- Effect size 0.4 with 80% power.
- Base sample around 98 per group.
- Total around 196 before dropoff.
Interpretation Guide
| Range | Meaning | Action |
|---|---|---|
| Under 80 | Light. | Broader effects only. |
| 80-150 | Standard. | Typical power. |
| 150-250 | High. | Tighter effects. |
| 250+ | Very high. | Large study. |
Optimization Playbook
- Increase effect size: lower sample needs.
- Balance groups: set ratio near 1.
- Reduce dropoff: improve retention.
- Check variance: lower std dev if possible.
Scenario Planning
- Baseline: current effect size.
- Higher power: raise to 90%.
- Lower alpha: reduce to 0.01.
- Decision rule: keep total under 250 if possible.
Common Mistakes to Avoid
- Overestimating effect size.
- Ignoring dropoff.
- Using wrong alpha.
- Skipping variance check.
Implementation Checklist
- Estimate effect size.
- Set power target.
- Plan recruitment.
- Monitor dropoff.
Measurement Notes
Treat this calculator as a directional planning instrument. Output quality improves when your inputs are anchored to recent real data instead of one-off assumptions.
Run multiple scenarios, document what changed, and keep the decision tied to trends, not a single result snapshot.
FAQ
How do I estimate effect size?
Use historical data or pilot studies.
What alpha should I use?
0.05 is common for most studies.
Why include dropoff?
It ensures you reach final sample goals.
Related Calculators
- Proportion Sample Size Planner Calculator
- Sampling Margin Planner Calculator
- Forecast Error Band Calculator
Frequently Asked Questions
How accurate are the results?
The Power Sample Size Curve applies a standard formula to your inputs — accuracy depends on how precisely you measure those inputs. For planning and estimation, results are reliable. For high-stakes or professional decisions, cross-check the output with a domain expert or primary source.
What sample size do I need for reliable results?
It depends on the desired confidence level, margin of error, and population variance. For a typical survey (95% confidence, ±5% margin), n ≈ 385 for a large population. Smaller samples are fine for exploratory analysis, but don't over-interpret the results — widen your confidence intervals to reflect the uncertainty.
How should I interpret the Power Sample Size Curve output?
The result is a calculated estimate based on the formula and your inputs. Compare it against the reference values or benchmarks shown on this page to understand whether your result is high, low, or typical. For decisions with real consequences, use the output as one data point alongside direct measurement and professional advice.
When should I use a different approach?
Use this calculator for quick, formula-based estimates. If your situation involves multiple interacting variables, time-varying inputs, or safety-critical decisions, consider a dedicated software tool, professional consultation, or direct measurement. Calculators are most reliable within their stated assumptions — check that your scenario matches those assumptions before relying on the output.