# summaryAcomp: Summarizing a compositional dataset in terms of ratios In compositions: Compositional Data Analysis

## Description

Summaries in terms of compositions are quite different from classical ones. Instead of analysing each variable individually, we must analyse each pair-wise ratio in a log geometry.

## Usage

 ```1 2 3``` ``` ## S3 method for class 'acomp' summary( object, ... ,robust=getOption("robust")) ```

## Arguments

 `object` a data matrix of compositions, not necessarily closed `...` not used, only here for generics `robust` A robustness description. See robustnessInCompositions for details. The parameter can be null for avoiding any estimation.

## Details

It is quite difficult to summarize a composition in a consistent and interpretable way. We tried to provide such a summary here, based on the idea of the variation matrix.

## Value

The result is an object of type `"summary.acomp"`

 `mean` the `mean.acomp` composition `mean.ratio` a matrix containing the geometric mean of the pairwise ratios `variation` the variation matrix of the dataset (`{variation.acomp}`) `expsd` a matrix containing the one-sigma factor for each ratio, computed as `exp(sqrt(variation.acomp(W)))`. To obtain a two-sigma-factor, one has to take its squared value (power 1.96, actually). `invexpsd` the inverse of the preceding one, giving the reverse bound. Additionally, it can be "almost" intepreted as a correlation coefficient, with values near one indicating high proportionality between the components. `min` a matrix containing the minimum of each of the pairwise ratios `q1` a matrix containing the 1-Quartile of each of the pairwise ratios `median` a matrix containing the median of each of the pairwise ratios `q1` a matrix containing the 3-Quartile of each of the pairwise ratios `max` a matrix containing the maximum of each of the pairwise ratios

## Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de, R. Tolosana-Delgado

## References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

`acomp`
 ```1 2``` ```data(SimulatedAmounts) summary(acomp(sa.lognormals)) ```