Group Discussion: Visualizing Group Means

When researchers report study results, they often want to visualize group means with ± (2) SE (or SEM) bars, and use their overlap (or not) to summarize significant differences between group means. However, in mixed or multi-factor models those error bars (and their overlap) can be easily misinterpreted. What meaningful (and easily interpretable) alternatives exist (or can be created) to visualize differences between group means? (We’re not looking at the often awkward diffogram.)