Power Sample Size Form
Example Data Table
| Design | Alpha | Power | Effect | Dropout | Estimated Use |
|---|---|---|---|---|---|
| Two Means | 0.05 | 0.80 | 0.50 | 10% | Balanced clinical comparison |
| One Mean | 0.05 | 0.90 | 0.40 | 5% | Before and after score test |
| Two Proportions | 0.05 | 0.80 | 0.50 to 0.60 | 15% | Conversion rate experiment |
| Correlation | 0.05 | 0.85 | 0.30 | 8% | Association strength planning |
Formula Used
One mean: n = ((Z alpha + Z power) / d)².
Two means: n1 = ((1 + 1 / k)(Z alpha + Z power)²) / d². Group two equals k times group one.
One proportion: n = (Z alpha√p0q0 + Z power√p1q1)² / (p1 - p0)².
Two proportions: n uses pooled planning variance and unequal allocation adjustment.
Correlation: n = ((Z alpha + Z power) / Fisher z)² + 3.
Dropout adjustment: adjusted total = base total / (1 - dropout rate).
How to Use This Calculator
- Select the study design that matches your statistical test.
- Choose one tailed or two tailed testing.
- Enter alpha, usually 0.05 for many studies.
- Enter target power, often 0.80 or 0.90.
- Enter effect size for means or correlation designs.
- Enter baseline and alternative proportions for rate studies.
- Add allocation ratio, dropout, and finite population if needed.
- Press calculate and review the result above the form.
Power Calculations Sample Size Guide
Why Sample Size Matters
Sample size planning protects a study from weak evidence. A small sample can miss a real effect. A large sample may waste time and budget. Power analysis balances these limits before data collection starts. It helps researchers define a practical target.
Core Planning Inputs
This calculator uses alpha, desired power, effect size, allocation, dropout, and study design. Alpha is the allowed false positive risk. Power is the chance of detecting the planned effect. Effect size describes the expected signal. Better inputs make the estimate more useful.
Choosing a Design
Use the one mean option for a single group or paired change. Use two means for independent group comparisons. Use one proportion for a rate against a planned value. Use two proportions for conversion, response, or event rate comparisons. Use correlation for association studies.
Understanding Effect Size
For mean tests, effect size is often Cohen d. It equals the expected mean difference divided by standard deviation. For correlation, enter the expected r value. For proportions, enter the baseline and alternative rates. Avoid entering optimistic effects without evidence.
Dropout and Allocation
Many studies lose participants. Dropout adjustment increases the final recruitment target. Unequal allocation also changes the group sizes. A ratio of 2 means group two is twice group one. Balanced designs usually need fewer total participants for the same effect.
Using the Result
The result gives group one, group two, and total sample size. Rounded values are used because partial participants are impossible. The download buttons help save the calculation. Keep the chosen assumptions with the study protocol.
Practical Caution
This tool gives planning estimates. Real projects may need exact methods, simulation, repeated measure models, cluster adjustment, or regulatory review. Discuss important studies with a statistician. Good planning improves confidence, budget control, and final interpretation.
FAQs
What is statistical power?
Statistical power is the chance of detecting a real effect. A common target is 80%. Higher power needs more observations, but it reduces the chance of a missed effect.
What alpha should I use?
Many studies use 0.05. This means a 5% false positive risk under the null model. Some fields need stricter alpha levels.
What is effect size?
Effect size measures the expected difference or association. Larger effects need fewer samples. Smaller effects need more samples to detect clearly.
Should I use one tailed testing?
Use one tailed testing only when an effect in the opposite direction is not meaningful. Many research plans prefer two tailed testing.
What is allocation ratio?
Allocation ratio sets the size relationship between groups. A value of 1 means equal groups. A value of 2 makes group two twice as large.
Why add dropout?
Dropout accounts for participants who leave, fail follow-up, or provide unusable data. It increases the recruitment target before the study begins.
Can this calculator handle proportions?
Yes. Use one proportion for one rate. Use two proportions for comparing two rates, such as response, success, or conversion rates.
Is this enough for every study?
No. Complex studies may need simulation, clustered designs, survival models, or repeated measures. Use this as a planning aid, not final approval.