Parametric vs Nonparametric Power Calculator

Calculator

Example Data Table

Formula Used

Standardized effect size:

d = expected shift / standard deviation

Information value:

One sample or paired design: I = n

Two sample design: I = n1 × n2 / (n1 + n2)

Parametric noncentrality:

NCP = |d| × √I

Nonparametric noncentrality:

NCP = |d| × √(I × ARE) − continuity adjustment

Approximate power:

One tailed power = 1 − Φ(zα − NCP)

Two tailed power = 1 − Φ(zα/2 − NCP) + Φ(−zα/2 − NCP)

Required sample estimate:

n uses (z critical + z target power)² divided by effect².

For rank tests, the denominator is also multiplied by ARE.

How to Use This Calculator

1. Select the study design used by your physics experiment.
2. Enter a standardized effect size or raw shift data.
3. Add sample sizes for one or both groups.
4. Set alpha, tails, target power, and allocation ratio.
5. Choose the nonparametric method or enter custom efficiency.
6. Press Calculate to compare the two power estimates.
7. Use CSV or PDF buttons to save the result.

Power Planning for Physics Data

Physics experiments often compare measured responses across conditions. A sensor may record force after calibration. A detector may count pulses after shielding. A material test may compare two treatments. Power planning estimates the chance that a planned study will detect a real effect. This calculator compares parametric and nonparametric approaches with one shared workflow.

Parametric Power

Parametric tests use assumptions about the measurement scale and distribution. The usual model expects a standardized mean shift. It also assumes variance is represented by a useful standard deviation. These tests are efficient when data are nearly normal. They are common for temperature, voltage, displacement, and timing studies. The calculator uses a normal approximation to the noncentral test statistic. It estimates critical value, noncentrality, beta, and power.

Nonparametric Power

Nonparametric tests use ranks or signs. They are helpful when values include outliers, skew, limits, or ordinal scores. Physics labs often face these issues. Saturated sensors can cap readings. Small samples can show rough distributions. Rank tests protect the analysis when the mean is not stable. The calculator applies asymptotic relative efficiency. It adjusts the parametric information by the selected efficiency factor.

Choosing a Method

Neither method is always best. A parametric test can need fewer observations when assumptions hold. A nonparametric test can be safer when readings are noisy. Use the parametric result for clean, calibrated, continuous data. Use the nonparametric result when ranks describe the evidence better. Compare both before collecting data. A small power gap may support the safer method.

Interpreting Results

Power near 80 percent is a common planning target. Higher power lowers the chance of a missed effect. It often requires more samples. The required sample estimate helps with lab time, materials, beam time, or battery cycles. The minimum detectable effect shows the smallest standardized shift likely to be found. Review alpha and tails carefully. A two tailed test is more conservative.

Practical Notes

The calculator gives planning estimates, not final proof. Real data may violate assumptions. Pilot data can improve the standard deviation estimate. Replication can improve confidence. For high cost experiments, compare several sample sizes. Record every assumption before the run. Clear planning makes later results easier to defend during peer review later.

FAQs