Calculator Inputs
Example Data Table
| Scenario | Exposed Risk | Control Risk | Power | Ratio | Dropout | Use Case |
|---|---|---|---|---|---|---|
| Radiation monitoring cohort | 12% | 6% | 80% | 1:1 | 10% | Compare outcome rates after exposure. |
| Laboratory safety exposure | 9% | 4% | 90% | 2:1 | 8% | Improve precision with extra controls. |
| Environmental physics study | 15% | 10% | 85% | 1.5:1 | 12% | Plan follow-up in field groups. |
Formula Used
This calculator uses a two-cohort comparison formula for two independent proportions.
n exposed = {[Zα × √((r + 1) × Pbar × Qbar)] + [Zβ × √(rP1Q1 + P0Q0)]}² / {r × (P1 - P0)²}
n unexposed = r × n exposed
Here, P1 is the exposed risk. P0 is the unexposed risk.
r is the unexposed-to-exposed ratio.
Pbar equals (P1 + rP0) / (1 + r).
Qbar equals 1 - Pbar.
The calculator then applies design effect, optional finite population correction, continuity correction, and dropout inflation.
How to Use This Calculator
- Enter the expected outcome risk for the exposed cohort.
- Enter the expected outcome risk for the unexposed cohort.
- Set the allocation ratio between unexposed and exposed groups.
- Choose alpha, power, and test direction.
- Add dropout, design effect, and finite population values if needed.
- Press the calculate button to view the required group sizes.
- Download the result as CSV or PDF for documentation.
Planning Cohort Sample Size in Physics Research
Why Sample Size Matters
Cohort studies follow groups through time. They compare outcome risk between exposed and unexposed people, samples, systems, or sites. In physics-related research, the exposure may be radiation dose, magnetic field level, heat load, vibration, optical intensity, or environmental energy transfer. A weak plan can miss a real effect. It can also waste resources. Sample size planning reduces that risk before data collection begins.
Using Risk Inputs
The main inputs are two expected risks. The first risk belongs to the exposed group. The second risk belongs to the comparison group. A larger difference needs fewer observations. A smaller difference needs more observations. Good estimates should come from pilot data, prior studies, safety logs, or expert review. Avoid using guesses without notes.
Power and Confidence
Power controls the chance of detecting the planned difference. Higher power gives stronger protection against false negative results. It also increases the required sample size. Alpha controls the false positive rate. A two-sided test is common when either direction matters. A one-sided test may be used only when the research question clearly supports one direction.
Advanced Adjustments
Real studies often need adjustments. Dropout accounts for lost follow-up. Design effect handles clustering, repeated facilities, grouped classrooms, or field stations. Finite population correction can reduce the count when the available cohort is small. The allocation ratio helps when one group is easier to recruit than another. Each setting should match the study protocol.
Reading the Result
The final output gives exposed, unexposed, and total sample size. It also reports risk difference, relative risk, odds ratio, and intermediate values. These details help reviewers check the calculation. They also make the planning record easier to defend. Use the result as a planning guide, not as a replacement for statistical review.
FAQs
1. What is a cohort study sample size?
It is the number of participants, samples, or units needed in exposed and unexposed groups to detect a planned risk difference with chosen power and confidence.
2. Can this calculator be used for physics research?
Yes. It can support physics-linked cohort designs where exposure status is observed over time, such as radiation, heat, vibration, or environmental exposure studies.
3. What does exposed risk mean?
Exposed risk is the expected percentage of the exposed group that will develop the outcome, event, failure, or measured condition during follow-up.
4. What does the allocation ratio do?
The allocation ratio sets how many unexposed units are planned for each exposed unit. Higher ratios may improve precision when controls are easier to recruit.
5. Why add dropout?
Dropout protects the final study from lost follow-up. The calculator inflates the sample size so the retained group remains near the target count.
6. What is design effect?
Design effect adjusts for clustering or complex sampling. A value above one increases the required sample size to protect statistical reliability.
7. Should I use a one-sided or two-sided test?
Use a two-sided test when either direction is meaningful. Use a one-sided test only when the protocol justifies one clear direction.
8. Is the PDF result suitable for reports?
The PDF gives a clean calculation summary. For formal research, include assumptions, citations, protocol notes, and statistical review.