Calculator
Formula used
The calculator uses the incremental F test for selected predictors in a regression style physics model.
- Delta R squared = full R squared - reduced R squared.
- Cohen f squared = Delta R squared / (1 - full R squared).
- Adjusted f squared = Cohen f squared x measurement reliability.
- df1 = tested predictors. df2 = sample size - total predictors - 1.
- Critical F is found from alpha, df1, and df2.
- Lambda = adjusted f squared x sample size.
- Power = 1 - noncentral F CDF at the critical F value.
- Unstandardized slope = standardized beta x outcome SD / predictor SD.
How to use this calculator
- Select the calculation mode.
- Enter sample size and predictor counts.
- Choose R squared values or direct Cohen f squared.
- Set alpha, target power, and measurement reliability.
- Press Calculate to show results above the form.
- Use CSV or PDF download for records.
Example data table
| Scenario | Sample | Total predictors | Tested predictors | Reduced R squared | Full R squared | Alpha |
|---|---|---|---|---|---|---|
| Thermal loss model | 120 | 6 | 2 | 0.25 | 0.35 | 0.05 |
| Sensor drift study | 90 | 5 | 1 | 0.18 | 0.27 | 0.05 |
| Motion predictor screen | 160 | 8 | 3 | 0.30 | 0.42 | 0.01 |
Power Selection in Physics Models
Physics experiments often collect many possible predictors. These may include voltage, mass, speed, temperature, pressure, time, frequency, and sensor uncertainty. A power calculation helps decide whether the chosen predictors can show a real effect. It also warns when a model has too many inputs for the available observations.
Why Predictor Power Matters
Predictor selection is not only a statistical task. It affects physical interpretation. A weakly powered model may hide a useful variable. It may also promote a noisy variable by chance. This calculator compares the tested predictor block against the remaining unexplained variance. The result helps you plan a cleaner experiment before data collection begins.
Inputs Used by the Tool
The main inputs are sample size, total predictors, tested predictors, alpha, and effect size. You can enter Cohen f squared directly. You can also use full and reduced R squared values. A reliability factor is included for practical measurements. Sensors, calibration drift, and rounding can reduce observed signal. Lower reliability therefore reduces the usable effect estimate.
Reading the Output
The calculator reports degrees of freedom, adjusted effect size, critical F value, estimated power, and selection stability. It also shows observations per predictor. This is useful because a model can have good power but poor stability when many candidate predictors are screened. Treat low stability as a warning. It means the selected predictors may change with another sample.
Good Planning Practice
Use conservative assumptions when planning. Choose an alpha level before testing. Keep tested predictor blocks small. Increase sample size when predictors are correlated or noisy. Compare several scenarios. A physics model should respect theory, not only the largest coefficient. Use this calculator as a planning aid. It does not replace experimental judgment, diagnostic plots, or validation data.
Repeat the calculation for optimistic, expected, and cautious cases today. This range shows how sensitive the study is to effect size. It also shows whether extra observations are more valuable than adding another predictor overall.
Exporting Results
CSV export is useful for spreadsheets. PDF export is useful for reports and lab notes. Save each scenario with clear assumptions. This makes the final model easier to explain. It also helps reviewers see why the selected predictors were reasonable.
FAQs
What does this calculator estimate?
It estimates whether a selected predictor block has enough sample support to show a reliable effect in a physics regression model.
What is Cohen f squared?
Cohen f squared measures added predictor strength against unexplained variance. Larger values usually need fewer observations for the same power.
When should I use R squared inputs?
Use them when you know reduced and full model fit values from prior work, pilot data, or a planned scenario.
What is the tested predictor block?
It is the predictor group being evaluated. Examples include new sensor terms, interaction terms, or a physics based variable group.
Why include measurement reliability?
Measurements are rarely perfect. Reliability reduces the usable effect size when sensors, rounding, calibration, or repeatability are limited.
What does selection stability mean?
It checks whether the sample is large enough compared with final and candidate predictors. Low stability suggests exploratory results.
Can this replace validation data?
No. It supports planning. Use validation data, residual checks, and physical theory before trusting selected predictors.
Why export CSV and PDF files?
CSV supports spreadsheets. PDF supports reports, proposals, and lab notes. Both keep assumptions visible for later review.