Permutation Threshold
Calculate upper-tail max-statistic permutation p-values with the plus-one correction and a separately labeled interpolated reference quantile; decisions use p-values, not an incompatible quantile cutoff.
Description
Permutation maxima can provide a familywise reference for a collection of observed statistics.
Permutation maxima can provide a familywise reference for a collection of observed statistics. A plus-one count prevents a zero estimated tail probability.
The tool returns referenceQuantile (reference quantile); correctedPValues (corrected p values); significantFlags (significant flags). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Permutation Threshold
Use Permutation Threshold when you already have permutationMaxStatistics, observedStatistics, alpha and want referenceQuantile, correctedPValues, significantFlags. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Permutation Threshold and understand its results
- Enter permutationMaxStatistics, observedStatistics, alpha using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read referenceQuantile, correctedPValues, significantFlags. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| permutationMaxStatistics | Permutation max statistics | list of number | Required |
| observedStatistics | Observed statistics | list of number | Required |
| alpha | Alpha | number | Required |
Compare each observation with every supplied maximum. Flag p≤alpha, with 0<alpha<1, and separately return a linearly interpolated 1−alpha reference quantile.
corrected p = (1 + number of maxima ≥ observed)/(permutations+1) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"permutationMaxStatistics": [
1,
2,
3,
4
],
"observedStatistics": [
2,
5
],
"alpha": 0.4
},
"output": {
"referenceQuantile": 2.8,
"correctedPValues": [
0.8,
0.2
],
"significantFlags": [
0,
1
]
}
}Limitations and assumptions
The quantile is descriptive; significance uses the discrete corrected p values. Permutations, exchangeability and maximum construction are supplied externally.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
TFCE Value: Approximate nonnegative TFCE by bounded midpoint height integration over face-connected voxel clusters; extent is voxel count, not physical volume, and inference requires an external permutation null. GLM t-Statistic: Evaluate a GLM contrast using the full already-scaled coefficient covariance; no additional residual variance multiplier is applied.
Methodological background: Randomise: nonparametric inference.1
References
-
Randomise: nonparametric inference — FMRIB Software Library developers
Similar or alternative tools
- TFCE Value
Approximate nonnegative TFCE by bounded midpoint height integration over face-connected voxel clusters; extent is voxel count, not physical volume, and inference requires an external permutation null.
- GLM t-Statistic
Evaluate a GLM contrast using the full already-scaled coefficient covariance; no additional residual variance multiplier is applied.