[R] CoDA: Interpreting acomp() Summary Output

[Rich Shepard]

   Using package 'compositions' on count data and scaling with Aitchison
geometry using function acomp(), the summary() function displays matrices
for (among other descriptive statistics) minimum, Q1, median, Q3, and
maximum. These matrices are not symmetric because they are based on
log-ratios. An example is the median matrix:

$med
             filter     gather     graze   predate     shred
filter   1.0000000 0.09060847 0.7083333 0.1833333  1.416667
gather  11.4166667 1.00000000 9.0000000 2.2083333 18.750000
graze    1.4166667 0.11111111 1.0000000 0.2403846  1.750000
predate  5.5000000 0.45299145 4.1666667 1.0000000  8.500000
shred    0.7083333 0.05341880 0.5833333 0.1180556  1.000000

   What should I read to learn how to interpret this output?[1]

   I need to explain the results to non-technical decision-makers so they can
see (boxplot() does a great job of this) and understand the variability of
each data set.

Rich

[1] 'Analyzing Compositional Data with R', page 79, mentions these measures
of center and distribution but not how to interpret them.