Calculator Inputs
Example Data Table
| Ordinal grade | Physics meaning | Control probability | Treatment probability |
|---|---|---|---|
| 1 | No detector response | 10% | 5% |
| 2 | Weak response | 20% | 15% |
| 3 | Moderate response | 30% | 25% |
| 4 | Strong response | 25% | 30% |
| 5 | Very strong response | 15% | 25% |
Formula Used
The calculator treats ordinal categories as ordered scores. It estimates the mean score and variance for each planned group.
Mean: μ = Σ score × probability
Variance: σ² = Σ probability × (score − μ)²
Standard error: SE = √(σ² control / n control + σ² treatment / n treatment)
Effect z: Z effect = (μ treatment − μ control) / SE
Two-sided power: Φ(Z effect − Z critical) + Φ(−Z effect − Z critical)
One-sided power: Φ(Z effect − Z critical)
Required sample size uses the normal planning form with the requested target power.
How to Use This Calculator
Enter the ordered score values first. Then enter the expected control and treatment category distributions. You may use percentages or proportions. Add the planned control sample size, allocation ratio, alpha level, target power, test side, and expected direction. Press calculate. The result appears above the form.
Use the CSV button to export the result table. Use the PDF button to save a compact report.
Power Planning for Ordinal Physics Data
Why ordinal outcomes matter
Physics experiments often create ordered outcomes. A detector may show no response, weak response, moderate response, or strong response. A material test may rate damage from none to severe. These values are not always truly continuous. Still, they contain ordered information. Power planning helps decide whether the planned sample can detect a meaningful shift.
What this tool estimates
This calculator compares two expected ordinal distributions. It converts each category into a score. It then finds the weighted mean score for the control group and the treatment group. The difference becomes the planned effect. Larger shifts usually improve power. Higher variation usually lowers power. More observations usually raise power.
Using category probabilities
Enter the expected percentage in each ordinal category. The calculator normalizes the values. Therefore, small rounding errors are acceptable. The two groups must use the same score list. The probabilities should describe realistic experimental expectations. Use pilot data when available. Use expert judgment when pilot data are missing.
Interpreting the result
The power value is the approximate chance of detecting the planned directional shift. A value near 80 percent is often used for planning. That rule is not universal. Critical physics studies may need higher power. Early screening work may accept lower power.
Sample size guidance
The calculator also estimates the sample size needed for the target power. This value is approximate. It uses a normal approximation based on ordinal score means. It is useful for early design work. Final protocols should consider the exact test, missing data, clustering, and measurement reliability.
Best practice
Try several scenarios. Compare optimistic, expected, and conservative distributions. This sensitivity check shows whether the design remains useful when assumptions change. Ordinal data can be powerful when categories are clear, balanced, and measured consistently.
FAQs
What is ordinal data?
Ordinal data has ordered categories. The distance between categories may not be equal. Examples include response grades, damage levels, quality ratings, and severity scores.
Can I enter percentages?
Yes. You may enter percentages or proportions. The calculator normalizes each probability list before computing means, variances, and power.
Why are category scores needed?
The scores convert ordered categories into numeric planning values. They allow the calculator to estimate weighted means and variances for power analysis.
Is this an exact ordinal test?
No. It is an approximate planning calculator. It uses ordinal scores and a normal approximation. Use exact or model-based software for final study confirmation.
What does allocation ratio mean?
It is treatment sample size divided by control sample size. A value of 1 gives equal groups. A value of 2 gives twice as many treatment observations.
What alpha level should I use?
Many studies use 0.05. Some screening studies use larger values. Confirmatory studies may require smaller values. Choose alpha before collecting data.
Why is power low?
Power may be low because the effect is small, variation is high, alpha is strict, or sample size is limited. Increase sample size or refine categories.
Can this help physics experiments?
Yes. It supports planning for ordered detector responses, material ratings, signal grades, and other ordinal outcomes in experimental physics.