# dot-wassersteinTestAsy: .wassersteinTestAsy In waddR: Statistical tests for detecting differential distributions based on the 2-Wasserstein distance

## Description

Two-sample test to check for differences between two distributions (conditions) using the 2-Wasserstein distance: Implementation using a test based on asymptotic theory

## Usage

 `1` ```.wassersteinTestAsy(x, y) ```

## Arguments

 `x` univariate sample (vector) representing the distribution of condition A `y` univariate sample (vector) representing the distribution of condition B

## Details

This is the asymptotic version of wasserstein.test, for the semi-parametric procedure see .wassersteinTestSp

Details concerning the testing procedure based on asymptotic theory can be found in Schefzik and Goncalves (2019).

## Value

A vector concerning the testing results, precisely (see Schefzik and Goncalves (2019) for details)

• d.wass: 2-Wasserstein distance between the two samples computed by quantile approximation

• d.wass^2 squared 2-Wasserstein distance between the two samples computed by quantile approximation

• d.comp^2: squared 2-Wasserstein distance between the two samples computed by decomposition approximation

• d.comp: 2-Wasserstein distance between the two samples computed by decomposition approximation

• location: location term in the decomposition of the squared 2-Wasserstein distance between the two samples

• size: size term in the decomposition of the squared 2-Wasserstein distance between the two samples

• shape: shape term in the decomposition of the squared 2-Wasserstein distance between the two samples

• rho: correlation coefficient in the quantile-quantile plot

• pval: p-value of the 2-Wasserstein distance-based test using asymptotic theory

• perc.loc: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.size: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.shape: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• decomp.error: relative error between the squared 2-Wasserstein distance computed by the quantile approximation and the squared 2-Wasserstein distance computed by the decomposition approximation

## References

Schefzik, R. and Goncalves, A. (2019).

waddR documentation built on Nov. 8, 2020, 8:32 p.m.