Description Usage Arguments Details Value References

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

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

`x` |
sample (vector) representing the distribution of
condition |

`y` |
sample (vector) representing the distribution of
condition |

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 et al (2020).

Note that the asymptotic theory-based test should only be employed when the two samples *x* and *y* can be assumed to come from continuous distributions.

A vector of 13, see Schefzik et al. (2020) 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 %) of the location part with respect to the overall squared 2-Wasserstein distance obtained by the decomposition approximation

perc.size: fraction (in %) of the size part with respect to the overall squared 2-Wasserstein distance obtained by the decomposition approximation

perc.shape: fraction (in %) of the shape part with respect to the overall squared 2-Wasserstein distance obtained by the decomposition approximation

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

Schefzik, R., Flesch, J., and Goncalves, A. (2020). waddR: Using the 2-Wasserstein distance to identify differences between distributions in two-sample testing, with application to single-cell RNA-sequencing data.

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