I designed a heuristic that solves a problem concerning network graphs. It was tested on thousands of different instances that have various different characteristics: Topology, template, number and position of users, capacities, ... It produced more than 300000 results that also depend on the random seed that was used.
In order to evaluate the results, I decided to use boxplots that I created with JFreeChart. I created different diagrams for the different topologies and with separate plots for every template. I felt that was a good way to visually summarize the results.
I was asked, why I didn't use confidence intervals instead to give an estimate. From what I know, these depend on a underlying distribution of a population parameter while boxplots don't. However, I summarize results of different seeds, numbers of users and capacities. All these influence the results. So I think I would not be possible to use confidence intervals unless I distinguished every single network characteristic.
Is that true? What are other advantages and disadvantages? And how could I argue, that I only use boxplots and not confidence intervals?