Sample Size Planning for Mediation Analysis
Mediation analysis is useful when a physics study explores a process. A researcher may test whether one variable changes another through an intermediate factor. For example, a field strength may affect detector response through temperature drift. The indirect effect is the product of two paths. The first path links the predictor to the mediator. The second path links the mediator to the outcome. A clear sample size plan helps this chain get tested with enough power.
Why Power Matters
Indirect effects are often smaller than direct effects. They can be difficult to detect. Small path values need larger samples. Higher power also increases the required sample. The alpha level changes the critical value. A stricter alpha protects against false claims. Yet it also raises the needed sample. Attrition matters too. Lost observations reduce usable data. This calculator adds an attrition adjustment so the starting sample can be planned early.
Physics Use Cases
Physics projects may use mediation when the mechanism matters. A material treatment may influence conductivity through grain size. Radiation exposure may affect sensor error through charge trapping. A cooling method may change signal quality through thermal noise. In each case, the mediator explains part of the relationship. The tool gives a practical planning estimate before collection begins. It can also support pilot studies and grant notes.
Inputs and Interpretation
The calculator uses standardized path coefficients. Enter the expected a path and b path. These values often come from pilot data, theory, or related experiments. Choose a power target and significance level. Add covariates when the model includes controls. Use design effect for clustered or repeated measurements. Use one tailed testing only when the direction is justified. The adjusted sample is usually the number to recruit.
Practical Notes
The result is an approximation, not a final protocol. Mediation power can depend on nonnormal products, measurement error, and model structure. Bootstrap tests can behave differently from a Sobel style estimate. Still, the estimate is useful for screening scenarios. Try several path values. Compare conservative and optimistic assumptions. Save the exports for documentation. When stakes are high, confirm the design with simulation or a statistician. This keeps planning transparent and easier to review later carefully.