The D statistic and the p-values are appropriate to report. I would say the appropriate visualization is the histogram or cumulative frequency histogram for each distribution, either with both on the same plot or in separate vertical plots with the same x-axis. ( https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/KS2_Example.png/300px-KS2_Example.png ). Note that the test is about whether the distributions differ. It's not necessarily that one group has greater of lower values. If that is your interest, you may want to use a different test.

You could consider extending what you have already done by reporting values for one-sided 2 sample Kolmogorov-Smirnov tests if you have ready access to corresponding software, and if you think these would be understandable. A basic reference is at: https://www.jstor.org/stable/2285616?seq=1#page_scan_tab_contents . It may not be obvious how to interpret the 3 variants of the test statistic taken together. It is probably more important to concentrate on finding some graphical presentation of the underlying data.

For some specific types of "properties" , such as life-times, a variant of plotting the distribution function has been found useful: the log-survivor plot. This essentially just plots log(1-F) instead of F, were F is the distribution function. A variant would be to use log(F/(1-F)). An alternative would be a "normal scores plot": https://en.wikipedia.org/wiki/Normal_probability_plot . The idea of any of these is to reveal differences in the tails of the distribution that might be hidden in a raw plot of F. If you are working in a field where there are established ways of showing data such as you have, then you may need to be guided by that, rather than trying something new.

My guess is that simple or smoothed histogram plots would be easiest for many other people to interpret.

APa or any other publication-standard format manual.

Hope this may be of some help,

Matthew

One idea is to report all the ranges of values for which the two group CDFs are statistically significantly different from each other. Looking at your empirical CDF plot will show you which CDF is higher (meaning lower values/quantiles) over each range. This provides more information than the KS test, which only reports a single p-value for the overall null hypothesis that the distributions are identical.

This "idea" is part of the recent multiple testing methodology from the Journal of Econometrics article

Article Comparing distributions by multiple testing across quantiles...

for which there is corresponding R and Stata code at

https://faculty.missouri.edu/~kaplandm

as well as a corresponding Stata Journal article

Article distcomp: Comparing distributions

It's fully nonparametric and controls the (familywise) error rate precisely even in small samples. It also improves upon the KS test's low power in the tails.