Calculator Inputs
What this tool estimates
It converts an odds ratio and baseline probability into a second-group event probability.
Then it computes achieved power or required sample size using normal approximation formulas for two independent proportions.
Example Data Table
| Scenario | p0 | Odds Ratio | Alpha | Allocation | Group 0 N | Group 1 N | Estimated Power |
|---|---|---|---|---|---|---|---|
| Balanced design | 0.18 | 1.85 | 0.05 | 1.00 | 220 | 220 | 77.53% |
| Unequal allocation | 0.10 | 2.10 | 0.05 | 1.50 | 180 | 270 | 77.91% |
| Smaller effect | 0.25 | 1.35 | 0.05 | 1.00 | 300 | 300 | 37.81% |
Formula Used
Convert odds ratio into the second-group probability:
p1 = (OR × p0) / (1 - p0 + OR × p0)
Standard error under the alternative design:
SE = √[p1(1-p1)/n1 + p0(1-p0)/n0]
Approximate achieved power:
Power ≈ Φ(|p1-p0| / SE - zα)
Approximate required control-group sample size:
n0 = [(zα + zβ)² × (p1(1-p1)/k + p0(1-p0))] / (p1-p0)², where k = n1/n0.
How to Use This Calculator
- Choose whether you want achieved power or required sample size.
- Enter the baseline event probability for the control or reference group.
- Provide the expected odds ratio that reflects your assumed effect.
- Set alpha, select one-sided or two-sided testing, and enter the allocation ratio.
- For achieved power, enter both group sample sizes.
- For required sample size, enter the target power instead.
- Submit the form to display the result summary above the calculator.
- Use the CSV or PDF buttons to export the result table.
FAQs
1. What does this calculator measure?
It estimates statistical power or required sample size for detecting a difference implied by an odds ratio between two independent groups.
2. Why do I need a control event probability?
An odds ratio alone does not determine event risk. The baseline probability is needed to convert the odds ratio into an expected probability for the second group.
3. What is the allocation ratio?
It is the planned size of group 1 divided by group 0. Balanced designs use 1. Larger ratios assign more observations to one side.
4. Does this use an exact test?
No. It uses a normal approximation for two independent proportions. That makes it fast and practical, but exact methods may differ for very small samples.
5. When should I use one-sided testing?
Use one-sided testing only when effects in the opposite direction are not scientifically meaningful and the directional choice was decided before data collection.
6. What does Cohen h add here?
Cohen h expresses the gap between probabilities on a standardized arc-sine scale, helping compare effect magnitudes across scenarios with different baseline risks.
7. Why might power stay low with a large odds ratio?
If the baseline probability is rare or sample sizes are modest, the absolute probability difference can still be small, which reduces detectable signal.
8. Can I use this for study planning?
Yes. It is useful for preliminary planning, sensitivity analysis, and checking whether a proposed design is likely to detect the assumed effect.