Calculator Inputs
Formula Used
f² = η² / (1 − η²)
λ = N × f² × tie correction ÷ allocation penalty
Power ≈ 1 − Fnoncentral χ²(H critical, df = k − 1, λ)
The calculator uses an asymptotic noncentral chi square approximation. It treats the Kruskal Wallis test as a right tailed rank test. Tie correction reduces the effective noncentrality. Allocation penalty reduces efficiency when group ratios are unequal.
How to Use This Calculator
- Select whether you need power, sample size, or detectable effect.
- Enter the number of independent groups.
- Add total sample size, or sample per group.
- Set alpha and target power for planning.
- Choose the effect type and enter its value.
- Add allocation ratios and tie blocks when known.
- Press calculate and review the result above the form.
Example Data Table
| Scenario | Groups | Total N | Effect | Alpha | Use |
|---|---|---|---|---|---|
| Balanced sensor study | 4 | 120 | 0.08 | 0.05 | Early power check |
| Material ranking plan | 5 | 200 | 0.06 | 0.01 | Strict evidence threshold |
| Simulation score review | 3 | 90 | 0.10 | 0.05 | Detect group separation |
Planning Rank Based Power
Kruskal Wallis Basics
Kruskal Wallis testing compares three or more independent groups. It uses ranks instead of raw measurements. That helps when measurements are skewed. It also helps when outliers are expected. Power planning asks a different question. It estimates the chance of detecting a true group difference. Good planning prevents weak experiments. It also prevents wasteful over collection.
Why Physics Teams Use It
Physics studies often compare ranked outcomes. Examples include sensor stability grades, material defect scores, beam quality ratings, or simulation performance ranks. Some measurements break normal assumptions. Others have heavy tails or clear limits. A rank based plan can be safer in those settings. The method is still an approximation. It should support study design, not replace expert review.
Effect Size Meaning
The calculator uses a rank scale effect. Epsilon squared or eta squared can describe the share of ranked variation linked to group membership. A small value means group ranks mostly overlap. A larger value means the groups separate more clearly. Cohen f is also supported. It is converted into an eta style measure before power is estimated.
Sample Size Choices
Equal group sizes give the cleanest design. Unequal allocation can reduce efficiency. The calculator lets you enter allocation ratios. It then applies an imbalance penalty. This helps compare equal and unequal plans quickly. You can solve for power at a chosen sample size. You can also solve for required sample size. A third mode estimates the smallest detectable effect.
Tie Handling
Ties occur when many observations share the same score. This is common with rating scales. Ties reduce rank information. The calculator uses a tie correction factor when tie block sizes are entered. Empty tie fields assume no correction. Large tie blocks can lower projected power. Treat the result as a planning signal.
Interpreting Output
Power near eighty percent is common in planning. Higher power needs more observations or stronger effects. A low alpha level raises the evidence threshold. It usually lowers power. More groups also change the critical value. Review total sample size, per group counts, critical statistic, noncentrality, and tie factor together.
Practical Limits
The noncentral chi square approach is useful. It is not exact for every data pattern. Very small samples need caution. Strong imbalance also needs caution. Simulations may be better for final protocols. Use this tool for early design comparisons. Then confirm the final plan with study specific assumptions and domain judgment.
Reporting Notes
Record the selected effect size before collecting data. State whether the effect came from prior studies, pilot ranks, or a practical threshold. Report alpha, group count, planned allocation, and tie assumptions. Mention that the estimate uses an asymptotic rank method. This transparency helps reviewers understand the design. It also makes later sensitivity checks easier. Keep an archived output beside project notes, so planning choices stay clear for collaborators, auditors, and future teams.
FAQs
What does Kruskal Wallis power mean?
It estimates the chance that the test detects real rank differences among independent groups. Higher power means a lower chance of missing a meaningful group effect.
Can this calculator replace simulation?
No. It gives a strong planning approximation. Use simulation when samples are tiny, distributions are unusual, ties are extreme, or reviewers request design specific validation.
Which effect size should I enter?
Use epsilon squared or eta squared when prior ranked studies report them. Use Cohen f when your planning notes already use an analysis style effect measure.
How are ties handled?
Enter tie block sizes such as 4,4,3. The calculator applies a rank tie correction. Blank tie input assumes no known tie correction.
What alpha level should I use?
Many studies use 0.05. Stricter values, like 0.01, demand stronger evidence. They usually require larger samples for the same power.
Why does unequal allocation matter?
Unequal group sizes often reduce efficiency. The allocation penalty estimates that loss. Equal ratios usually give the best power for a fixed total sample.
Can I solve required sample size?
Yes. Choose required sample size mode. Enter the target power, alpha, group count, effect size, allocation, and tie assumptions.
Can I find the detectable effect?
Yes. Choose detectable effect mode. The result gives the approximate smallest eta or epsilon squared that reaches your target power.
Is this useful for physics projects?
Yes. It helps when outcomes are ranked, ordinal, skewed, or outlier prone. Examples include sensor grades, material rankings, and simulation score comparisons.
Why is the result approximate?
The method uses a noncentral chi square approximation. Real rank distributions can differ, especially with small samples or strong ties.
How should I report the calculation?
Use sensitivity runs before final protocol choices are made.