I really like statistics being presented such that you can draw useful inferences by a single glance. Error bars help there, assuming they’re the right ones (I wrote on when to use SD vs. SEM here: http://dx.doi.org/10.1007/s10633-010-9249-7). So even if you know that the “antennas” represent SEM or 95%CI or whatever, how does graphical overlap relate to significance? I usually refer to the Cumming et al. papers (2007 & 2007), but in the attached entry at RPsychologist, which today was featured on R-bloggers, nicely depicts this. I knew about the necessary gap between SEMs, but the overlap in 95%CIs corresponding to p=.05 was another eye-opener. Thanks!
http://rpsychologist.com/how-to-tell-when-error-bars-correspond-to-a-significant-p-value/