TIP: bar plot with estimates and connecting letters from TukeyA tip related to the Tukey connecting letters report: Did you know you can save the connecting letters table and get an easy plot of estimates, confidence intervals and the letters?
Use the hotspot by the Tukey output, select Save Connecting Letters Table as shown below and use the Graph Builder script in the resulting table. If you don't like the colors or the ordering, just make your own Graph Builder plot instead 

Re: TIP: bar plot with estimates and connecting letters from Tukeynice thx for sharing
Re: TIP: bar plot with estimates and connecting letters from TukeyWell, it was a stupid model - just for illustration - probably should have chosen a better example...
But the reason is that it is a Mixed Model - a model with a Fixed effect (Tech) and a Random effect (Days). The confidence intervals shown in the barplot represent the uncertainty of each Tech level INCLUDING the day-to-day variation, while in the testing the day-to-day variation is modelled (/corrected for) and thus the certainty of each level is higher than what the confidence intervals indicate.
Re: TIP: bar plot with estimates and connecting letters from TukeyCool feature, thanks for sharing! I have to say though, that from the bar plot with the 95% confidence intervals I'm a bit suprised that T1 and T3 are significantly different from each other. Am I missing something?