Calculator Inputs
Example Data Table
| Scenario | Mode | Main inputs | Planning meaning |
|---|---|---|---|
| Neutron shielding pilot | Interaction | Base R² 0.30, added R² 0.05, power 0.80 | Tests whether moderator thickness changes response slope. |
| Coolant moderation trial | Mean precision | Sigma 2.5, error 0.5, confidence 95% | Estimates readings needed for a stable mean value. |
| Detector geometry study | Interaction | Design effect 1.2, valid data 90%, repeats 3 | Accounts for clustering, repeated readings, and losses. |
About the Moderation Sample Size Calculator
Physics experiments test whether a moderator changes a measured relationship. A moderator can be shielding thickness, coolant condition, absorber fraction, temperature band, detector setting, or another controlled factor. This calculator estimates how many independent samples or runs may be needed before the study starts.
The tool supports two planning paths. The first path targets a moderation interaction. It uses expected base R squared, added R squared, power, alpha, predictor count, design effect, repeated readings, attrition, and finite population size. The second path targets a mean estimate. It uses standard deviation, allowed error, confidence, design effect, repeated readings, and losses.
Why Sample Size Matters
A small study can miss a real moderation effect. A very large study can waste time, materials, and beam access. Good planning balances risk, cost, and accuracy. It also makes reports easier to defend during review.
Formula Used
For interaction planning, the calculator estimates Cohen f squared from the added variance. It uses f squared equals delta R squared divided by one minus full R squared. The core sample estimate is based on normal critical values for alpha and power. Predictors and tested interaction terms are then added. Design effect increases the need. Repeated readings reduce the independent unit need only as an approximate planning aid.
For mean precision planning, the calculator uses n equals z squared times sigma squared divided by error squared. A finite population correction may reduce the required count when the available sample frame is limited. Attrition and valid data rates raise the recruitment target.
How to Use This Calculator
Select the planning mode first. Enter the best effect estimates from pilot data, literature, or engineering judgment. Add the expected loss rate and valid data percentage. Enter a population size only when the available frame is truly limited. Press Calculate to view the usable sample, recruited sample, effective observations, and assumptions. Use the export buttons to save the result for protocols or lab notes.
Practical Notes
Use conservative assumptions when pilot data are weak. Increase sample size when sensors are noisy, conditions drift, or batches are not independent. This calculator is a planning aid. Final designs should be checked against the exact physics model and analysis method.
FAQs
What is a moderation sample size?
It is the number of units, runs, specimens, or observations needed to test a moderator effect or estimate a moderation-related measurement with planned confidence.
What is a moderator in a physics study?
A moderator is a factor that changes a relationship. It may be shielding thickness, temperature, absorber fraction, geometry, detector setting, or coolant condition.
Which mode should I choose?
Choose interaction power when testing whether a factor changes a relationship. Choose mean precision when estimating one physical moderation measurement within an allowed error.
What does added R squared mean?
Added R squared is the extra explained variance expected from the moderation term after the base predictors are already in the model.
What is design effect?
Design effect adjusts for clustering, batch effects, correlated runs, or unequal sampling. Values above one increase the required sample size.
Can repeated readings reduce sample need?
Repeated readings can improve precision, but they are not always independent. Use this option carefully when repeated measurements truly add useful information.
Why enter a finite population size?
Use it only when the available sample frame is limited. The correction can reduce the count when the planned sample is large relative to the population.
Is this calculator a final study design?
No. It is a planning tool. Final designs should be reviewed with the exact physics model, measurement uncertainty, and analysis method.