Wellner's Two-Sample Test

Wellner's (1979, Example 1a) Rayleigh-style T-statistic, which quantifies the dissimilarity between two sets of vectors. The statistic increases with the degree of difference between the datasets.

Usage

wellner(x, y)

# S3 method for class 'Ray'
wellner(x, y)

# S3 method for class 'Line'
wellner(x, y)

# S3 method for class 'Vec3'
wellner(x, y)

# S3 method for class 'Plane'
wellner(x, y)

wellner_inference(x, y, n_perm)

# S3 method for class 'Vec3'
wellner_inference(x, y, n_perm = 1000)

# S3 method for class 'Line'
wellner_inference(x, y, n_perm = 1000)

# S3 method for class 'Ray'
wellner_inference(x, y, n_perm = 1000)

# S3 method for class 'Plane'
wellner_inference(x, y, n_perm = 1000)

Source

modified after geologyGeometry (J.R. Davis): http://www.joshuadavis.us/software/

Arguments

x, y

objects of class "Vec3", "Line", "Ray", or "Plane", where the rows are the observations and the columns are the coordinates.

n_perm

integer. Number of permutations.

Value

wellner() computes Wellner's T-statistic, a non-negative measure of dissimilarity between two datasets. The value is zero when the datasets are identical.

wellner_inference() estimates the fraction of permutation tests in which the computed T-statistic exceeds the observed T for the original data (a number between 0 and 1). This value can be interpreted as a p-value for the null hypothesis that the two populations are identical (not merely that their means coincide). Thus, smaller p-values indicate stronger evidence that the two populations differ in a meaningful way.

Details

wellner_inference() performs a permutation-based inference using Wellner's T-statistic to assess whether the two datasets are drawn from the same population.

References

Jon A. Wellner. "Permutation Tests for Directional Data." Ann. Statist. 7(5) 929-943, September, 1979. doi:10.1214/aos/1176344779

Examples

test <- rvmf(100)
wellner(test, Line(120, 50))
#> [1] 7.620339
wellner_inference(test, Line(120, 50))
#> [1] 0.022