If you put side by side on a bar chart diagram, the interval of confidence (either 90, 95 or 99%) then if any overlapping of the confidence interval would mean non-siginficant.
Say group 1 has a mean X and confdence interval X plus or minus 95%CI and a group 2 has mean of Y plus or minus 95%CI. Any overlapping of confidence interval of the two group would indicate no statistical difference between the two groups at level 95%. Same with 90 or 99% vele of confidence. A bar chart with confidence interval or boxplot can add up on the graph confidence interval
A. Robichaud, it is worth stressing what you mean by giving the different confidence intervals levels and how these map onto the alpha levels of the significance test. I know teaching intro stats some students think that at least in the simple case (with multiple comparisons, for example) that 95% -> 5%. Of course they learn otherwise, but it is worth making this explicit for the RG audience. You would not want readers to think that if the 95% confidence intervals overlap that it implies the test is non-significant at alpha=.05. Attached is an example with p=.01 (I show both the equal variance t-test and Welch's test) and the 95% intervals overlap.