Calculator
Example Data Table
| Study case | Test type | Effect size | Alpha | Power | Design note |
|---|---|---|---|---|---|
| Material strength comparison | Two independent means | 0.50 d | 0.05 | 0.80 | Equal groups |
| Sensor calibration shift | Paired mean difference | 0.35 d | 0.05 | 0.90 | Repeated readings |
| Detector pass rate | One proportion | 0.20 h | 0.01 | 0.85 | Strict alpha |
| Field response model | Multiple regression | 0.15 f² | 0.05 | 0.80 | Three predictors |
Formula Used
The calculator uses normal approximation formulas for planning. It first finds zα from alpha and tail choice. It then finds zβ from desired power.
Two means: n1 = (zα + zβ)² × (1 + 1/r) / d². The second group is n2 = r × n1.
One mean, paired mean, or proportion: n = (zα + zβ)² / effect². Paired tests can adjust effect size using measurement correlation.
Correlation: n = (zα + zβ)² / FisherZ(r)² + 3.
Regression: n ≈ (zα + zβ)² / f² + predictors + 1.
Design adjustment: design effect = 1 + (cluster size − 1) × ICC. Final sample also includes dropout inflation.
How to Use This Calculator
Select the analysis type that matches the planned physics study. Enter the effect size on the correct scale. Use Cohen's d for means, h for proportions, r for correlation, and f² for regression.
Enter alpha, desired power, and tail choice before collecting data. Add allocation ratio for two group studies. Add dropout, cluster size, and ICC when measurements may be lost or grouped.
Press calculate to view the required sample size above the form. Use CSV for spreadsheet records. Use PDF for a simple report file.
A Priori Power Analysis for Physics Studies
Planning Before Measurement
A priori power analysis estimates sample size before measurements start. It helps a researcher plan a test that can detect a real effect with chosen sensitivity. In physics work, this can guide sensor trials, material tests, calibration checks, beam experiments, and classroom laboratory comparisons.
Why Power Matters
Power is the chance of rejecting the null hypothesis when the planned effect is real. Low power wastes time. It may miss meaningful behavior. Very high power can demand more samples, money, and machine time than needed. A balanced target is often near 0.80 or 0.90. The right value depends on safety, cost, and uncertainty.
Key Inputs
The calculator needs effect size, alpha, desired power, test tails, and design type. Effect size should come from pilot data, published studies, engineering tolerance, or the smallest useful physical change. Alpha controls false positive risk. A two tailed test is safer when change can occur in either direction. A one tailed test is only suitable when the opposite direction is not useful and is defined before data collection.
Advanced Design Adjustments
Real experiments are rarely perfect. Unequal group allocation changes the needed count per group. Clustered readings can reduce information when samples within a batch are correlated. The design effect adjusts for that issue. Dropout or unusable measurements should also be included. For repeated measures, pairing can improve precision when two readings on the same unit are strongly related.
Reading the Result
The result is a planning estimate, not a guarantee. It assumes the selected statistical model is reasonable. It also assumes the effect size scale matches the chosen test. Two independent mean tests use Cohen's d. Proportion tests use Cohen's h. Correlation tests use Fisher z. Regression uses Cohen's f squared. Always document assumptions with the final report.
Good Practice
Use conservative inputs when uncertainty is large. Compare several scenarios. Check whether the required sample count is practical. If the result is too large, improve measurement precision, reduce noise, or use a stronger repeated design. Do not lower alpha or power after seeing data. That weakens the study. A clear a priori plan supports transparent physics decisions. It also improves review, replication, and ethical resource planning.
FAQs
What is a priori power analysis?
It is a sample size plan made before data collection. It uses expected effect size, alpha, desired power, and test type to estimate how many observations are needed.
Which effect size should I use?
Use the effect size scale that matches the test. Means often use Cohen's d. Proportions use Cohen's h. Correlations use r. Regression models use f².
What is a good power value?
Many studies use 0.80 as a minimum target. Higher values, such as 0.90, may be better when missed effects are costly or unsafe.
Should I choose one tailed or two tailed?
Use two tailed when an effect in either direction matters. Use one tailed only when the direction is justified before data collection.
What does allocation ratio mean?
It is the size of group two divided by group one. A value of 1 means equal groups. A value of 2 makes group two twice as large.
Why include dropout percentage?
Some measurements may fail, become unusable, or be removed during cleaning. Dropout inflation adds extra observations to protect the final usable sample.
What is design effect?
Design effect adjusts sample size for clustered measurements. If readings inside a batch are similar, each reading adds less independent information.
Can this replace expert statistical review?
No. It gives a planning estimate. Complex physics experiments may need simulation, exact power methods, or review by a statistician.